A sample of 25 students was tested for their weight before they joined a 4 year
ID: 3157440 • Letter: A
Question
A sample of 25 students was tested for their weight before they joined a 4 year college and after they completed the 4 year college. The mean weight gain for these students during the 4 year college was found to be 12 pounds with a standard deviation of 26 pounds. At the .01 significance level, was there a significant weight gain for these students? Write the hypothesis statements. Explain what test statistic will be used and why. Compute the test statistic. State the decision rule and sketch it. Based on the decision rule, do you accept or reject the Null Hypothesis? State your findings.
Explanation / Answer
H0: dbar=12 (mean weight gain is 12 pounds)
H1:dbar not equal to 12 (mean weight gain is different from 12 pounds)
Assumptions: Paired data collection: The students were weighted before and after the 4 year college.
Independnece assumption: Each weight is independent of other, so the difference are mutually independnet.
Randomization condition: This is an experiment, so randomization condition is met.
The conditions are met, use t model with 24 (df=n-1) degrees of freedom.
Test statistic:
t=(dbar-0)/(sd/sqrt n), where dbar is mean difference in weight gain, sd is standard deviation and n is sample size.
=(12-0)/(26/sqrt 25)
=2.31
The t critical at alpha=0.01, and df=24 is 2.797.
Reject H0, if t test statistic falls in critical region.
The test statistic do not fall in critical region. Fail to reject null hypothesis. There is no significant weight gain for these students.