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AP STATISTICS AP STATISTICS EXAM REVIEW EXAM REVIEW TOPIC I: Describing Data (15 questions) TOPIC II: Experimental De sign (15 questions) TOPIC III: Probability (18 questions) TOPIC IV: Inference (15 questions)
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0. AP STATISTICS EXAM REVIEW. TOPIC II: Experimental Design (15 questions). TOPIC I: Describing Data (15 questions). TOPIC III: Probability (18 questions). TOPIC IV: Inference (15 questions). 0. TOPIC I: Describing Data. Univariate Data Normal Distributions Bivariate Data. - PowerPoint PPT Presentation

### Transcript of AP STATISTICS EXAM REVIEW

• AP STATISTICSEXAM REVIEW

TOPIC I:Describing Data(15 questions)TOPIC II:Experimental Design(15 questions)TOPIC III:Probability(18 questions)TOPIC IV:Inference(15 questions)0

• TOPIC I: Describing DataUnivariate DataNormal DistributionsBivariate Data0

Topic I123456789101112131415back to main

• Which observation has the higher z-score?

I. x=25.4; =12.9; =3.7II. x=25.4; =15.3; =2.7IIIz-scores are equalcannot be determined since we dont know the standard deviations of the populationscannot be determined since we dont know if the populations are normalI.1.Topic I Menu0

• Which observation has the higher z-score?

I. x=25.4; =12.9; =3.7II. x=25.4; =15.3; =2.7IIIz-scores are equalcannot be determined since we dont know the standard deviations of the populationscannot be determined since we dont know if the populations are normalI.1.SOLUTIONThe z-score for I is 3.38; the z-score for II is 3.74Topic I Menu0

• The Quartile and Percentile positions of the value 10 in the set

{10, 6, 8, 9, 12, 17, 32, 16}are:Q3; 38Q2; 38Q2; 26Q3; 26none of theseI.2.Topic I Menu0

• The Quartile and Percentile positions of the value 10 in the set

{10, 6, 8, 9, 12, 17, 32, 16}are:Q3; 38Q2; 38Q2; 26Q3; 26none of theseI.2.SOLUTIONWhen the values are in order, there are 3 values below 10. This puts 10 in the 37.5 percentile and the 2nd quartile.Topic I Menu0

• The Standard Deviation of the set {5, 7, 7, 8, 10, 11} is 2. Which of the following sets also has a Standard Deviation of 2?{4, 5, 8, 12, 14}{2, 4, 6, 8, 10, 12}{3, 5, 5, 6, 8, 9}{10, 14, 14, 16, 20, 22}none of the aboveI.3.Topic I Menu0

• The Standard Deviation of the set {5, 7, 7, 8, 10, 11} is 2. Which of the following sets also has a Standard Deviation of 2?{4, 5, 8, 12, 14}{2, 4, 6, 8, 10, 12}{3, 5, 5, 6, 8, 9}{10, 14, 14, 16, 20, 22}none of the aboveI.3.There is a uniform decrease of 2 units in this set. The st. deviation must be the same.SOLUTIONTopic I Menu0

• If 12% of the values of a data set lie between a and b and d is added to each value, then which of the following is true?

12% still lies between a and b12% lies between a + d and b + d(12+d)% lies between a and b(12+d)% lies between a + d and b + dthere is no way to tell how much data is between a and bI.4.Topic I Menu0

• If 12% of the values of a data set lie between a and b and d is added to each value, then which of the following is true?

12% still lies between a and b12% lies between a + d and b + d(12+d)% lies between a and b(12+d)% lies between a + d and b + dthere is no way to tell how much data is between a and bI.4.A uniform shift of all the data maintains the percentages of data in shifted intervals.SOLUTIONTopic I Menu0

• If a distribution is relatively symmetric and mount-shaped, order the following (from least to greatest)1. a z-score of 12. the value of Q33. a value in the 70th percentile1, 2, 31, 3, 23, 2, 13, 1, 22, 3, 1

• If a distribution is relatively symmetric and mount-shaped, order the following (from least to greatest)1. a z-score of 12. the value of Q33. a value in the 70th percentile1, 2, 31, 3, 23, 2, 13, 1, 22, 3, 1

I.5.SOLUTIONThe percentile of a z-score of 1 is about 84%, and the percentile of Q3 is 75%Topic I Menu0

• Which of the following would NOT be a correct interpretation of a correlation coefficient of r = -.30

The variables are inversely relatedThe coefficient of determination is 0.0930% of the variation between the variables is linearThere exists a weak relationship between the variablesAll are correctI.6.Topic I Menu0

• Which of the following would NOT be a correct interpretation of a correlation coefficient of r = -.30

The variables are inversely relatedThe coefficient of determination is 0.0930% of the variation between the variables is linearThere exists a weak relationship between the variablesAll are correctI.6.SOLUTIONThe value of r2 explains the variation between the variables. Not r.Topic I Menu0

• Which of the following displays is best suited for categorical data?

