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MAT 155 Statistical Analysis Sample Test 3 Chapters 7-10.3 M155SampleT3Ch7-10.3.doc

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Student’s Name ____________________________________________________________ Row___ Seat___ Score_____

Date: Instructor: Dr. Claude S. Moore

INSTRUCTIONS: Mark your answers on the Answer Sheet. Read each statement and problem carefully.

Perform and show calculations, as necessary.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the

question. You must show correct work in order to receive partial credit for an incorrect answer.

1. Construct a 95% confidence interval for the population proportion p with the sample data n = 53 and

x = 15.

(a) ( 0.162, 0.404) (b) ( 0.18, 0.386) (c) ( 0.161, 0.405) (d) ( 0.181, 0.385)

2. Find the critical value 2

αt for a confidence level of 99% and a sample size of 17.

(a) 2.567 (b) 2.583 (c) 2.921 (d) 2.898

3. Identify the null hypothesis H0 and the alternative hypothesis H1. Use µ for a claim about a mean, p for a

claim about a proportion, and σ for a claim about standard deviation. A researcher claims that the amounts

of acetaminophen in a certain brand of cold tablets have a standard deviation different from 3.3 mg.

(a) H0: σ ≥ 3.3 mg H1: σ < 3.3 mg (b) H0: σ ≠ 3.3 mg H1: σ = 3.3 mg

(c) H0: σ ≤ 3.3 mg H1: σ > 3.3 mg (d) H0: σ = 3.3 mg H1: σ ≠ 3.3 mg

4. Formulate the indicated conclusion by using the flow chart from the formula card. Be sure to address the

original claim. A psychologist claims that more than 37 percent of the population suffers from professional

problems due to extreme shyness. Assume that a hypothesis test of the claim has been conducted and that the

conclusion is fail to reject the null hypothesis, state the conclusion in non-technical terms.

(a) There is not sufficient evidence to support the claim that the true proportion is less than 37 percent.

(b) There is sufficient evidence to support the claim that the true proportion is greater than 37 percent.

(c) There is sufficient evidence to support the claim that the true proportion is less than 37 percent.

(d) There is not sufficient evidence to support the claim that the true proportion is greater than 37 percent.


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5. Compute the value of an appropriate test statistic for the given hypothesis test. You wish to test the claim

that µ < 25.0 with a significance level of α = 0.05. In a sample of n = 52, the sample mean is 27.1, and the

population standard deviation is 3.3.

(a) z = -4.59 (b) z = 33.09 (c) z = 4.59 (d) z = 0.64

6. Find the critical t-value or values for the given hypothesis, sample size, and significance level. α = 0.01;

n = 12; H0: µ = 81.1

(a) ±3.106 (b) 2.718 (c) ±2.718 (d) ±3.055

7. Should the statistician use a t distribution, a normal distribution, or neither to test the null hypothesis? In a

study of monthly incomes, x = 4070, σ = 1980, and n = 7. The data has a slight skew to the right.

The null hypothesis is: Ho: µ ≤ 4400

(a) Normal distribution (b) t distribution (c) Neither

8. State the decision rule to test the null hypothesis. 319 people were asked if they were satisfied with their

jobs. 45% said they were satisfied. H0: p ≤ 0.21 Confidence level: 99%.

(a) Reject H0 if 0005.0

21.0ˆ −p > 2.05 (b) Reject H0 if

0011.0

21.0ˆ −p < 2.085

(c) Reject H0 if 0005.0

45.0ˆ −p > 2.575 (d) Reject H0 if

0011.0

21.0ˆ −p > 2.05

9. Compute the test statistic used to test the null hypothesis. 401 people were asked if they were satisfied with

their jobs. 47% said they were satisfied. H0: p ≤ 0.42 Confidence level: 98%.

(a) 2.612 (b) 4.125 (c) 0.101 (d) 2.029


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10. Find the critical value or values of χ2 based on the given information. α = 0.01 n = 10 H0: σ = 8.0

(a) 1.735 & 23.589 (b) 21.666 (c) 23.209 (d) 2.088 & 21.666

11. A researcher wishes to compare the weights of women in different age groups. The mean weight for 90

randomly selected women aged 40-49 was 148 lb with a standard deviation of 29.2 lb. The mean weight for

97 randomly selected women aged 30-39 was 140 lb with a standard deviation of 27.2 lb. The researcher

wishes to test the claim that the population mean for women aged 40-49 is greater than the population

mean for women aged 30-39. What is the value of the appropriate test statistic?

