Based on a sample of repair records, an engineer calculates a 95% confidence interval for the mean cost to repair a fiber-optic component to be ($ 140, $ 160). A supervisor summarizes this result in a report, saying, “We are 95% confident that the mean cost of repairs is less than $160.” Is the supervisor underestimating the confidence, overestimating it, or getting it right? Explain.

Step 1of 4:

Based on a sample of repair records, 95% confidence interval for the mean cost to repair a fiber- optic component is ($140,$160).A supervisor summarizing this result as,” We are having 95% confident that the mean cost is less than $160. We have to find whether the supervisor underestimating the confidence,or overestimating it, or getting it right.

Step 2 of 4:

To find the 95% confidence interval for the mean cost,

Set t= .95

1- t = 0.05

= 0.025

We have to find the Z-score , = .

We can find from the normal table (area under normal curve). The value 0.975 falls in the row 1.9 under column 0.06.

If the population mean and variance is unknown the we can estimate the 95% confidence interval as

…….(1)