Box PlotBar GraphStem and Leaf PlotDot PlotScatterplotI.7.Topic I Menu0

• Which of the following displays is best suited for categorical data?

Box PlotBar GraphStem and Leaf PlotDot PlotScatterplotI.7.SOLUTIONIn a bar graph, each column is separate, allowing for categorical separation.Topic I Menu0

• Linear regression usually employs the method of least squares. Which of the following is the quantity that is minimized by the least squares process? I.8.Topic I Menu0

• Linear regression usually employs the method of least squares. Which of the following is the quantity that is minimized by the least squares process? I.8.SOLUTIONLeast Squares Regression minimizes the residuals in the y-direction.Topic I Menu0

• Which of the following is NOT true?

Two sets of data can have the same means but different variancesTwo sets of data can have the same variance but different meansTwo different values in a data set can have the same z-scoreAll the absolute values of z-scores for a data set can be equalAll of the above are trueI.9.Topic I Menu0

• Which of the following is NOT true?

Two sets of data can have the same means but different variancesTwo sets of data can have the same variance but different meansTwo different values in a data set can have the same z-scoreAll the absolute values of z-scores for a data set can be equalAll of the above are trueI.9.SOLUTIONSince each value is a distinct distance from the mean, the z-scores must all be differentTopic I Menu0

• In a symmetric, mount-shaped distribution, what percentile has a z-score of -2?

• Topic I MenuIn a symmetric, mount-shaped distribution, what percentile has a z-score of -2?

I.10.SOLUTIONWe should be able to approximate this with the normal distribution. Area to the left of -2?

On the TI-83: Normalcdf(-1E99, -2) = .022752.5th percentile0

• Lees z-score on his math test was 1.5. The class average was a 62.1 and the variance was 6.76. What was Lees actual grade on the test?6062646668I.11.Topic I Menu0

• Lees z-score on his math test was 1.5. The class average was a 62.1 and the variance was 6.76. What was Lees actual grade on the test?6062646668I.11.SOLUTIONWe need to solve the following equation for x:

so x=66

• Does the following problem have a unique solution? If so, find it. If not, show at least two answers:

5 numbers have Q1=12, Median=15, Q3=18. Find the mean.I.12.Topic I Menu0

• Does the following problem have a unique solution? If so, find it. If not, show at least two answers:

5 numbers have Q1=12, Median=15, Q3=18. Find the mean.I.12.SOLUTION{11, 13, 15, 17, 19} =15 { 9, 15, 15, 17, 19} =15

the data sets are not unique, but the mean is always 15! YES!!!surprisingly!Topic I Menu0

• The average grade on a math test given to two sections is 60.98. Section I has 27 students with a mean grade of 57.30. If the mean grade of Section 2 is 65.30, how many students are in section 2?I.13.Topic I Menu0

• Topic I MenuThe average grade on a math test given to two sections is 60.98. Section I has 27 students with a mean grade of 57.30. If the mean grade of Section 2 is 65.30, how many students are in section 2?I.13.SOLUTION23 students.

we arrive at n=230

• If the mean of 75 values is 52.6 and the mean of 25 values is 48.4; find the mean of all 100 values.

• If the mean of 75 values is 52.6 and the mean of 25 values is 48.4; find the mean of all 100 values.

• In skewed-right distributions, what is most frequently the relationship of the mean, median, and mode?mean > median > modemedian > mean > modemode > median > meanmode > mean > medianmean > mode > medianI.15.Topic I Menu0

• Topic I MenuIn skewed-right distributions, what is most frequently the relationship of the mean, median, and mode?mean > median > modemedian > mean > modemode > median > meanmode > mean > medianmean > mode > medianI.15.SOLUTIONThe median is resistant, the mean, not at all. So a right skewed distribution will have a mean much higher than median, much higher than mode. 0

• TOPIC II: Experimental DesignSamplingDesigning ExperimentsObservational Studies0

Topic II123456789101112131415back to main

• A personnel director studied the eating habits of employees by watching a group of employees at lunch. He wishes to see who buys in the cafeteria, who brings a home lunch, and who goes out.The study is categorized as:a censusa survey samplean observational studya designed experimentnone of theseII.1.Topic II Menu

• A personnel director studied the eating habits of employees by watching a group of employees at lunch. He wishes to see who buys in the cafeteria, who brings a home lunch, and who goes out.The study is categorized as:a censusa survey samplean observational studya designed experimentnone of theseII.1.SOLUTIONThe director is observing behavior, not implementing treatments on the groupTopic II Menu

• A personnel director studied the eating habits of employees by watching a group of employees at lunch. He wishes to see who buys in the cafeteria, who brings a home lunch, and who goes out.If the director only looks at those in one department, she is performing:a simple random samplea quota samplea convenience samplea multi-stage cluster samplea censusII.2.Topic II Menu

• Topic II MenuSOLUTIONWithout a properly randomized selection, she is introducing bias to the study.A personnel director studied the eating habits of employees by watching a group of employees at lunch. He wishes to see who buys in the cafeteria, who brings a home lunch, and who goes out.If the director only looks at those in one department, she is performing:a simple random samplea quota samplea convenience samplea multi-stage cluster samplea censusII.2.

