Question

In a random sam of 55 refrigerators, the mean repair cost was $120 00 and the population standard deviation is $15.10 Construct a 50% confidence interval for the population mean repair cost. Interpret the res

Construct a 90% confidence interval for the population mean repair cost
The 90% confidence interval a C
Interpret you results. Choose the correct answer below
(Round to two decimal places as needed)
OA. With 90% confidence it can be said that the confidence interval contains the sample mean repair cost
OB With 90% confidence it can be said that the confidence interval contains the true mean repair cost
OC. The confidence interval contains 90% of the mean repair costs

Answer 1

Answer: To construct the confidence intervals, we'll use the formula:

Confidence Interval = Sample Mean ± (Critical Value * Standard Error)

where:

Sample Mean = $120.00 (given)

Population Standard Deviation = $15.10 (given)

Sample Size = 55

Critical Value is obtained from the t-distribution or z-distribution table for the desired confidence level (50% or 90%)

Standard Error = Population Standard Deviation / √(Sample Size)

Let's start with the 50% confidence interval:

50% Confidence Interval:

Critical Value for 50% confidence level: Since the sample size is relatively large (n = 55), we can use the z-distribution table. For a 50% confidence level, the critical value is 0.674.

Standard Error = $15.10 / √(55) ≈ $2.03006 (rounded to two decimal places)

Confidence Interval = $120.00 ± (0.674 * $2.03006)

Confidence Interval ≈ $120.00 ± $1.3677

Confidence Interval ≈ ($118.63, $121.37)

Interpretation: With 50% confidence, we can say that the true population mean repair cost is between $118.63 and $121.37.

90% Confidence Interval:

Critical Value for 90% confidence level (using z-distribution table) is approximately 1.645.

Standard Error = $15.10 / √(55) ≈ $2.03006 (rounded to two decimal places)

Confidence Interval = $120.00 ± (1.645 * $2.03006)

Confidence Interval ≈ $120.00 ± $3.3410

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.