Question

89. 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. 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.

Short answer

The correct answer is option (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 solution

Given information

Let, the mean and standard deviation for $35$statistics day students were $75.86$and $16.91$. And the mean and standard deviation for $37$ statistics night students were $75.41$ and $19.73$.

Explanation

The null hypothesis is described as follows:
$H_0:{\mu }_{\text{day}}={\mu }_{\text{night}}$

And alternate hypothesis is described as follows:
$H_0:{\mu }_{\text{day}}\ne {\mu }_{\text{night}}$
Determine the $p$-value, by using TI-83 calculator as follows:

Explanation

Press ENTER to get the results as follows:

Hence, the test level significance is $\alpha =0.05$
So,$\alpha <p$-value,
Not to reject null hypothesis.
As a result, the correct answer is part (c). There is insufficient information to indicate that the means of the statistics for day and night students on Exam $2$are significantly different.