• A personnel director studied the eating habits of employees by watching a group of employees at lunch. He wishes to see who buys in the cafeteria, who brings a home lunch, and who goes out.If the director selects 50 employees at random and categorizes by gender, she is:blocking for gendertesting for a lurking variablepromoting sexual harassmenttesting for biasnone of theseII.3.Topic II Menu

• A personnel director studied the eating habits of employees by watching a group of employees at lunch. He wishes to see who buys in the cafeteria, who brings a home lunch, and who goes out.If the director selects 50 employees at random and categorizes by gender, she is:blocking for gendertesting for a lurking variablepromoting sexual harassmenttesting for biasnone of theseII.3.SOLUTIONShe is investigating whether gender affects lunchtime behaviorTopic II Menu

• Which of the following is NOT a concern in data collection?

lurking variablesblockingbiasnon-responseall of the above are concernsII.4.Topic II Menu

• Which of the following is NOT a concern in data collection?

lurking variablesblockingbiasnon-responseall of the above are concernsII.4.SOLUTIONEven blocking methods need to be analyzedTopic II Menu

• Which of the following is NOT a valid sample design?

Code every member of a population and select 100 randomly chosen membersDivide a population by gender and select 50 individuals randomly from each groupSelect individuals randomly and place into gender groups until you have the same proportion as in the populationSelect five homerooms at random from all the homerooms in a large high school.All of these are validII. 5.Topic II Menu

• Which of the following is NOT a valid sample design?

Code every member of a population and select 100 randomly chosen membersDivide a population by gender and select 50 individuals randomly from each groupSelect individuals randomly and place into gender groups until you have the same proportion as in the populationSelect five homerooms at random from all the homerooms in a large high school.All of these are validII. 5.SOLUTIONBut you may be able to question the validity of answer (C)Topic II Menu

• An insurance company conducted a study to determine the percent of cardiologists who had been sued over the last 5 yrs.

The variable of interest is:the doctors specialty, e.g. cardiology, obstetrics, etc.the number of doctors who are cardiologistsall cardiologists in the American Medical Association directorya random sample of 100 cardiologistsnone of theseII.6.Topic II Menu

• An insurance company conducted a study to determine the percent of cardiologists who had been sued over the last 5 yrs.

The variable of interest is:the doctors specialty, e.g. cardiology, obstetrics, etc.the number of doctors who are cardiologistsall cardiologists in the American Medical Association directorya random sample of 100 cardiologistsnone of theseII.6.SOLUTIONwe are interested in the percentage of doctors who have been suedTopic II Menu

• An insurance company conducted a study to determine the percent of cardiologists who had been sued over the last 5 yrs.

The population of interest is:the set of all doctors who were sued for malpracticethe set of cardiologists who were sued for malpracticeall doctorsall cardiologistsall doctors who have malpractice insuranceII.7.Topic II Menu

• An insurance company conducted a study to determine the percent of cardiologists who had been sued over the last 5 yrs.

The population of interest is:the set of all doctors who were sued for malpracticethe set of cardiologists who were sued for malpracticeall doctorsall cardiologistsall doctors who have malpractice insuranceII.7.SOLUTIONJust cardiologists, not all doctors.Topic II Menu

• An insurance company conducted a study to determine the percent of cardiologists who had been sued over the last 5 yrs.

Which could be used to gather the data?a designed experimenta census of all cardiologistsan observational study of randomly selected cardiologistsa survey sent to randomly selected cardiologistsany answer except (A)II.8.Topic II Menu

• Topic II MenuAn insurance company conducted a study to determine the percent of cardiologists who had been sued over the last 5 yrs.

Which could be used to gather the data?a designed experimenta census of all cardiologistsan observational study of randomly selected cardiologistsa survey sent to randomly selected cardiologistsany answer except (A)II.8.SOLUTIONThis population of this observational study is too large to track everyone down.

• Which of the following is NOT a source of bias in sample surveys?non-responsewording of questionsvoluntary responseuse of a telephone surveyall are sources of biasII.9.Topic II Menu

• Which of the following is NOT a source of bias in sample surveys?

non-responsewording of questionsvoluntary responseuse of a telephone surveyall are sources of biasII.9.SOLUTIONand dont forget even a huge sample size cant correct a poorly selected sample. Remember the Literary Digest Poll!Topic II Menu0

• Which of the following is NOT a requirement of a controlled experiment?controlcomparisonreplicationrandomizationall of these are requiredII.10.Topic II Menu0

• Which of the following is NOT a requirement of a controlled experiment?controlcomparisonreplicationrandomizationall of these are requiredII.10.SOLUTIONTopic II Menu0

