Question

You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. A sample of 20 night students and 21 day students and their GPA's are recorded below. Test the claim using a 10% level of significance. Assume the population variances are unequal and that GPAs are normally distributed. Give answers to 4 decimal places. 3.33 GPA-Night GPA-Day 3.3 2.84 3.06 3.05 3.67 2.98 3.31 3.5 3.48 3.17 3.01 2.81 2.84 3.33 2.7 3.05 3.08 3.4 3.26 3.18 2.94 3.1 4.03 3.21 3.23 2.97 3.24 2.94 3.46 3.3 3.6 3.1 3.48 2.84 2.83 3.16 3.11

Answer 1

Solution:

Here, we have to use two sample t test for the difference between two population means.

The null and alternative hypotheses for this test are given as below:

H₀: µ₁= µ₂

H₁: µ₁≠ µ₂

The test statistic formula is given as below:

t = (X1bar – X2bar) / sqrt[(S₁² / n₁)+(S₂² / n₂)]

From given data, we have

X1bar = 3.2505

X2bar = 3.0667

S1 = 0.2769

S2 = 0.2734

n1 = 20

n2 = 21

df = 38 (by using df formula)

α = 0.10

Critical value = - 1.6860 and 1.6860

(by using t-table)

p-value = 0.0390

(by using t-table)

p-value < α = 0.10

So, we reject the null hypothesis

The correct decision is to reject the null hypothesis.

The correct summary would be: There is sufficient evidence to conclude that the mean GPA of night students is different from the mean GPA of day students.