You are interested in the weight gain of the College Freshman. You think that the average weight gain of the College Freshman student is not 15 pounds. You collect a random sample of measurements. The weight gains are (a negative value indicates a weight loss):

12.9, 7.1, 6.6, 12

You may assume for the following questions that the distribution of weight gain is normal. 

1 State the appropriate hypothesis test: (a, b, or c)

a. H0: µ ≤ 15 versus Ha: µ > 15

b. H0: µ = 15 versus Ha: µ ≠ 15

c. H0: µ ≥ 15 versus Ha: µ < 15

2 Calculate the test statistic for the previous question.

Round your answer to the nearest 0.0001.

3 For the previous problem, the test statistic follows a t-distribution. The number of degrees of freedom is ?

4 The p-value for the test in the previous problem is ?

Round your answer to the nearest 0.0001.

5 For the previous question, should you reject the null hypothesis in favor of the alternative at significance level α = 0.01? (Yes or No)

6 Based on the result of the test, is the weight gain significantly different from 15 lbs

(Yes or No)