This question is incomplete, the complete question is;
Test the claim that the mean GPA of night students is larger than 2.2 at the .10 significance level.
The test is based on a sample of 55 people, the sample mean GPA was 2.23 with a standard deviation of 0.06
Answer:
P-value is less than the significance level.
We reject null hypothesis.
Therefore, there is enough evidence to conclude that the mean GPA of night students is larger than 2.2
Step-by-step explanation:
Given the data in the question;
Claim : The mean GPA of night student is larger than 2.2
μ = 2.2
sample size n = 55
sample mean x' = 2.23
standard deviation s = 0.06
Hypothesis
Null hypothesis H₀ : μ ≤ 2.2
Alternative hypothesis H₁ : μ > 2.2
Right-tailed Test.
Significance Level ∝ = 0.10
so critical value [tex]t_{(0.10, df=54)[/tex] = 1.297
Test Statistic
T[tex]_{cal[/tex] = (x'-μ) / (s/√n)
we substitute
T[tex]_{cal[/tex] = (2.23 - 2.2 ) / (0.06 / √55)
= 0.03 / 0.00809
T[tex]_{cal[/tex] = 3.71
T[tex]_{cal[/tex] is greater than critical value, so it falls in the rejection region;
p-value = P( t > 3.71 ) = 0.000245
P-value is less than the significance level.
We reject null hypothesis.
Therefore, there is enough evidence to conclude that the mean GPA of night students is larger than 2.2
