Question

A researcher wishes to find out if the published max speed of a 737 jet is accurate. From past studies, it is known that the population standard deviation of speeds is 68 mph.

(a) Assuming that she would like to be 90% confident of the results, indicate the critical value that corresponds to this given level of confidence.
(b) If she would like to have a maximum error of 15 mph, how many jets should be sampled?

Answer 1

To determine the critical value for a 90% confidence level, use a z-score table. To find the sample size, use the formula n = (z * σ)^2 / E^2.

Step-by-step explanation:

(a) To determine the critical value that corresponds to a 90% confidence level, we need to find the z-score associated with a 90% confidence interval.

We can use a z-score table or a calculator to find that the z-score corresponding to a 90% confidence level is approximately 1.645.

(b) To calculate the sample size needed to have a maximum error of 15 mph, we can use the formula:

n = (z * σ)^2 / E^2

where n is the sample size, z is the critical value, σ is the population standard deviation, and E is the maximum error.

Plugging in the values, we get:

n = (1.645 * 68)^2 / 15^2

n ≈ 27.5

Therefore, she should sample at least 28 jets to have a maximum error of 15 mph.