Question

A mathematics professor wants to determine whether there has been a significant difference in the final percentage averages between the Fall and Spring semesters (semester I and semester II respectively) of his Business Statistics classes he taught for the past 25 years. During this time, the professor taught very large sections of the courses in large lecture theaters. In a random sample of 62 students from semester I, the mean of the final percentages was 80 with a standard deviation of 4. In a random sample of 69 students from semester II, the mean of the final percentages was 74 with a standard deviation of 6.

If the final percentages from semesters I and II are assumed to be normally distributed, the P-value for the appropriate test is

a. 0.150

b. 0.2100

c. 0.1691

Answer 1

using minitab>stat>basic stat>two sample t

we have

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 62 80.00 4.00 0.51
2 69 74.00 6.00 0.72

Difference = μ (1) - μ (2)
Estimate for difference: 6.000
95% CI for difference: (4.216, 7.784)
T-Test of difference = 0 (vs ≠): T-Value = 6.66 P-Value = 0.000 DF = 129
Both use Pooled StDev = 5.1520

p value is 0.0000