Question

The designers of the problem-solving course wish to investigate whether there is a significant improvement in math scores, at a 5% significance level, subsequent to taking the course. Select the correct null hypothesis, where:

μTC denotes the mean score of those who took the course;
μNC denotes the mean score of those who did not take the course.
Select one:
a) μTC - μNC = 0
b) μTC - μNC ≠ 0
c) μTC - μNC > 0
d) μTC - μNC < 0

Answer 1

The correct null hypothesis for the improvement in math scores after a course is a) μTC - μNC = 0, suggesting no initial difference between the groups.

Step-by-step explanation:

The correct null hypothesis for investigating whether there is a significant improvement in math scores after taking a problem-solving course is a) μTC - μNC = 0. This states that there is no difference in the mean scores of those who took the course (μTC) and those who did not take the course (μNC). It is the standard starting point for a two-sample hypothesis test where we compare two means. If we were to find sufficient evidence to reject this null hypothesis at a 5% significance level, it would suggest that there is a statistically significant difference in the math scores due to taking the course.