Question

The Gidget Company makes widgets. If the production process is working​ properly, it turns out that the widgets are normally distributed with a mean length of at least 3.3 feet. Larger widgets can be used or altered but shorter widgets must be scrapped. You select a sample of 25 ​widgets, and the mean length is 3.28 feet and the sample standard deviation is 0.18 foot. Do you need to adjust the production​ equipment? Complete parts​ (a) through​ (d).

a. If you test the null hypothesis at the 0.05 level of​ significance, what decision do you make using the critical value approach to hypothesis​ testing?

What are the null and alternative hypotheses for this​ test?

A. H0: μ<3.3

H1: μ≥3.3

B. H0: μ>3.3

H1: μ≤3.3

C. H0: μ≥3.28

H1: μ<3.28

D. H0: μ≥3.3

H1: μ<3.3

E. H0: μ≤3.3

H1: μ>3.3

F. H0: μ≤3.28

H1: μ>3.28

What is the test statistic for this​ test?

​(Round to four decimal places as​ needed.)

What is the critical value for this​ test?

​(Round to four decimal places as​ needed.)

What is the conclusion for this​ test?

Since the test statistic is _ than the critical​ value, _ the null hypothesis and conclude that there is _ evidence that you need to adjust the production equipment.

b. If you test the null hypothesis at the 0.05 level of​ significance, what decision do you make using the​ p-value approach to hypothesis​ testing?

What is the​ p-value for this​ test?

​(Round to four decimal places as​ needed.)

What is the conclusion for this​ test?

Since the​ p-value is _ critical value, _ the null hypothesis and conclude that there is _ evidence that you need to adjust the production equipment.

c. Interpret the meaning of the​ p-value in this problem. Choose the correct answer below.

A.The​ p-value is the probability that the sample of widgets have a mean length of 3.3 feet or greater.

B.The​ p-value is the probability that the sample of widgets have a mean length of 3.28 feet or​ less, given that the the mean length is actually 3.3 feet.

C.The​ p-value is the probability that the sample of widgets have a mean length of 3.28 feet or less.

D. The p-value is the probability that the sample of widgets have a mean length of 3.3 feet or greater, given that the mean length is actually 3.28 feet.

d. Compare your conclusions in​ (a) and​ (b). Choose the correct answer below.

A.Using the critical value approach the null hypothesis was rejected and using the​ p-value approach the null hypothesis was rejected.The critical value approach and the​ p-value approach are two different methods of finding the same answer.

B.Using the critical value​ approach, the null hypothesis was not rejected and using the​ p-value approach, the null hypothesis was rejected. The critical value approach and the​ p-value approach yeild opposite results.

C.Using the critical value approach the null hypothesis was not rejected and using the​ p-value approach the null hypothesis was not rejected. The critical value approach and the​ p-value approach are two different methods of finding the same answer.

D.Using the critical value​ approach, the null hypothesis was rejected and using the​ p-value approach, the null hypothesis was not rejected. The critical value approach and the​ p-value approach yield opposite results.

Answer 1