Question

in a random sample of five mobile devices, the mean repair cost was $70.00 and the standard deviation was $11.50. assume the population is normally distributed and use a t - distribution to find the margin of error and construct a 90% confidence interval for the population mean. interpret the results.
the 90% confidence interval for the population mean μ is (59.03, 80.97).
(round to two decimal places as needed.)
the margin of error is $10.97.
(round to two decimal places as needed.)
interpret the results. choose the correct answer below.
a. with 90% confidence, it can be said that the repair cost is between the bounds of the confidence interval.
b. if a large sample of mobile devices are taken approximately 90% of them will have repair costs between the bounds of the confidence interval.
c. it can be said that 90% of mobile devices have a repair cost between the bounds of the confidence interval.
d. with 90% confidence, it can be said that the population mean repair cost is 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. In this case, the population parameter is the population mean repair cost. A 90% confidence interval means that if we were to take many samples and construct confidence intervals in the same way, about 90% of those intervals would contain the true population mean.
Option A is incorrect because it refers to the repair cost (a single value) instead of the population mean. Option B is wrong as it refers to a proportion of a large sample having repair costs in the interval, not the population mean. Option C is incorrect as it implies 90% of mobile devices (individual values) have repair costs in the interval, not the population mean. Option D is correct as it correctly states that with 90% confidence, the population mean repair cost is within the bounds of the confidence interval.

Answer:

D. With 90% confidence, it can be said that the population mean repair cost is between the bounds of the confidence interval.