Question

A researcher records the repair cost for 10 10 randomly selected VCRs. A sample mean of $79.18 $ ⁢ 79.18 and standard deviation of $11.06 $ ⁢ 11.06 are subsequently computed. Determine the 90% 90 % confidence interval for the mean repair cost for the VCRs. 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. Step 2 of 2 : Construct the 90% confidence interval. Round your answer to two decimal places.

Step 2 of 2 :

Construct the 90% confidence interval. Round your answer to two decimal places.

Answer 1

Solution:

Given:

Sample size = n = 10

Sample mean = = 79.18

Sample Standard Deviation = s = 11.06

Confidence level = c = 90%

Step 1 of 2: Find the critical value that should be used in constructing the confidence interval.

df = n - 1 = 10 - 1 = 9

two tail area = 1 - c = 1 - 0.90 = 0.10

Look in t table for df = 9 and two tail area = 0.10 and find t critical value

t critical value = t_c = 1.833

Step 2 of 2 : Construct the 90% confidence interval.

where

thus

Thus 90% confidence interval for mean  repair cost for the VCRs is between $72.77 and $85.59