Question

A manager records the repair cost for 4 randomly selected stereos. A sample mean of $82.64 and standard deviation of $14.32 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the stereos. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answer 1

CI = (70.861 , 94.418)

Explanation:

In order to determine the 90% confidence interval you use the following formula (for a population approximately normal):

`CI=(\overline{x}-Z_(\alpha/2)(\sigma)/(√(n)),\overline{x}+Z_(\alpha/2)(\sigma)/(√(n)))` (1)

`\overline{x}`: mean = 82.64

σ: standard deviation = 14.32

n: sample = 4

α: tail area = 1 - 0.9 = 0.1

Z_α/2 = Z_0.05: Z factor = 1.645

You replace these values and you obtain:

`Z_(0.05)((14.32)/(√(4)))=(1.645)((14.32)/(√(4)))=11.778`

The confidence interval will be:

`CI=(82.64-11.778,82.64+11.778)=(70.861,94.418)`

The 90% confidence interval is (70.861 , 94.418)