SOLUTION: #18 Test the claim that the mean GPA of night students is smaller than 2.1 at the 0.005 significance level. The null and alternative hypothesis would be: H0:μ≤2.1

Question 1120294: #18
Test the claim that the mean GPA of night students is smaller than 2.1 at the 0.005 significance level.
The null and alternative hypothesis would be:
H0:μ≤2.1 and H1:μ>2.1
or
H0:p=0.525 and H1:p≠0.525
or
H0:μ≥2.1 and H1:μ<2.1
or
H0:p≥0.525 and H1:p<0.525
or
H0:p≤0.525 and H1:p>0.525
or
H0:μ=2.1 and H1:μ≠2.1

The test is:
right-tailed
or left-tailed
or two-tailed

Based on a sample of 65 people, the sample mean GPA was 2.06 with a standard deviation of 0.08
The p-value is:_______ (to 2 decimals)
Based on this we:
Reject the null hypothesis
or Fail to reject the null hypothesis

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Because the question asks for a single directional answer, this is a one-way test. Hypothesis testing is about parameters, not statistics.
It is the third,
Ho: mu >=2.1 and Ha: mu < 2.1
The rejection region will be in the left tail, so a left tail test.
Test stat is a t 0.005, df=64, critical value is t<-2.65
t=(x-mean)/s/sqrt(n)
=-0.05/0.08/sqrt(65)
This is -0.05*sqrt(65)/0.08, or -5.039, Reject Ho
p-value <0.0001 or <0.01

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SOLUTION: #18 Test the claim that the mean GPA of night students is smaller than 2.1 at the 0.005 significance level. The null and alternative hypothesis would be: H0:&#956;&#8804;2.1

SOLUTION: #18 Test the claim that the mean GPA of night students is smaller than 2.1 at the 0.005 significance level. The null and alternative hypothesis would be: H0:μ≤2.1