Question

One test was carried out a few times and found female students obtained a score better than boys. However, the value of the probability for the sample data you are 0.12 cause you fail to reject the null hypothesis that says women students ' performance is on par with the performance of male students. Specify and give descriptions about the type of error that has been committed

Answer 1

here the outcome of hypothesis test is to fail to reject the null hypothesis.

Type II error occurs when one incorrectly fails to reject the null hypothesis.

Here there could be a chance that the outcome is to fail to reject H0 is due to sampling error,

Hence Type II error is possible

Answer 2

Based on the given information, the null hypothesis states that there is no difference between the performance of female students and male students. The alternative hypothesis would then suggest that there is a difference, specifically that female students perform better than male students.

In hypothesis testing, there are two types of errors that can be committed:

1. Type I error (False Positive): This occurs when the null hypothesis is rejected, even though it is true. In this case, it means concluding that there is a difference in performance between female and male students when, in fact, there is no significant difference. The probability of committing a Type I error is denoted by the significance level (α).

2. Type II error (False Negative): This occurs when the null hypothesis is not rejected, even though it is false. It means failing to detect a significant difference when there is, in fact, a difference in performance between female and male students. The probability of committing a Type II error is denoted by β.

In the given scenario, the value of the probability for the sample data is 0.12. Since this probability is greater than the significance level (α), which is not specified, it suggests that the null hypothesis is not rejected. Therefore, the decision made in this case is to fail to reject the null hypothesis.

Based on this decision, the error that has been committed is a Type II error (False Negative). This means that there is a failure to detect the actual difference in performance between female and male students, even though the alternative hypothesis is true.

In summary, the type of error committed in this scenario is a Type II error, as the null hypothesis is not rejected despite the actual difference in performance between female and male students.