Question

Ten randomly selected automobiles were stopped and the tread depth of the right front tire was measured. The mean was 0.32 inch, and the standard deviation was 0.08 inch.

a) Find the 95% confidence interval of the mean depth. Assume that the variable is approximately normally distributed.
b) Does the 95% confidence interval suggest 0.30 a plausible value for the average tread depth of the right front tire?

Answer 1

The 95% confidence interval for the mean tread depth is approximately (0.2694, 0.3706) inch. The value 0.30 inch is plausible.

Step-by-step explanation:

To find the 95% confidence interval of the mean tread depth of the right front tires, we can use the formula:

CI = mean ± (critical value) × (standard deviation / √n)

Given that the mean tread depth is 0.32 inch, the standard deviation is 0.08 inch, and the sample size is 10, we can calculate the confidence interval as follows:

CI = 0.32 ± (1.96) × (0.08 / √10)

Simplifying the equation gives:

CI = 0.32 ± 0.05062

Therefore, the 95% confidence interval for the mean tread depth is approximately (0.2694, 0.3706) inch.

To determine if the value 0.30 inch is plausible for the average tread depth, we can check if it falls within the confidence interval. Since 0.30 inch is within the interval (0.2694, 0.3706) inch, it is plausible.