Business statistics

Question

Test the claim that the mean GPA of night students is larger than 2.2 at the 0.10 significance level.

The null and alternative hypothesis would be:

H0:μ=2.2H0:μ=2.2

H1:μ≠2.2H1:μ≠2.2

H0:μ≤2.2H0:μ≤2.2

H1:μ>2.2H1:μ>2.2

H0:p≤0.55H0:p≤0.55

H1:p>0.55H1:p>0.55

H0:p=0.55H0:p=0.55

H1:p≠0.55H1:p≠0.55

H0:p≥0.55H0:p≥0.55

H1:p<0.55H1:p<0.55

H0:μ≥2.2H0:μ≥2.2

H1:μ<2.2H1:μ<2.2

The test is right-tailed

left-tailed

two-tailed

Based on a sample of 50 people, the sample mean GPA was 2.21 with a standard deviation of 0.07

The p-value is: ______ (to 2 decimals)

Based on this we:

1. Reject the null hypothesis
2. Fail to reject the null hypothesis

Answer 1

Hi Salma,

For the first part, note that we are testing mean, not proportion, so any answer choices with p should be eliminated. Also note that the question asked specifically " larger than," so anything without H_A > some value should be eliminated. Only choice that meets these criteria is:

H0:μ≤2.2H0:μ≤2.2

H1:μ>2.2H1:μ>2.2

Now, we know nothing about population standard deviation, so we have to test via t:

t=(xbar-mu)/SE

xbar=2.21

mu=2.2

SE=s/sqrt(n)

s=sample standard deviation

n=sample size

SE=0.07/sqrt(50)

SE=0.010

t=(2.21-2.2)/0.010

t=1.010

Now, we need degrees of freedom: df=n-1

df=50-1

df=49

Looking at t-table, the closest we have to 49 without exceeding is 40. Our test statistic, 1.010, falls between 0.851 and 1.050. Corresponding p-values for a one-tailed test are:

0.15 < p < 0.20

This is our best approximation without statistical software. Based on this, we fail to reject the null and conclude that true mean GPA does not differ significantly from 2.2.

I hope this helps.