• A randomized block design is NOT:

similar to a stratified random sample for surveysa strategy to control for an influence that would affect the outcome of the experimenta strategy that depends on randomizationonly used for gender comparisonsall of these describe a randomized block design.II.11.Topic II Menu0

• A randomized block design is NOT:

similar to a stratified random sample for surveysa strategy to control for an influence that would affect the outcome of the experimenta strategy that depends on randomizationonly used for gender comparisonsall of these describe a randomized block design.II.11.SOLUTIONYou can block with any categorical variables!Topic II Menu0

• A research team is comparing performance in AP Statistics based on whether traditional or activity-based instruction methods were used. The final grades of 500 students will be collected.The population of interest is:the 500 students chosenthe students taught by activity-based statisticsthe students taught by traditional methodsall students in high school.none of theseII.12.Topic II Menu0

• Topic II MenuA research team is comparing performance in AP Statistics based on whether traditional or activity-based instruction methods were used. The final grades of 500 students will be collected.The population of interest is:the 500 students chosenthe students taught by activity-based statisticsthe students taught by traditional methodsall students in high school.none of theseII.12.SOLUTIONWe are interested in knowing about ALL AP STATISTICS STUDENTS0

• A research team is comparing performance in AP Statistics based on whether traditional or activity-based instruction methods were used. The final grades of 500 students will be collected.An appropriate design for the study is:a blocked design experimenta stratified random samplea completely randomized designa simple random samplenone of theseII.13.Topic II Menu

• A research team is comparing performance in AP Statistics based on whether traditional or activity-based instruction methods were used. The final grades of 500 students will be collected.An appropriate design for the study is:a blocked design experimenta stratified random samplea completely randomized designa simple random samplenone of theseII.13.SOLUTIONB or C. Either one is fine.Topic II Menu

• A survey is to be conducted in your school. There is to be a total of 40 students in the sample. Describe how you would choose the participants if

there are to be the same number of freshmen, sophomores, juniors, and seniors in the sample.II.14.Topic II Menu0

• A survey is to be conducted in your school. There is to be a total of 40 students in the sample. Describe how you would choose the participants if

there are to be the same number of freshmen, sophomores, juniors, and seniors in the sample.II.14.SOLUTIONSelect a simple random sample of 10 from each class.Topic II Menu0

• II.15.A survey is to be conducted in your school. There is to be a total of 40 students in the sample. Describe how you would choose the participants if there are to be the same number of males and females in the sampleTopic II Menu

• II.15.A survey is to be conducted in your school. There is to be a total of 40 students in the sample. Describe how you would choose the participants if there are to be the same number of males and females in the sampleSOLUTIONSelect a simple random sample of 20 males and 20 females.Topic II Menu

• TOPIC III: ProbabilityRandom VariablesBinomial DistributionsGeometric DistributionsSampling Distributions

Topic III123456789101112131415161718back to main

• If 3 people, Joe, Betsy, and Sue, play a game in which Joe has a 25% chance of winning and Betsy has a 40% chance of winning, what is the probability that Sue will win?25%35%40%65%cannot be determinedIII.1.Topic III Menu

• If 3 people, Joe, Betsy, and Sue, play a game in which Joe has a 25% chance of winning and Betsy has a 40% chance of winning, what is the probability that Sue will win?25%35%40%65%cannot be determinedIII.1.SOLUTIONAssuming one winner, the probabilities must add up to 100%Topic III Menu

• A local law enforcement agency published the following chart.

The percentage of altercations involving at least one teenager is:

• A local law enforcement agency published the following chart.

The percentage of altercations involving at least one teenager is:

• What proportion of Republicans are over 50?61/23832/9696/23832/61cannot be determinedIII.3.Topic III Menu

DemocratRepublicanIndepend18 30 25181231 4032211041 50172517over 50143215

• What proportion of Republicans are over 50?61/23832/9696/23832/61cannot be determinedIII.3.SOLUTIONThere are 96 Republicans of whom 32 are over age 50Topic III Menu

DemocratRepublicanIndepend18 30 25181231 4032211041 50172517over 50143215

• If one person is chosen at random, what is the probability he is a Democrat between 41 and 50 years old?17/23817/8861/23817/6188/238III.4.Topic III Menu

DemocratRepublicanIndepend18 30 25181231 4032211041 50172517over 50143215

• If one person is chosen at random, what is the probability he is a Democrat between 41 and 50 years old?17/23817/8861/23817/6188/238III.4.SOLUTIONTotal # of adults is 238. 17 are democrats between 41 and 50Topic III Menu

DemocratRepublicanIndepend18 30 25181231 4032211041 50172517over 50143215

• Given that a person chosen is between 31 and 40, what is the probability the person is an Independent?10/23810/6310/5454/23863/238III.5.Topic III Menu

DemocratRepublicanIndepend18 30 25181231 4032211041 50172517over 50143215

• Given that a person chosen is between 31 and 40, what is the probability the person is an Independent?10/23810/6310/5454/23863/238III.5.SOLUTIONThere are 63 people between 31 and 40 of whom 10 are Independent.Topic III Menu

DemocratRepublicanIndepend18 30 25181231 4032211041 50172517over 50143215

• What proportion of the citizens sampled are over 50 OR Independent?54/23861/238100/238115/238cannot be determinedIII.6.Topic III Menu

DemocratRepublicanIndepend18 30 25181231 4032211041 50172517over 50143215

• What proportion of the citizens sampled are over 50 OR Independent?54/23861/238100/238115/238cannot be determinedIII.6.SOLUTION61/238 + 54/238 15/238

DemocratRepublicanIndepend18 30 25181231 4032211041 50172517over 50143215

• If P(A)=0.4, P(B)=0.2, and P(A and B)= 0.08Which is true?Events A and B are independent and mutually exclusiveEvents A and B are independent but not mutually exclusiveEvents A and B are mutually exclusive but not independentEvents A and B are neither independent nor mutually exclusiveEvents A and B are independent but whether they are mutually exclusive cannot be determined.III.7.Topic III Menu

• If P(A)=0.4, P(B)=0.2, and P(A and B)= 0.08Which is true?Events A and B are independent and mutually exclusiveEvents A and B are independent but not mutually exclusiveEvents A and B are mutually exclusive but not independentEvents A and B are neither independent nor mutually exclusiveEvents A and B are independent but whether they are mutually exclusive cannot be determined.III.7.SOLUTION--Since P(A and B) is non-zero, they are not mutually exclusive.--Since P(A and B) does not equal P(A)P(B), the events are independentthey just happen in sequenceTopic III Menu

• What is the probability that a family with 6 children will have 3 boys and 3 girls?POSSIBLE NAME OF DISTRIBUTION?Binomial ModelGeometric ModelUniform ModelNormal Model

• What is the probability that a family with 6 children will have 3 boys and 3 girls?POSSIBLE NAME OF DISTRIBUTION?Binomial ModelGeometric ModelUniform ModelNormal Model

III.8.SOLUTIONThis is a binomial distribution:

n=6p=0.56C3 (0.5)3 (0.5)3 = 0.3125x=3

• What is the probability that a person is over 6 feet tall if the mean height of her age group is 56 and a standard deviation of 10?POSSIBLE NAME OF DISTRIBUTION?Binomial ModelGeometric ModelUniform ModelNormal Model

• What is the probability that a person is over 6 feet tall if the mean height of her age group is 56 and a standard deviation of 10?POSSIBLE NAME OF DISTRIBUTION?Binomial ModelGeometric ModelUniform ModelNormal Model

III.9.SOLUTIONThis is a normal distribution:

normalcdf(6, 1E99, 5+6/12, 10/12)

= 0.2743

• What is the probability that a shipment of 100 fruit will have no more than 6 rotten fruits if the probability that any one fruit is rotten is 0.04?POSSIBLE NAME OF DISTRIBUTION?Binomial ModelGeometric ModelUniform ModelNormal Model

• What is the probability that a shipment of 100 fruit will have no more than 6 rotten fruits if the probability that any one fruit is rotten is 0.04?POSSIBLE NAME OF DISTRIBUTION?Binomial ModelGeometric ModelUniform ModelNormal Model

III.10.SOLUTIONDid you think to use the normal approximation? = np = 4 =p(1p)/n = .0196normalcdf(-1E99, 6, 4, .0196) = 1.00 How come that didnt work?

This is a binomial distribution:binomcdf(100, 0.04, 6) = 0.8936

• What is the probability that the first base hit will occur during the fourth at-bat if the probability that the hitter gets a base hit is 0.27 for any at-bat?POSSIBLE NAME OF DISTRIBUTION?Binomial ModelGeometric ModelUniform ModelNormal Model

• What is the probability that the first base hit will occur during the fourth at-bat if the probability that the hitter gets a base hit is 0.27 for any at-bat?POSSIBLE NAME OF DISTRIBUTION?Binomial ModelGeometric ModelUniform ModelNormal Model

III.11.SOLUTIONThis is a geometric (waiting time) distribution:

n=??? (there isnt one! Thats why its Geometric!)p=0.27; x=4

geometpdf(0.27, 4) = (.73)(.73)(.73)(.27) = 0.7160

• Suppose a basketball player scores 70% of her free throws. Assume each shot is independent and the probability is the same on each trial.

Find the probability she scores on 3 of her next 5 attemptsIII.12.Topic III Menu

• Suppose a basketball player scores 70% of her free throws. Assume each shot is independent and the probability is the same on each trial.

Find the probability she scores on 3 of her next 5 attemptsIII.12.SOLUTIONThis is a binomial distribution:

n=5p=0.705C3 (0.7)3 (0.3)2 = 0.3087x=3

• Suppose a basketball player scores 70% of her free throws. Assume each shot is independent and the probability is the same on each trial.

