12-11-2018

Recap

Problem 1. A simple random sample of 49 items resulted in a sample mean of 10. The population standard deviation is σ = 7.

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

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

  3. How large a sample should be selected to provide a 95% confidence interval with a margin of error of 5?

Sigma unknown

Problem 1. 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 60 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 40 degrees of freedom

Problem 2. A simple random sample with n = 61 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 3. 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 101 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 4. Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 61 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.