In 1995, the mean math SAT score for students at one school was 488. A teacher i

Question

In 1995, the mean math SAT score for students at one school was 488. A teacher introduces a new teaching method to prepare students for the SAT. One year later, he performs a hypothesis test to determine whether the mean math SAT schore has increased.

If the null hypothesis is rejected at the 10% significance level, do you think the teacher would feel confident that his teaching method works? What about if the null hypoethesis was rejected at the 1% level? Which of these two results would constitute stronger evidence that his teaching method works? Explain.

Explanation / Answer

If the null hypothesis is rejected at the 1% level of significance this provides much stronger evidence(i.e. 99% confidence) that > 488 than if the null hypothesis is rejected at the 10% level of significance( 90% confidence).

Suppose that his teaching method actually does not work and that = 488. Then the chance that the null hypothesis would be rejected at the 10% level is 10%. This is not so unlikely.

However, the chance that the null hypothesis would be rejected at the 1% level is only 1%.

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