Suppose a statistics instructor believes that there is no significant difference between the mean class scores of statistics day students on Exam 2 and statistics night students on Exam 2. She takes random samples from each of the populations. The mean and standard deviation for 35 statistics day students were 75.86 and 16.91.The mean and standard deviation for 37 statistics night students were 75.41 and 19.73. The day" subscript refers to the statistics day students. The "night subscript refers to the statistics night students. Assume that the standard deviations are equal. A concluding statement is:
a. There is sufficient evidence to conclude that statistics night students' mean on Exam 2 is better than the statistics day students' mean on Exam 2.
b. There is insufficient evidence to conclude that the statistics day students' mean on Exam 2 is better than the statistics night students' mean on Exam 2.
c. There is insufficient evidence to conclude that there is a significant difference between the means of the statistics day students and night students on Exam 2
d. There is sufficient evidence to conclude that there is a significant difference between the means of the statistics day students and night students on Exam 2

c. There is insufficient evidence to conclude that there is a significant difference between the means of the statistics day students and night students on Exam 2

Step-by-step explanation:

Given that a statistics instructor believes that there is no significant difference between the mean class scores of statistics day students on Exam 2 and statistics night students on Exam 2.

Group Group One Group Two

Mean 75.8600 75.4100

SD 16.9100 19.7300

SEM 2.8583 3.2436

N 35 37

*SEM is std error/sqrt n

Mean difference = 0.4500

[tex]H_0: \bar x = \bar y\\H_a: \bar x \neq \bar y[/tex]

(two tailed test)

Std error for difference = 4.342

Test statistic t = [tex]\frac{0.45}{4.342} \\=0.1036[/tex]

df =70

p value = 0.9178

Since p >0.05 we accept H0

c. There is insufficient evidence to conclude that there is a significant difference between the means of the statistics day students and night students on Exam 2