# Statistics and Probability Homework Week 5 Complete Solution

Homework Week 5

4. Why is a 99% confidence interval wider than a 95% confidence interval?

12. A person claims to be able to predict the outcome of flipping a coin. Thisperson is correct 16/25 times. Compute the 95% confidence interval on theproportion of times this person can predict coin flips correctly. Whatconclusion can you draw about this test of his ability to predict the future?

15. You take a sample of 22 from a population of test scores, and the mean of yoursample is 60.

(a) You know the standard deviation of the population is 10.What is the 99% confidence interval on the population mean.

(b) Now assumethat you do not know the population standard deviation, but the standarddeviation in your sample is 10. What is the 99% confidence interval on themean now?

18. You were interested in how long the average psychology major at your collegestudies per night, so you asked 10 psychology majors to tell you the amountthey study. They told you the following times: 2, 1.5, 3, 2, 3.5, 1, 0.5, 3, 2, 4.

(a) Find the 95% confidence interval on the population mean.

(b) Find the 90%confidence interval on the population mean.

100. What is meant by the term “90% confident” when constructing a confidence interval for a mean?

a. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.

b. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples wouldcontain the sample mean.

c. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples wouldcontain the true value of the population mean.

d. If we took repeated samples, the sample mean would equal the population mean in approximately 90% of thesamples.

106. Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested inthe mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly

surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standarddeviation of four hours.

a.

i. ¯x¯ = __________

ii. sx= __________

iii. n= __________

iv. n– 1 = __________

b. Define the random variables X and ¯Xin words.

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 95% confidence interval for the population mean time wasted.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

e. Explain in a complete sentence what the confidence interval means.

116. A quality control specialist for a restaurant chain takes arandom sample of size 12 to check the amount of soda served in the 16 oz. serving size. The sample mean is 13.30 with asample standard deviation of 1.55. Assume the underlying population is normally distributed.What is the error bound?

a. 0.87

b. 1.98

c. 0.99

d. 1.74

130. On May 23, 2013, Gallup reported that of the 1,005 people surveyed, 76% of U.S. workers believe that they willcontinue working past retirement age. The confidence level for this study was reported at 95% with a ±3% margin of error.

a. Determine the estimated proportion from the sample.

b. Determine the sample size.

c. Identify CL and α.

d. Calculate the error bound based on the information provided.

e. Compare the error bound in part d to the margin of error reported by Gallup. Explain any differences between thevalues.

f. Create a confidence interval for the results of this study.

g. A reporter is covering the release of this study for a local news station. How should she explain the confidenceinterval to her audience?

4. Why is a 99% confidence interval wider than a 95% confidence interval?

12. A person claims to be able to predict the outcome of flipping a coin. Thisperson is correct 16/25 times. Compute the 95% confidence interval on theproportion of times this person can predict coin flips correctly. Whatconclusion can you draw about this test of his ability to predict the future?

15. You take a sample of 22 from a population of test scores, and the mean of yoursample is 60.

(a) You know the standard deviation of the population is 10.What is the 99% confidence interval on the population mean.

(b) Now assumethat you do not know the population standard deviation, but the standarddeviation in your sample is 10. What is the 99% confidence interval on themean now?

18. You were interested in how long the average psychology major at your collegestudies per night, so you asked 10 psychology majors to tell you the amountthey study. They told you the following times: 2, 1.5, 3, 2, 3.5, 1, 0.5, 3, 2, 4.

(a) Find the 95% confidence interval on the population mean.

(b) Find the 90%confidence interval on the population mean.

100. What is meant by the term “90% confident” when constructing a confidence interval for a mean?

a. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.

b. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples wouldcontain the sample mean.

c. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples wouldcontain the true value of the population mean.

d. If we took repeated samples, the sample mean would equal the population mean in approximately 90% of thesamples.

106. Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested inthe mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly

surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standarddeviation of four hours.

a.

i. ¯x¯ = __________

ii. sx= __________

iii. n= __________

iv. n– 1 = __________

b. Define the random variables X and ¯Xin words.

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 95% confidence interval for the population mean time wasted.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

e. Explain in a complete sentence what the confidence interval means.

116. A quality control specialist for a restaurant chain takes arandom sample of size 12 to check the amount of soda served in the 16 oz. serving size. The sample mean is 13.30 with asample standard deviation of 1.55. Assume the underlying population is normally distributed.What is the error bound?

a. 0.87

b. 1.98

c. 0.99

d. 1.74

130. On May 23, 2013, Gallup reported that of the 1,005 people surveyed, 76% of U.S. workers believe that they willcontinue working past retirement age. The confidence level for this study was reported at 95% with a ±3% margin of error.

a. Determine the estimated proportion from the sample.

b. Determine the sample size.

c. Identify CL and α.

d. Calculate the error bound based on the information provided.

e. Compare the error bound in part d to the margin of error reported by Gallup. Explain any differences between thevalues.

f. Create a confidence interval for the results of this study.

g. A reporter is covering the release of this study for a local news station. How should she explain the confidenceinterval to her audience?

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