I need help on this statistics problem please. Thanks

1.

The building specifications in a certain city require that the sewer pipe used in residential areas have a mean breaking strength of more than 2,500 pounds per lineal foot. A manufacturer who would like to supply the city with sewer pipe has submitted a bid and provided the following additional information: An independent contractor randomly selected seven sections of the manufacturer's pipe and tested each for breaking strength. The results (pounds per lineal foot) are shown: 2,610 2,750 2,420 2,510 2,540 2,490, and 2,680 (the sample mean is 2,571.4 and the sample standard deviation is 115). Using a right-tailed test with a significance level of =0.05, you perform a hypothesis test to see if there is sufficient evidence to conclude that the manufacturer's sewer pipe meets the required specifications. Which of the following is NOT a correct statement about the results?

a. The t-test statistic is 1.6419

b. The t-critical value of 2.4469

c. The p-value is 0.0759

d. We conclude that there is no sufficient evidence to conclude that the manufacturer's sewer pipe meets the required specifications.

e. None of the above (the above statements are all true)

2.

Referring to the previous question, find the probability of making a Type-II error if the true breaking strength of the pipe is assumed to be 2,580 pounds. The true strengths of pipes are normally distributed with a standard deviation of 115 pounds (Use t-distribution to determine the answer)

a. 0.0234 (or 2.34%)

b. 0.1533 (or 15.33%)

c. 0.3337 (or 33.37%)

d. 0.4251 (or 42.51%)

e. 0.5000 (or 50.00%)

3.

Referring to the previous question, in testing the hypothesis H0: <= 2500 pounds versus H1: > 2500 pounds regarding the strength of pipe, how many samples (at least) must be collected so that a test conducted at a significance level of 5% will have power 0.80 against the alternative =2,550 (expected true mean), if it is assumed that =115?

a. 9

b. 13

c. 25

d. 35

e. 78