Hypothesis Testing, Statistics Problem Example

In order to evaluate whether attending private school leads to higher test scores than attending public school, the researcher took the average from the test and performed a number of tests to come up with a z-score:

• The researcher should likely use a two-tailed test because he/she is interested in a more conservative appraisal of whether private students perform better on these tests;
• The null hypothesis is: there is no difference in performance on the test between students from public and private schools
• The alternate hypothesis is: there is a difference in performance on the test between students from public and private schools
• With a z score of -1.54, the researcher would see that it is less than the criteria of -1.96 and would fail to reject the null hypothesis
• No, the results are not statistically significant because they are less than the critical value established
• The probability of making a type 1 error is 5%- it is failing to accept something that is true. In this example, the probability of making a type 1 error is equal to alpha or 5%
• The probability of making a type 2 error is 20%- a type 2 error would mean that the individual failed to accept a result that is true.