Question

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?

Answer 1

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.