Question

IQ scores on a certain IQ test are known to have a mean of 100 and a random sample of 60 students attend a series of coaching classes before taking the test let μ be the population mean IQ score that would occur if every student took the coaching classes. the classes are successful if μ is greater than 100. a test is made of the hypothesis Ho: μ explain=100 vs. H1: μ= > 100. Consider three possible conclusions number 1, the classes are successful. 2. the classes are not successful. 3. the classes might not be successful. Assume that the classes are not successful, is it possible to make a type 1 error ? explain

Answer 1

This means that the mean IQ test results are 100 that is the classes are not successful.

This means that the mean IQ test results are greater than 100 that is the classes are successful.

Type 1 error: This is the error where we reject the null hypothesis when is it is true.

In our case :

The null hypothesis being true means that the classes are not successful (opposite of alternative hypo). Rejecting this means that we are concluding that the classes are successful and accepting this means that we are concluding that the classes are not successful.

Assumption: The classes are not successful. That is we are accepting the null hypothesis. Since type 1 error is to reject the null hypothesis when it is true, this assumption invalidates the possibility of making type 1 error.