In: Statistics and Probability
You would like to see whether providing extra time to students
on their test allows for them to achieve a higher grade. In the
past, the average mark on this test is 68 percent. You select 25
students from your current class, who were given extra time on the
test and see their average grade was 72 minutes (St Dev = 8).
What is the appropriate hypothesis test? Why this is the correct
test? What is the effect size?
Note: In the question, it was given "average grade was 72 minutes (St Dev = 8)".. I think it is a mistake and I am proceeding by assuming that it is the avearge marks as given before in the question. You may please ask your instructor for clarifictions).
Here,we need to assess whether the scores in the test had improved after the extra time. Therefore, it is testing for a single mean. Since, the population SD value is not known, we have to use a t-test.
Null Hypothesis:
Alternate Hypothesis:
Level of significance:
will follow a t distribution with n-1 df.
The critical region of t:
Since the calculated value of t falls in the region of rejection, we reject the null hypothesis and conclude that there is enough evidence that providing extra time to students on their test allows for them to achieve a higher grade.
Effect size:
The effect size is given by :