(a) z = 4.02 (b) z = 0.47 (c) z = 1.93 (d) z = 10.29

12. The two data sets are dependent. Find d to the nearest tenth. [ d = Group 1 – Group 2 ]

Group 1 53 69 55 63 51

Group 2 24 28 30 25 22

(a) 42.1 (b) 32.4 (c) 19.4 (d) 40.5

13. Assume that you want to test the claim that the paired sample data come from a population for which the

mean difference is hypothesized to be µd = 0. Compute the value of the t test statistic. [HINT: Use Statdisk

or calculator.] x 6 1 12 6 9

y 3 3 8 7 4

(a) t = 2.890 (b) t = 0.578 (c) t = 0.415 (d) t = 1.292


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14. Find the appropriate p-value to test the null hypothesis for the following information.

n1 = 16 n2 = 20

H1: µ1 > µ2

Computed value t = 2.602

(a) less than 0.01 (b) 0.02 (c) less than 0.02 (d) 0.01

15. Find the number of successes (defective computers) x suggested by the given statement. A computer

manufacturer randomly selects 2690 of its computers for quality assurance and finds that 2.6% of these

computers are found to be defective.

(a) 68 (b) 73 (c) 70 (d) 75

16. Compute the test statistic used to test the alternative hypothesis that p1 > p2.

n1 = 178 and x1 = 41 n2 = 170 and x2 = 34

(a) 10.740 (b) 0.688 (c) 0.221 (d) 19.946

17. Given the hypothesis and the sample data, find the decision criterion that would be used for rejecting the

null hypothesis. Assume that the samples are independent and that they have been randomly selected.

Assume that np ≥ 5 and nq ≥ 5 for both samples. The table shows the number of people having a certain

characteristic in samples from two different populations.

We wish to test the hypothesis at the 10% level of significance: H0: p1 ≥ p2 against H1: p1 < p2. What

decision rule would you use? (a) Reject H0 if test statistic is greater than -1.28 (b) Reject H0 if test statistic is less than -1.28

(c) Reject H0 if test statistic is less than 1.28 (d) None of the above is correct.

Sample 1 2__

Sample size 80 100_

Number with characteristic 40 53_


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18. Find the appropriate p-value to test the null hypothesis, H0: p1 = p2, using a significance level of 0.05 with

a test statistic of z = -0.29.

n1 = 100 and x1 = 38 n2 = 100 and x2 = 40

(a) 0.7719 (b) 0.1610 (c) 0.2130 (d) 0.0412

19. Compute the test statistic you would use to test the null hypothesis. Ten observations are drawn from two

independent populations with the following sample statistics.

34.7741 =x 07.3812 =x

23.5162

1 =s 05.2542

2 =s

H0: 2

2

2

1 σσ = α = 0.02

(a) 4.06 (b) 2.03 (c) 3.45 (d) 1.62

20. Given the hypothesis and the sample data, find the decision criterion that would be used for rejecting the

null hypothesis. Assume that all populations are normally distributed. Assume that independent random

samples have been drawn from populations with unknown variances, and not assumed equal.

H0: µ1 ≥ µ2 and H1: µ1 < µ2.

Sample A Sample B

2.271 =x 0.352 =x

8.61 =s 2.92 =s

n1 = 14 n2 = 9

α = 0.01

What values of the test statistic would result in rejection of the null hypothesis?

(a) Reject H0 if test statistic < -2.896 (b) Reject H0 if test statistic < -2.33

(c) Reject H0 if test statistic < -2.650 (d) Reject H0 if test statistic > -2.896


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21. The value of the linear correlation coefficient, r, and the sample size, n, are given. Find the critical values

that would be used in a test of the null hypothesis ρ = 0 against ρ ≠ 0, and determine whether there is

significant linear correlation. Use a significance level of 0.05 and assume that the test statistic is r = -0.248

and n = 15

(A) Critical value: r = 0.514, no significant linear correlation

(B) Critical values: r = ±0.514, significant linear correlation

(C) Critical values: r = ±0.514, no significant linear correlation

(D) Critical values: r = ±0.532, no significant linear correlation

22. Construct a scatter diagram for the given data.

x -4 -3 -2 -5 -3 -1 -4 6 -4 -2

y -5 -3 -5 6 2 2 -3 4 -6 -2

(A) (B) (C) (D)

23. Find the value of the linear correlation coefficient r. The paired data below consist of the test scores of 6

randomly selected students and the number of hours they studied for the test.

Hours 5 10 4 6 10 9

Score 64 86 69 86 59 87

(A) -0.224 (B) 0.224 (C) -0.678 (D) 0.678

24. Find the coefficient of determination, given that the value of the linear correlation coefficient, r, is -0.935.

(A) 0.065 (B) 0.874 (C) 0.935 (D) 0.126

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