Question

A manager records the repair cost for 14 randomly selected dryers. A sample mean of $88.34 and standard deviation of $19.22 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the dryers. 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

Solution :

Given that,

Point estimate = sample mean = = 88.34

sample standard deviation = s = 19.22

sample size = n = 14

Degrees of freedom = df = n - 1 = 13

Critical value = t _/2,df = 1.771

Margin of error = E = t_/2,df * (s /n)

= 1.771 * (19.22 / 14)

Margin of error = E = 9.10

The 90% confidence interval estimate of the population mean is,

- E < < + E

88.34 - 9.10 < < 88.34 + 9.10

79.24 < < 97.44

(79.24 , 97.44)