Question

A supervisor records the repair cost for 17 randomly selected stereos. A sample mean of $66.34 and standard deviation of $15.22 are subsequently computed. Determine the 80% confidence interval for the mean repair cost for the stereos. Assume the population is approximately normal. Find the critical value that should be used in constructing the confidence interval.

A supervisor records the repair cost for 17 randomly selected stereos. A sample mean of $66.34 and standard deviation of $15.22 are subsequently computed. Determine the 80 % confidence interval for the mean repair cost for the stereos. Assume the population is approximately normal. Construct the 80% confidence interval.

Answer 1

To determine the 80% confidence interval, find the critical value using the t-distribution table and calculate the upper and lower limits.

Step-by-step explanation:

To determine the 80% confidence interval for the mean repair cost for the stereos, we need to find the critical value that corresponds to an 80% confidence level. The critical value is obtained from the t-distribution table.

For an 80% confidence level with a sample size of 17, the critical value is approximately 1.337.

Using the sample mean of $66.34, the standard deviation of $15.22, and the critical value, we can calculate the confidence interval:
Lower limit = sample mean - (critical value * standard deviation) = $66.34 - (1.337 * $15.22) ≈ $45.09
Upper limit = sample mean + (critical value * standard deviation) = $66.34 + (1.337 * $15.22) ≈ $87.59

Therefore, the 80% confidence interval for the mean repair cost for the stereos is approximately ($45.09, $87.59).