Question

An educational psychologist would like to know if 25 children in a gifted program have unique IQs. The IQ test has a mean of 100 and a standard deviation of 15. It is found that the mean of the sample of children is 122. Do the children of the gifted program have unique IQs (a =.05)?

a. Name the test to be conducted and explain why you selected this test:

b. State the null and alternative hypotheses:

c. State the CV and the decision rule. Sketch a curve to assist your answer:

d. Calculate the standard error and the observed test statistic:

e. Write an APA style conclusion based on this finding:

Answer 1

Part a)

Since we know the population standard deviation, we can conduct one sample Z test.

Part b)

To Test :-
H0 :- µ = 100
H1 :- µ ≠ 100

Part c)

Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2 )
Z(α/2) = Z( 0.05 /2 ) = 1.96
| Z | > Z( α/2 ) = 7.3333 > 1.96
Result :- Reject null hypothesis

Shaded region is the critical value area.

Part d)

Standard Error = =   = 3.0

Part e)

There is insufficient evidence to support the claim that children of the gifted program have unique IQs.