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.

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