08-11-2018

Chapter 8

Sigma known

Problem 1. A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is σ = 5.

• 1. What is the standard error of the mean?

  2. At 95% confidence, what is the margin of error?

  3. Provide a 95% confidence interval for the population mean.

Problem 2. The average cost per person for crashes in the Tampa, Florida, area was reported to be $1600. Suppose this average cost was based on a sample of 50 persons who had been involved in car crashes and that the population standard deviation is σ = $600. What is the margin of error for a 95% confidence interval? What would you recommend if the study required a margin of error of $150 or less?

Problem 3. How large a sample should be selected to provide a 95% confidence interval with a margin of error of 10? Assume that the population standard deviation is 40.

Sigma unknown

Problem 4. Find the t value(s) for each of the following cases.

• 1. Upper tail area of .025 with 12 degrees of freedom

  2. Lower tail area of .05 with 50 degrees of freedom

  3. Upper tail area of .01 with 30 degrees of freedom

  4. Where 90% of the area falls between these two t values with 25 degrees of freedom

  5. Where 95% of the area falls between these two t values with 45 degrees of freedom

Problem 5. A simple random sample with n = 54 provided a sample mean of 22.5 and a sample standard deviation of 4.4.

• 1. Develop a 90% confidence interval for the population mean.

  2. Develop a 95% confidence interval for the population mean.

  3. Develop a 99% confidence interval for the population mean. d.What happens to the margin of error and the confidence interval as the confidence level is increased?

Problem 6. The mean number of hours of flying time for pilots at Continental Airlines is 49 hours per month. Assume that this mean was based on actual flying times for a sample of 100 Continental pilots and that the sample standard deviation was 8.5 hours.

• 1. At 95% confidence, what is the margin of error?

  2. What is the 95% confidence interval estimate of the population mean flying time for the pilots?

  3. The mean number of hours of flying time for pilots at United Airlines is 36 hours per month. Use your results from part (b) to discuss differences between the flying times for the pilots at the two airlines. The Wall Street Journal reported United Airlines as having the highest labor cost among all airlines. Does the information in this exercise provide insight as to why United Airlines might expect higher labor costs?

Problem 7. Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 65 weekly reports showed a sample mean of 19.5 customer contacts per week. The sample standard deviation was 5.2. Provide 90% and 95% confidence intervals for the population mean number of weekly customer contacts.

Proportion

Problem 8. The president of Doerman Distributors, Inc., believes that 30% of the firm’s orders come from first-time customers. A random sample of 100 orders will be used to estimate the proportion of first-time customers.

• 1. Assume that the president is correct and p = .30. What is the sampling distribution of sample proportion for this study?

  2. What is the probability that the sample proportion p will be between .20 and .40?

  3. What is the probability that the sample proportion will be between .25 and .35?

Problem 9. A simple random sample of 400 individuals provides 100 Yes responses.

• 1. What is the point estimate of the proportion of the population that would provide Yes responses?

  2. What is your estimate of the standard error of the proportion?

  3. Compute the 95% confidence interval for the population proportion.

Problem 10. A poll for the presidential campaign sampled 491 potential voters in June. A primary purpose of the poll was to obtain an estimate of the proportion of potential voters who favored each candidate. Assume a planning value of p* = .50 and a 95% confidence level.

• 1. For p* = .50, what was the planned margin of error for the June poll?

  2. Closer to the November election, better precision and smaller margins of error are desired. Assume the following margins of error are requested for surveys to be conducted during the presidential campaign. Compute the recommended sample size for each survey.

Survey Month             Margin of Error

September                           .04

October                                .03

Early November                   .02

Pre-Election Day                  .01