205k views
0 votes
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?

User Divya MV
by
8.3k points

1 Answer

6 votes

Final answer:

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.

User Abishek Aditya
by
7.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories