show work You are interested in the weight gain of the Aubur

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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): 19,10,8,21,6,8,11,14,13,14,6,8,11,11,9,19,1 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: The weight gain is equal to 15 pounds. Alternative Hypothesis: The weight gain is not equal to 15 pounds. (b) Calculate the sample mean bar x. bar x = (c) Calculate the sample standard deviation s. s = (d) Evaluate the test statistic T= (e) The test statistic is t-distributed with degrees of freedom. (f) The p-value for the test is . (g) Should you reject the null hypothesis in favor of the alternative at significance level a = 0.01? Yes. (h) Is the weight gain significantly different from 15 lbs? Yes. Check

Solution

(b) sample mean= 11.11765

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(c) sample standard deviaton = 5.194737

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(d) The test statisitc is

t=(xbar-mu)/(s/vn)

=(11.11765-15)/(5.194737/sqrt(17))

=-3.081453

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(e) The degree of freedom =n-1=17-1=16

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(f) It is a two-tailed test.

So the p-value= 2*P(t with df=16 <-3.081453) =0.0072 (from student t table)

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(g) Yes.

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(h) Yes.