Question

92. 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, respectively. 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. An appropriate alternative hypothesis for the hypothesis test is:
a. ${\mu }_{\text{day}}>{\mu }_{\text{night}}$
b. ${\mu }_{\text{day}}<{\mu }_{\text{night}}$
c. ${\mu }_{\text{day}}={\mu }_{\text{night}}$
d. ${\mu }_{\text{day}}\ne {\mu }_{\text{night}}$

Short answer

The correct answer is option (d) ${\mu }_{\text{day}}\ne {\mu }_{\text{night}}$.

Step-by-step solution

Given information

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

Explanation

The statistics instructor considers there is insufficient evidence between the class mean of statistics day on Exam $2$and statistics night on Exam $2$,
As a result, the alternative hypothesis has two tails.
The following is an alternative hypothesis:
${\mu }_{\text{day}}\ne {\mu }_{\text{night}}$
Therefore, the correct answer is option (d).