Question

in a random sample of six mobile devices, the mean repair cost was $75.00 and the standard deviation was $14.00. 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 (51.95, 98.05). (round to two decimal places as needed.) the margin of error is $23.05. (round to two decimal places as needed.) interpret the results. choose the correct answer below. a. if a large sample of mobile devices are taken approximately 99% of them will have repair costs between the bounds of the confidence interval. b. with 99% confidence, it can be said that the repair cost is between the bounds of the confidence interval. c. with 99% confidence, it can be said that the population mean repair cost is between the bounds of the confidence interval. d. it can be said that 99% of mobile devices have a repair cost between the bounds of the confidence interval.

Explanation:

A confidence interval for the population mean gives a range within which we are confident the true population mean lies. A 99% confidence interval means that if we were to construct many such intervals (using the same method), approximately 99% of them would contain the true population mean. Option C correctly interprets this as being about the population mean, not individual repair costs (as in B and D) or a large sample of devices (as in A).

Answer:

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