Find the probability that the first time she scores is on her 3rd attemptIII.13.Topic III Menu

• Suppose a basketball player scores 70% of her free throws. Assume each shot is independent and the probability is the same on each trial.

Find the probability that the first time she scores is on her 3rd attemptIII.13.SOLUTIONThis is a geometric distribution:

n=??? (we wait til a successtheres no n!)p=0.70; x=3

geometpdf(0.7, 3) = (.3)(.3)(.7) = 0.063

• The Central Limit Theorem for sample means is critical because

It states that for large sample sizes, the population distribution is approximately normalIt states that for large sample sizes, the sample is approximately normalIt states that for any population, the sampling distribution is normal regardless of sample sizeIt states that for large sample sizes, the sampling distribution is approximately normal regardless of the population distributionIt states that for any sample size, the sampling distribution is normalIII.14.Topic III Menu

• The Central Limit Theorem for sample means is critical because

It states that for large sample sizes, the population distribution is approximately normalIt states that for large sample sizes, the sample is approximately normalIt states that for any population, the sampling distribution is normal regardless of sample sizeIt states that for large sample sizes, the sampling distribution is approximately normal regardless of the population distributionIt states that for any sample size, the sampling distribution is normalIII.14.SOLUTIONTopic III Menu

• The amount of time it takes a high school class of 1000 freshmen to swim 10 lengths of the school pool has a distribution that is skewed left due to some excellent swimmers. The mean amount of time needed is 9.2 minutes and the standard deviation is 5.3 min. If 64 students are chosen at random, then what is the probability their mean time will exceed 10 minutes?III.15.Topic III Menu

• The amount of time it takes a high school class of 1000 freshmen to swim 10 lengths of the school pool has a distribution that is skewed left due to some excellent swimmers. The mean amount of time needed is 9.2 minutes and the standard deviation is 5.3 min. If 64 students are chosen at random, then what is the probability their mean time will exceed 10 minutes?III.15.SOLUTIONnormalcdf(10, 1E99, 9.2, 5.3/64) = 0.113Topic III Menu

• It is assumed that 50% of all people catch one or more colds each year. What is the probability that out of 400 randomly selected people, 216 or more will catch one or more colds this year?0.00550.01210.0550.110.55III.16.Topic III Menu

• It is assumed that 50% of all people catch one or more colds each year. What is the probability that out of 400 randomly selected people, 216 or more will catch one or more colds this year?0.00550.01210.0550.110.55III.16.SOLUTIONWe want p(p > 216/400 = .054)Since np and n(1-p) exceed 10, we can apply the normal approximation with =.5 and =.025

Normalcdf(.54, 1E99, .5, .025)= .055Topic III Menu

• The decision whether the distribution ofo a sample mean follows a normal or a t-distribution depends on:Sample sizeWhether you have the actual data or only statistics of the dataWhether you know the population standard deviationWhether np>10 and n(1-p)>10None of the aboveIII.17.Topic III Menu

• The decision whether the distribution ofo a sample mean follows a normal or a t-distribution depends on:Sample sizeWhether you have the actual data or only statistics of the dataWhether you know the population standard deviationWhether np>10 and n(1-p)>10None of the aboveIII.17.SOLUTIONTopic III Menu

• National studies show that 14% of male teenagers and 12% of female teenagers will be involved in a major traffic accident while driving. Whats the probability that independent samples of 100 female teens and 75 male teens will have results that differ by more than 3% in either direction?.042.085.42.85Cannot be determinedIII.18.Topic III Menu

• National studies show that 14% of male teenagers and 12% of female teenagers will be involved in a major traffic accident while driving. Whats the probability that independent samples of 100 female teens and 75 male teens will have results that differ by more than 3% in either direction?.042.085.42.85Cannot be determinedIII.18.SOLUTIONFor both genders, np and n(1-p) exceed 5 so we can use the CLT.

z = (.03-.02) = .1938 (.14*.86/75 + .12*.88/100)

Using normalcdf(.1938, 1E99) = .423But we want both directions so add in the other tail to get an answer of .846

• TOPIC IV: InferenceInference on MeansInference on ProportionsInference on 2-way TablesInference on Regression

Topic IV123456789101112131415back to main

• Given H0: =30, HA:
• Given H0: =30, HA:
• The local news station reports that the 97% confidence interval for a candidates support was (43%, 48%). What does the phrase 97% confidence mean?97% of the voters support the candidate97% of the time, this candidates level of support will be between 43% and 48%There is a 97% probability that the true level of support is between 43% and 48%There is a 97% probability that any other sample percentage is in the interval (43%, 48%)none of these is trueIV.2.Topic IV Menu

• The local news station reports that the 97% confidence interval for a candidates support was (43%, 48%). What does the phrase 97% confidence mean?97% of the voters support the candidate97% of the time, this candidates level of support will be between 43% and 48%There is a 97% probability that the true level of support is between 43% and 48%There is a 97% probability that any other sample percentage is in the interval (43%, 48%)none of these is trueIV.2.SOLUTIONnot (D) because youre predicting the range of the TRUE proportion; youre not interested in predicting the range of other samples!!!

