You are testing the claim that the mean GPA of night students is less than the mean GPA of day students. You sample 30 night students and 30 day students. Test the claim using a 10% level of significance. Assume the population standard deviations are unequal.

 

The Hypotheses for this problem are:

H0: μ1 = μ2

H1: μ1 < μ2

 

Find the p-value. Round answer to 2 decimal places. Make sure you include the 0 in front of the decimal.

 

p - value = ____________

 

Night Day

Mean 2.8967 3.1872

Variance 0.2669 0.277582

Observations 30 30

Hypothesized Mean Difference 0

df 58

t Stat -2.1557

P(T<=t) one-tail 0.01763

t Critical one-tail 1.6716

P(T<=t) two tail 0.03526

t Critical two-Tail 2.0017

H0: μ1 = μ2

H1: μ1 < μ2 (claim)

Test statistic:

t Stat -2.1557

Critical value:

t Critical one-tail = 1.6716

P - value = 0.01763

P(T<=t) one-tail 0.01763

Decision:

Alpha= 0.10

Since P -value (0.01763) < alpha ( 0.10), reject the null hypothesis, Ho. The study is statistically significant at 10% level of significance.

Conclusion:

There is sufficient evidence to support the claim that the you are testing the claim that the mean GPA of night students is less than the mean GPA of day students.

This is one tailed test

From the EXCEL output:

Test statistic:

t Stat -2.1557

Critical value:

t Critical one-tail = 1.6716

P - value for one tailed test:

P(T<=t) = 0.01763

Decision:

Alpha= 0.10

Since P -value (0.01763) < alpha ( 0.10), reject the null hypothesis, Ho. The study is statistically significant at 10% level of significance.

Conclusion:

There is sufficient evidence to support the claim that the you are testing the claim that the mean GPA of night students is less than the mean GPA of day students.