Question

Test the claim that the mean GPA for student athletes is lower than 3.5 at the .10 significance level. Based on a sample of 45 people, the sample mean GPA was 3.47 with a standard deviation of 0.08

The test statistic is:_____ (to 3 decimals)

The p-value is: ______(to 3 decimals)

Based on this we:

-Fail to reject the null hypothesis

-Reject the null hypothesis

Answer 1

H0: >= 3.5

Ha: < 3.5

Test statistics

t = - / ( S / sqrt(n) )

= 3.47 - 3.5 / (0.08 / sqrt(45) )

= -2.516

The statistics is -2.516

df = n - 1 = 45 - 1 = 44

From T table,

Using test statistics -2.516 and df of 44 ,

p-value = 0.008

Since p-value < 0.10 significance level, Reject the null hypothesis.