Answer: To construct a 90% confidence interval for the population mean repair cost, we'll use the formula for the confidence interval:
Confidence Interval = Sample Mean ± (Critical Value * (Population Standard Deviation / √Sample Size))
Given:
Sample Mean = $120.00
Population Standard Deviation = $15.10
Sample Size = 55
Step 1: Find the critical value for a 90% confidence level.
Since the sample size is relatively large (n = 55), we can use the z-distribution table. For a 90% confidence level, the critical value is approximately 1.645.
Step 2: Calculate the confidence interval.
Confidence Interval = $120.00 ± (1.645 * ($15.10 / √55))
Confidence Interval ≈ $120.00 ± ($1.645 * $2.03454)
Confidence Interval ≈ $120.00 ± $3.34
Confidence Interval ≈ ($116.66, $123.34)
Interpretation:
With 90% confidence, we can say that the true population mean repair cost is between $116.66 and $123.34.
The correct answer is:
OB. With 90% confidence, it can be said that the confidence interval contains the true mean repair cost.