Question

# Test the claim that the mean GPA of night students is smaller than 2.9 at the...

Test the claim that the mean GPA of night students is smaller than 2.9 at the 0.025 significance level.

The null and alternative hypothesis would be: (MULTIPLE CHOICE)

A.) H0:p=0.725H0:p=0.725
H1:p?0.725H1:p?0.725

B.) H0:p=0.725H0:p=0.725
H1:p<0.725H1:p<0.725

C.) H0:?=2.9H0:?=2.9
H1:?>2.9H1:?>2.9

D.) H0:?=2.9H0:?=2.9
H1:??2.9H1:??2.9

E.) H0:?=2.9H0:?=2.9
H1:?<2.9H1:?<2.9

F.) H0:p=0.725H0:p=0.725
H1:p>0.725H1:p>0.725

The test is: left tailed, right tailed or two tailed?

Based on a sample of 75 people, the sample mean GPA was 2.86 with a standard deviation of 0.07. The p-value is: ____ (to 2 decimals)

Based on this we: reject the null hypothesis or fail to reject the null hypothesis?

Here, we are testing whether the mean GPA of night students is smaller than 2.9, therefore the null and the alternate hypothesis here are given as:

Therefore E is the correct answer here.

This is clearly a left tailed test as can be seen from the alternate hypothesis.

b) The test statistic here is computed as:

Now for n - 1 = 74 degrees of freedom, we get the p-value from the t distribution tables as:

p = P( t74 < -4.9487 ) = approx. 0

Therefore p -value = 0

Based on this the test is significant and we can reject the null hypothesis here.