Question

Test the claim that the mean GPA of night students is larger than the mean GPA of day students at the 0.10 significance level.

The null and alternative hypothesis would be:

H0:μN≤μD
H1:μN>μD

H0:μN≥μD
H1:μN<μD

H0:pN≤pD
H1:pN>pD

H0:μN=μD
H1:μN≠μD

H0:pN=pD
H1:pN≠pD

H0:pN≥pD
H1:pN<pD

The test is:

two-tailed

left-tailed

right-tailed

The sample consisted of 35 night students, with a sample mean GPA of 2.74 and a standard deviation of 0.07, and 35 day students, with a sample mean GPA of 2.73 and a standard deviation of 0.03.

The test statistic is:  (to 2 decimals)

The p-value is:  (to 2 decimals)

Based on this we:

• Reject the null hypothesis
• Fail to reject the null hypothesis

Answer 1

The null and alternative hypotheses

H0:μN≤μD
H1:μN>μD

Test is right tailed

Test statistic t

t = (X1bar - x2bar )/ sp * sqrt[ 1/n1 + 1/n2]

Where sp = sqrt[ (n1-1)*s1​​​​​2​​​​ + (n2-1)*s2​​​​​2/n1+n2-2]

Sp = [ 34*0.072+34*0.032/68] = 0.054

t = (2.74- 2.73)/0.054*sqrt(1/35+1/35)

t = 0.78

p-value for t = 0.78 and d.f = n1 + n2 -2 = 68

P-value = P[ t > 0.78] d.f = 68

p-value = 0.22

Decision rule : if p-value < a we reject the null hypothesis otherwise we fail to reject the null hypothesis

Our p-value = 0.22 > 0.10

Fail to reject the null hypothesis