Question

Ryan (a school psychologist) wants to test the cognitive ability of children at a large inner-city elementary school. However, because the battery of cognitive tests must be individually administered, and are very expensive, Ryan can only test a small number of the total children at the school. To select his sample, Ryan numbers all the children on the playground during recess time and then uses a random-number table (analogous to drawing names out of a hat) to select 20 students for testing.

3) Does Ryan have a truly random sample? Why or why not?

Assume that each of following statements is in error: Each describes a researcher’s conclusions, but the researcher is mistaken. Indicate whether the error is Type I or Type II.

4) “The data indicate that there are significant differences between males and females in their ability to perform a task 1.”

5) “There are no significant differences between males and females in their ability to perform task 2.”

Answer 1

3) Yes, Ryan has a random sample. This is because he has randomly selected 20 students using random number table from the playground for testing.

The hypothesis is:

H0: There is no significant difference between males and females ability to perform the task

vs H1: There is a significant difference between males and females ability to perform the task

Note: Type I error is Rejection of a true null hypothesis. That means concluding H0 is false when it actually isn't.

Type II error is non rejection of a false null hypothesis. That means concluding that H0 is true when it actually isn't.

4) By concluding that there's a significant difference, we have Rejected H0, so a type I error has occurred.

5) By concluding that there's no significant differences, we have failed to Rehect Ho, so a type II error has occurred.