Question

Test the claim that the mean GPA of night students is smaller than 2.9 at the 0.01 significance level.

The null and alternative hypothesis would be:

H0:p≥0.725H0:p≥0.725
H1:p<0.725H1:p<0.725

H0:μ≥2.9H0:μ≥2.9
H1:μ<2.9H1:μ<2.9

H0:μ=2.9H0:μ=2.9
H1:μ≠2.9H1:μ≠2.9

H0:μ≤2.9H0:μ≤2.9
H1:μ>2.9H1:μ>2.9

H0:p=0.725H0:p=0.725
H1:p≠0.725H1:p≠0.725

H0:p≤0.725H0:p≤0.725
H1:p>0.725H1:p>0.725

The test is:

right-tailed

two-tailed

left-tailed

Based on a sample of 65 people, the sample mean GPA was 2.89 with a standard deviation of 0.02

The p-value is:  (to 2 decimals)

Based on this we:

Fail to reject the null hypothesis

Reject the null hypothesis

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   = 2.9

H_a : < 2.9

Test statistic = z

= ( - ) / / n

= (2.89 - 2.9) / 0.02 / 65

= -4.03

P(z < -4.03) = 0

P-value = 0

0.01

P-value <

Reject the null hypothesis .