Question

in a random sample of four mobile devices, the mean repair cost was $80.00 and the standard deviation was $12.00. 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 (44.95, 115.05) (round to two decimal places as needed.) the margin of error is $35.05 (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 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. 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 of values within which the population mean is likely to lie. A 99% confidence interval means that if we were to construct many such intervals from different samples, approximately 99% of them would contain the true population mean.

• Option A is incorrect because it refers to a large sample and repair costs (individual values) instead of the population mean.
• Option B is correct as it correctly states that with 99% confidence, the population mean repair cost is within the confidence interval bounds.
• Option C is incorrect as it refers to the repair cost (a single value, not the population mean)
• Option D is incorrect as it refers to 99% of mobile devices (individuals) having repair costs in the interval, not the population mean.

Answer:

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