Correct interpretation:

If this process were repeated over and over again, about 97% of our INTERVALS would capture the true proportion.Topic IV Menu

• A study of 20 teachers in a school district indicated that the 95% confidence interval for the mean salary of all teachers is (\$38,945, \$41,245). What assumptions must be true for this interval to be valid?no assumptions are necessary. The CLT appliesThe sample is randomly selected from a population of salaries that is a t-distributionthe distribution of the sample means is approximately normalthe distribution of all teachers salaries is approximately normalNone of the above.IV.3.Topic IV Menu

• A study of 20 teachers in a school district indicated that the 95% confidence interval for the mean salary of all teachers is (\$38,945, \$41,245). What assumptions must be true for this interval to be valid?no assumptions are necessary. The CLT appliesThe sample is randomly selected from a population of salaries that is a t-distributionthe distribution of the sample means is approximately normalthe distribution of all teachers salaries is approximately normalNone of the above.IV.3.SOLUTIONBecause our sample size is only 20, you have to know the population was normal to begin with. (D) is the best response.

I might accept choice (C) too since the CLT is all about when x-bar is normal, which is the goal I suppose.Topic IV Menu

• In order to reduce the width of a confidence interval, we can:increase sample size onlyincrease confidence level onlyincrease sample size and increase confidence levelincrease sample size and decrease confidence levelnone of these would reduce the width of the interval

• In order to reduce the width of a confidence interval, we can:increase sample size onlyincrease confidence level onlyincrease sample size and increase confidence levelincrease sample size and decrease confidence levelnone of these would reduce the width of the interval

IV. 4.SOLUTIONLess confidence affords you to predict a much tighter range of values.Topic IV Menu

• If the 95% confidence interval for is (6,9), what conclusion can we draw if we test Ho: =10 vs. Ha: 10 at =.05?reject Hofail to reject Hoaccept Hoaccept HaThere is insufficient information given to draw a conclusionIV.5.Topic IV Menu

• If the 95% confidence interval for is (6,9), what conclusion can we draw if we test Ho: =10 vs. Ha: 10 at =.05?reject Hofail to reject Hoaccept Hoaccept HaThere is insufficient information given to draw a conclusionIV.5.SOLUTIONA two tailed test of =.05 is equivalent to a 95% confidence interval. 10 is not within the interval.Topic IV Menu

• A bakery determines that it will be profitable if the time it takes to decorate a cake does not exceed 45 minutes. The owner documents the time spent on 20 cakes and performs a test. If the P-value of the test is 0.032, then he should conclude:at =.05, fail to reject Hoat =.05, reject Hoat =.03, reject Hoat =.025, reject HoWe cannot draw a conclusion from this informationIV.6.Topic IV Menu

• A bakery determines that it will be profitable if the time it takes to decorate a cake does not exceed 45 minutes. The owner documents the time spent on 20 cakes and performs a test. If the P-value of the test is 0.032, then he should conclude:at =.05, fail to reject Hoat =.05, reject Hoat =.03, reject Hoat =.025, reject HoWe cannot draw a conclusion from this informationIV.6.SOLUTIONa p-value of .032 is significant at the 5% levelTopic IV Menu

• Do boys perform better in math than girls? A randomly selected group of each gender were given the same math assessment.What design seems to be employed?Matched Pairs DesignSimple Random DesignMulti-State Cluster DesignIndependent Samples DesignRandomized Block DesignIV.7.Topic IV Menu

boysgirlsn110135Mean71.668.3St.Deviation10.411.2

• Do boys perform better in math than girls? A randomly selected group of each gender were given the same math assessment.What design seems to be employed?Matched Pairs DesignSimple Random DesignMulti-State Cluster DesignIndependent Samples DesignRandomized Block DesignIV.7.SOLUTIONWe have 2 independent samples here: boys and girls.Topic IV Menu

boysgirlsn110135Mean71.668.3St.Deviation10.411.2

• Do boys perform better in math than girls? A randomly selected group of each gender were given the same math assessment.What are Ho and Ha to determine if boys scores are higher than girls?Ho: b g = 0; Ha: b g < 0Ho: b g = 0; Ha: b g 0Ho: b g = 0; Ha: b g > 0Ho: b g < 0; Ha: b g = 0Ho: b = g; Ha: b g

boysgirlsn110135Mean71.668.3St.Dev10.411.2

• Do boys perform better in math than girls? A randomly selected group of each gender were given the same math assessment.What are Ho and Ha to determine if boys scores are higher than girls?Ho: b g = 0; Ha: b g < 0Ho: b g = 0; Ha: b g 0Ho: b g = 0; Ha: b g > 0Ho: b g < 0; Ha: b g = 0Ho: b = g; Ha: b g

