Question

in a random sample of five mobile devices, the mean repair cost was $65.00 and the standard deviation was $12.50. assume the population is normally distributed and use a t - distribution to find the margin of error and construct a 99% confidence interval for the population mean. interpret the results. the 99% confidence interval for the population mean μ is (39.26, 90.74) (round to two decimal places as needed.) the margin of error is $25.74 (round to two decimal places as needed.) interpret the results. choose the correct answer below. a. it can be said that 99% of mobile devices have a repair cost between the bounds of the confidence interval. b. with 99% confidence, it can be said that the population mean repair cost is between the bounds of the confidence interval. c. with 99% confidence, it can be said that the repair cost is between the bounds of the confidence interval. d. if a large sample of mobile devices are taken approximately 99% of them will have repair costs between the bounds of the confidence interval.

Explanation:

A confidence interval gives an estimated range of values which is likely to include an unknown population parameter. A 99% confidence interval for the population mean means that if we were to take many samples and construct confidence intervals in the same way, about 99% of those intervals would contain the true population mean.

• Option A is incorrect because the confidence interval is about the population mean, not about individual mobile devices.
• Option B is correct. The 99% confidence interval is constructed to estimate the population mean. So, with 99% confidence, we can say that the population mean repair cost is between the bounds of the confidence interval.
• Option C is incorrect as it doesn't specify that it's about the population mean.
• Option D is incorrect as it again misinterprets the confidence interval (it's about the population mean, not about a large sample of individual repair costs).

Answer:

B. With 99% confidence, it can be said that the population mean repair cost is between the bounds of the confidence interval.