The College Board states that the average math SAT score is 514 with a standard deviation of 117. Colleen gathered data from 50
students in her graduating class and found the average score to be 523. She thinks that her class’s math SAT score is different from the average. Which of the following are the correct null hypothesis and alternate hypothesis?
In hypothesis testing, A null hypothesis (H0) is a claim which the person conducting the research wants to test while an alternative hypothesis (H1) is a contradiction of the null hypothesis.
There are two types of tests in hypothesis testing.
One tailed test: In one tailed test, a claim that a parameter is greater than/ less than a value is being tested. i.e mean > value or mean < value.
Two tailed test: In a two tailed test, a claim that a value is equal to a value is tested, i.e mean = value.
In the question above, Colleen is testing the claim that the average score of her class is the same as others against that it is different from others. Therefore, the null hypothesis is H0: mean = 514 while the alternative hypothesis is H1: mean ≠ 514
The lowest time out of all of them is 10.75, so to all the 5th swimmer needs to do to win is to undercut the swimmer who got 10.75s by a 100th of a second. i.e 10.74s or faster (lower) would win.
