You are interested in the weight gain of the Auburn Freshman. You think that the

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): 14, 10, 7, 15, 14, 8, 9, 16, 5, 13, 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? Alternative Hypothesis?

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

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

(d) Evaluate the test statistic T=(x¯)/(s/sqrt(n)). T= ?

(e) The test statistic is t-distributed with how many 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 =0.01?

(h) Is the weight gain significantly different from 15 lbs?

Explanation / Answer

Set Up Hypothesis
Null, H0: U=15
Alternate, H1: U!=15
Test Statistic
Population Mean(U)=15
Sample X(Mean)=11.3636
Standard Deviation(S.D)=3.6952
Number (n)=11
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =11.3636-15/(3.6952/Sqrt(11))
to =-3.264
| to | =3.264
Critical Value
The Value of |t | with n-1 = 10 d.f is 3.169
We got |to| =3.264 & | t | =3.169
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != -3.2638 ) = 0.0085
Hence Value of P0.01 > 0.0085,Here we Reject Ho

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