Question

A high school principal gathers a sample of the academic records of past and present high school scholarship basketball players at the high school. The principal reports that no significant difference was found in the mean GPA (grade point average) for male and female scholarship basketball players (P = 0.287). This means that

Question 1 options:

- the maximum difference in GPAs between male and female scholarship basketball player is 0.287.

- the GPAs for male and female scholarship basketball players are identical, except for 28.7% of the players.

- the chance that a pair of randomly chosen male and female scholarship basketball player would have a significant difference in GPAs is 0.287.

- the chance of obtaining a difference in GPAs between male and female scholarship basketball players as large as that observed in the sample if there is no difference in mean GPAs is 0.287.

Answer 1

Since we need to know if there is a difference in the mean GPA.

The Hypothesis is 2 tailed:

H0:

H1:

Since the principal find that the results are not significant, it means the null hypothesis is not rejected and that we do not have sufficient evidence that the alternative is true.

Therefore Option 4: The chance of obtaining a difference in GPA between male and female scholarship basketball players as large as that observed in the sample if there is no difference in mean GPAs is 0.287

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Definition of the p - value: The P-value is the probability that the test statistic obtained is as large as or greater than the one obtained under assumption that the null hypothesis is true.

A large p value (greater than 0.1) indicate that the null has a higher chance of being true, whereas a smaller p value (lesser than 0.01) would indicate that the alternative hypothesis is true.

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In Hypothesis testing the question ‘is the result significant?’ asks if the null hypothesis (H0) has been rejected, i.e there is sufficient evidence to support the alternative hypothesis, H1.

If yes, then the results are said to be significant, and if there isn't sufficient evidence they are not significant.

The decision to Reject the Null is based on two different criteria

(i) The Critical value method, where H0 is Rejected under the following type of tests

(a) Left Tailed: Test Statistic is < Critical value

(b) Right Tailed: Test Statistic is > Critical value

(c) Two Tailed: Test Statistic is < Critical value or if the test Statistic is > Critical value

(ii) The p value method: If p value is < , where is the level of significance

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