Question

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

16, 13, 13, 15, 14, 18, 19, 14

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

(a) State the appropriate hypothesis test. (This was done before collecting the data)

Null Hypothesis: AnswerThe weight gain is less than 15 pounds.The weight gain is at most 15 pounds.The weight gain is equal to 15 pounds.The weight gain is not equal to 15 pounds.The weight gain is at least 15 pounds.The weight gain is greater than 15 pounds.

Alternative Hypothesis: AnswerThe weight gain is less than 15 pounds.The weight gain is at most 15 pounds.The weight gain is equal to 15 pounds.The weight gain is not equal to 15 pounds.The weight gain is at least 15 pounds.The weight gain is greater than 15 pounds.

(b) Calculate the sample mean x¯.x¯. x¯=x¯= Answer

(c) Calculate the sample standard deviation s.s. s=s= Answer

(d) Evaluate the test statistic

T=x¯−μ0s/n‾√.T=x¯−μ0s/n.

T=T= Answer

(e) The test statistic is t-distributed with Answer degrees of freedom.

(f) The p-value for the test is Answer.

(g) Should you reject the null hypothesis in favor of the alternative at significance level α=0.01α=0.01? AnswerYes.No.

(h) Is the weight gain significantly different from 15 lbs? AnswerYes.No.

Answer 1