Question

The average GPA of a random sample of 18 college students who take evening classes was calculated to be 2.94 with a standard deviation of 0.04. The average GPA of a random sample of 12 college students who take daytime classes was calculated to be 2.89 with a standard deviation of 0.05. Test the claim that the mean GPA of night students is larger than the mean GPA of day students at the .01 significance level.

Claim: Select an answer μ 1 < μ 2 μ 1 ≤ μ 2 p 1 = p 2 p 1≠p 2 p 1 < p 2 p 1 > p 2 p 1 ≤ p 2 μ 1 = μ 2 p 1 ≥ p 2 μ 1 > μ 2 μ 1≠μ 2 μ 1 ≥ μ 2  which corresponds to Select an answer H1: μ 1 < μ 2 H0: μ 1 = μ 2 H1: μ 1≠μ 2 H1: p 1≠p 2 H0: μ 1 ≤ μ 2 H1: p 1 > p 2 H1: μ 1 > μ 2 H0: p 1 ≤ p 2 H1: p 1 < p 2 H0: μ 1≠μ 2

Opposite: Select an answer p 1 < p 2 p 1 ≤ p 2 μ 1 ≥ μ 2 μ 1 < μ 2 μ 1 = μ 2 μ 1 > μ 2 μ 1 ≤ μ 2 p 1 ≥ p 2 p 1 > p 2 μ 1≠μ 2 p 1 = p 2 p 1≠p 2  which corresponds to Select an answer H0: p 1≠p 2 H1: μ 1 > μ 2 H0: μ 1 ≤ μ 2 H1: μ 1≠μ 2 H1: p 1 ≥ p 2 H0: p 1 > p 2 H1: p 1 <= p 2 H1: p 1 = p 2 H0: μ 1 = μ 2 H1: μ 1 < μ 2 H0: μ 1≠μ 2


The test is: Select an answer two-tailed right-tailed left-tailed

The test statistic is: tt = Select an answer 2.9 2.415 2.546 3.007 3.181

The critical value is: tαtα= Select an answer  2.384  2.453  2.718  2.919  2.563

Based on this we: Select an answer Cannot determine anything Accept the null hypothesis Fail to reject the null hypothesis Reject the null hypothesis

Conclusion There Select an answer does not does  appear to be enough evidence to support the claim that the mean GPA of night students is larger than the mean GPA of day students.

Answer 1

Let : Mean GPA of night students.

: Mean GPA of day students.

We have to test the claim that mean GPA of night students is larger than mean GPA of day students.

Claim : ( alternative hypothesis)

opposite to ( Null hypothesis)

We have to test  mean GPA of night students is larger than mean GPA of day students, hence test is right tailed.

Given :

Assums samples are coming from normal population and population variances are unknown and equal.

We use two-sample t-test for testing difference in two means.

The value of test statistic t is

Where S is pooled sample standard deviation.

Value of test statistic t is

Correct Answer: the test statistic t = 2.9

Critical value:

Alpha : level of significance = 0.01

Degrees of freedom = n1+ n2 -2 = 28

From t-table

Critical value is

The critical value

Decision: Since calculated value of test statistic is greter than critical value ( 2.9 > 2.453), we reject the null hypothesis.

Correct answer- reject the null hypothesis.

Conclusion: There is sufficient evidence support to claim that mean GPA of night students is larger than mean GPA of day students.