Question

Test the claim that the mean GPA of night students is larger than 2.2 at the .10 significance level.

Answer 1

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 $t_{(0.10, df=54)$ = 1.297

Test Statistic

T$_{cal$ = (x'-μ) / (s/√n)

we substitute

T$_{cal$ = (2.23 - 2.2 ) / (0.06 / √55)

= 0.03 / 0.00809

T$_{cal$  = 3.71

T$_{cal$  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