Question

Assume IQ is 100 with a standard deviation of 15. An educational diagnostician wishes to determine whether learning disabled students in her school district exceed the mean IQ of 100. (Note: One criterion for learning disabled students is having IQ in the normal or above normal range). She takes a random sample of 33 students and finds a mean IQ of 108. Using alpha = .05, test the null hypothesis. Be sure to list the following: 1) Research Problem; 2) alternative hypotheses (H0, H1) 3) decisions rule 4) test statistic calculation 5) interpretation of your hypothesis test.

1) Research Problem;

2) alternative hypotheses (H0, H1)

3) decisions rule

4) test statistic calculation

5) interpretation of your hypothesis test.

Answer 1

1) Research Problem;

To determine whether learning disabled students in the school district exceed the mean IQ of 100.

2) alternative hypotheses (H0, H1)

H0: = 100

H1: > 100

3) decisions rule

Z score for alpha = .05 is 1.645

We reject the null hypothesis if the test statistic is greater than 1.645

4) test statistic calculation

Standard error of mean , SE = = 15 / = 2.61

Test statistic, z = () / SE = (108 - 100) / 2.61 = 3.065

5) interpretation of your hypothesis test.

Since the calculated test statistic is greater than the critical value (1.645) , we reject null hypothesis H0 and conclude that there is strong evidence that learning disabled students in the school district exceed the mean IQ of 100.