Question

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) μ_day ≠ μ_night

b) μ_day > μ_night

c) μ_day < μ_night

d) μ_day = μ_night

Answer 1

The appropriate alternative hypothesis for the hypothesis test is μ_day ≠ μ_night.

Step-by-step explanation:

The appropriate alternative hypothesis for the hypothesis test is: a) μday ≠ μnight.

In hypothesis testing, the null hypothesis assumes that there is no significant difference between the means of two populations, while the alternative hypothesis suggests that there is a significant difference.

Since the instructor believes there is no significant difference, the appropriate alternative hypothesis is the one that suggests inequality in means, which is option (a).

In this case, the instructor wants to test if there is a significant difference between the mean class scores of statistics day students and statistics night students. The null hypothesis would be μday = μnight, and the alternative hypothesis would be μday ≠ μnight.