IV.8.SOLUTIONAnother way to write this would beHo: b = g; Ha: b > g

boysgirlsn110135Mean71.668.3St.Dev10.411.2

• Do boys perform better in math than girls? A randomly selected group of each gender were given the same math assessment.Suppose the p-value is .0344. We can then conclude:IV.9.at =.025, reject Hoat =.02, reject Hoat =.01, reject Hoat =.025, fail to reject HoWe cannot draw a conclusion from this informationTopic IV Menu

boysgirlsn110135Mean71.668.3St.Dev10.411.2

• Do boys perform better in math than girls? A randomly selected group of each gender were given the same math assessment.Suppose the p-value is .0344. We can then conclude:IV.9.at =.025, reject Hoat =.02, reject Hoat =.01, reject Hoat =.025, fail to reject HoWe cannot draw a conclusion from this informationSOLUTION.0344 is not significant at .025, .02, or .01. We must fail to reject it at these levels.Topic IV Menu

boysgirlsn110135Mean71.668.3St.Dev10.411.2

• The rejection region for a test Ho: p=.4 vs. Ha: p 1.96 or z < -1.96Reject Ho if z > 1.645 or z < -1.645Reject Ho if z < -1.96Reject Ho if z < -1.645Reject Ho if t > 2.59IV.10.Topic IV Menu

• The rejection region for a test Ho: p=.4 vs. Ha: p 1.96 or z < -1.96Reject Ho if z > 1.645 or z < -1.645Reject Ho if z < -1.96Reject Ho if z < -1.645Reject Ho if t > 2.59IV.10.SOLUTIONinvnorm(.05)

because the entire .05 rejection region is in the left tail.Topic IV Menu

• The power of a test is described by all of the following EXCEPT

Power = p( rejecting Ho when Ha is true)Power = 1 Power = + The calculation of power requires knowing the values of 0, a, , and All of these are correct descriptions of the concept of power.IV.11.Topic IV Menu

• The power of a test is described by all of the following EXCEPT

Power = p( rejecting Ho when Ha is true)Power = 1 Power = + The calculation of power requires knowing the values of 0, a, , and All of these are correct descriptions of the concept of power.IV.11.SOLUTIONBut it IS true that as one increases, the other has to decrease.

just not always by the same amount Topic IV Menu

• In a matched pairs test of 75 pairs, which of the following assumptions is necessary?

The distribution of the paired differences should be approximately normalThe population variances should be equalThe samples are randomly and independently selectedThe sets of values for each variable are approximately normalNone of these assumptions is necessary.IV.12.Topic IV Menu

• In a matched pairs test of 75 pairs, which of the following assumptions is necessary?

The distribution of the paired differences should be approximately normalThe population variances should be equalThe samples are randomly and independently selectedThe sets of values for each variable are approximately normalNone of these assumptions is necessary.IV.12.SOLUTIONTopic IV MenuAnd being good stats students, you will either make sure n>25 or do a quick little graph to show there arent any outliers. Right?

• A pharmaceutical company claims that 50% of adult males living in a city in the Midwest get at least two colds per year. A random sample of 100 adult males living in the city reported that only 42% got two or more colds.

Do these data provide evidence (at the 5% significance level) that the true proportion of people is less than 50%IV.13.Topic IV Menu

• A pharmaceutical company claims that 50% of adult males living in a city in the Midwest get at least two colds per year. A random sample of 100 adult males living in the city reported that only 42% got two or more colds.

Do these data provide evidence (at the 5% significance level) that the true proportion of people is less than 50%Of course you would want to run through the entire test properly, but

we fail to reject at the 5% level. there is not enough evidence to say the proportion is less than 50%

• If a 90% confidence interval for the slope of a regression line does not contain 0, then which of the following is a valid conclusion?The confidence interval is not validA significance test will not be significant at the 10% levelThere is sufficient evidence to conclude that the slope of the true regression line is 0There is sufficient evidence to conclude that the slope of the true regression line is not 0.None of these is valid.IV.14.Topic IV Menu

• If a 90% confidence interval for the slope of a regression line does not contain 0, then which of the following is a valid conclusion?The confidence interval is not validA significance test will not be significant at the 10% levelThere is sufficient evidence to conclude that the slope of the true regression line is 0There is sufficient evidence to conclude that the slope of the true regression line is not 0.None of these is valid.IV.14.SOLUTIONIf 0 isnt in the interval, we are 90% confident that the slope is NOT zero.

This is exactly what a regression test would conclude: the slope is NOT zero.Topic IV Menu

• Topic IV MenuWhat is the expected number of males who prefer chocolate?

27.829.231.336.3None of theseIV.15.

malefemalechocolate3216vanilla144strawberry310

• What is the expected number of males who prefer chocolate?

27.829.231.336.3None of theseIV.15.SOLUTION48 of 79 people prefer chocolate (60.76%), so we expect 60.76% of the 49 males to like chocolate.

.6076(49) = 29.77

or if you prefer the book formula: (row total x column total)total number= 29.77Topic IV Menu

malefemalechocolate3216vanilla144strawberry310