Stat 202 Business Statistics II Student Name: _______________________________________

Additional Exercises on Chapter 8: Interval Estimation

Solve the problem.

1) Find the value of α that corresponds to a level of confidence of 83%.

2) Find the value of α that corresponds to a level of confidence of 85.5%.

Find the confidence interval specified.

3) The mean score, x, on an aptitude test for a random sample of 8 students was 68. Assuming that σ = 16,

construct a 95.44% confidence interval for the mean score, μ, of all students taking the test.

4) A random sample of 88 light bulbs had a mean life of x = 497 hours. Assume that σ = 27 hours. Construct a 90%

confidence interval for the mean life, μ, of all light bulbs of this type.

5) A laboratory tested 77 chicken eggs and found that the mean amount of cholesterol was 199 milligrams.

Assume that σ = 16.1 milligrams. Construct a 95% confidence interval for the true mean cholesterol content, μ,

of all such eggs.

6) 34 packages are randomly selected from packages received by a parcel service. The sample has a mean weight

of 21.1 pounds. Assume that σ = 2.4 pounds. What is the 95% confidence interval for the true mean weight, μ,

of all packages received by the parcel service?

7) 30 students were randomly selected from a large group of students taking a certain calculus test. The mean

score for the students in the sample was 90. Assume that σ = 6.5. Construct a 99% confidence interval for the

mean score, μ, of all students taking the test.

Determine the margin of error in estimating the population mean, μ.

8) A sample of 57 eggs yields a mean weight of 1.66 ounces. Assuming that σ = 0.37 ounces, find the margin of

error in estimating μ at the 95% level of confidence.

9) A sample of 68 college students yields a mean annual income of $3248. Assuming that σ = $885, find the

margin of error in estimating μ at the 99% level of confidence.

10) A telephone company wishes to estimate the mean duration of local calls. Given that σ = 3.4 minutes and that

the sample size is 460, find the margin of error in estimating μ at the 85% level of confidence.

11) Based on a sample of size 42, a 95% confidence interval for the mean score of all students, μ, on an aptitude test

is from 64.5 to 71.5. Find the margin of error.

Find the necessary sample size.

12) A population is normal with a variance of 68. Suppose you wish to estimate the population mean μ. Find the

sample size needed to assure with 68.26 percent confidence that the sample mean will not differ from the

population mean by more than 3 units.

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13) Weights of women in one age group are normally distributed with a standard deviation σ of 13 lb. A researcher

wishes to estimate the mean weight of all women in this age group. Find how large a sample must be drawn in

order to be 90 percent confident that the sample mean will not differ from the population mean by more than

3.9 lb.

14) The weekly earnings of students in one age group are normally distributed with a standard deviation of 54

dollars. A researcher wishes to estimate the mean weekly earnings of students in this age group. Find the

sample size needed to assure with 98 percent confidence that the sample mean will not differ from the

population mean by more than 4 dollars.

15) The monthly credit card debts for individual accounts are normally distributed with a standard deviation of 43

dollars. A researcher wishes to estimate the mean monthly credit card debt for all individual accounts. Find the

sample size needed to assure with 95.44 percent confidence that the sample mean will not differ from the

population mean by more than 3 units.

16) You wish to estimate the mean weight of machine components of a certain type and you require a 96% degree

of confidence that the sample mean will be in error by no more than 0.008 g. After using the range rule of

thumb to estimate the standard deviation, find the sample size required. Typical weights range from 8.73 g to

9.09 g.

Find the specified t-value.

17) For a t-curve with df = 11, find t0.10

.

18) For a t-curve with df = 15, find t0.025

.

19) For a t-curve with df = 24, find t0.005

.

20) For a t-curve with df = 9, find the t-value having area 0.005 to its left.

21) For a t-curve with df = 6, find the two t-values that divide the area under the curve into a middle 0.99 area and

two outside areas of 0.005.

Find the confidence interval specified. Assume that the population is normally distributed.

22) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 210 milligrams

with s = 18.1 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such

eggs.

23) A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected

subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95%

confidence interval for the mean score of all such subjects.

24) The principal randomly selected six students to take an aptitude test. Their scores were:

89.8 76.3 79.4 87.6 79.4 70.9

Determine a 90% confidence interval for the mean score for all students.

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25) The football coach randomly selected ten players and timed how long each player took to perform a certain

drill. The times (in minutes) were:

5.1 7.5 9.2 13.8 7.9

13.2 10.8 5.3 6.4 6.7

Determine a 95% confidence interval for the mean time for all players.

Find the indicated margin of error.

26) In a sample of 185 observations, there were 87 positive outcomes. Find the margin of error for the 95%

confidence interval used to estimate the population proportion.

27) In a survey of 6600 T.V. viewers, 1980 said they watch network news programs. Find the margin of error for

the 95% confidence interval used to estimate the population proportion.

28) In a clinical test with 2213 subjects, 1230 showed improvement from the treatment. Find the margin of error for

the 95% confidence interval used to estimate the population proportion.

29) In a survey of 1500 T.V. viewers, 50% said they watch network news programs. Find the margin of error for the

95% confidence interval used to estimate the percentage of TV viewers who watch network news programs.

Find the indicated confidence interval.

30) A researcher wishes to estimate the proportion of adults in the city of Darby who are vegetarian. In a random

sample of 1774 adults from this city, the proportion that are vegetarian is 0.046. Find a 90% confidence interval

for the true proportion of vegetarians in the city of Darby.

31) A survey of 300 union members in New York State reveals that 112 favor the Republican candidate for

governor. Construct the 98% confidence interval for the true population proportion of all New York State union

members who favor the Republican candidate.

32) Of 80 adults selected randomly from one town, 66 have health insurance. Find a 90% confidence interval for

the true proportion of all adults in the town who have health insurance.

33) Of 103 randomly selected adults, 30 were found to have high blood pressure. Construct a 95% confidence

interval for the true percentage of all adults that have high blood pressure.

34) Of 122 adults selected randomly from one town, 27 of them smoke. Construct a 99% confidence interval for the

true percentage of all adults in the town that smoke.

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Answer KeyTestname: ADDITIONAL EXERCISES ON CHAPTER 8 _ INTERVAL ESTIMATION

1) 0.17

2) 0.145

3) 56.7 to 79.3

4) 492.3 to 501.7 hours

5) 195.4 to 202.6 milligrams

6) 20.3 to 21.9 pounds

7) 86.94 to 93.06

8) 0.10 oz

9) $276

10) 0.228 minutes

11) 3.5

12) 8

13) 30

14) 990

15) 822

16) 532

17) 1.363

18) 2.131

19) 2.797

20) -3.250

21) -3.707, 3.707

22) 198.5 to 221.5 milligrams

23) 67.7 to 84.7

24) 74.76 to 86.37

25) 6.40 to 10.80 minutes

26) 0.0719

27) 0.0111

28) 0.0207

29) 2.53%

30) From 0.0378 to 0.0542

31) From 0.308 to 0.438

32) From 0.755 to 0.895

33) From 20.4% to 37.9%

34) From 12.5% to 31.8%

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