   Chapter 15, Problem 17P Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Solutions

Chapter
Section Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

Research results suggest that IQ scores for boys are more variable than IQ scores for s girls (Arden & Plomin, 2006). A typical study looking at 10-year-old children classifies participants by gender and by low, average, or high IQ. Following are hypothetical data representing the research results. Do the data indicate a significant difference between the frequency distributions for males and females? Test at the 05 level of significance and describe the difference. To determine

To check: Whether the data indicate a significant difference between the frequency distribution for males and females for the given question.

Explanation

Given info:

A sample of 160 students was involved in a study based on “the relation between the gender and the IQ level”. Use α=0.05 to test the claim.

Calculations:

Step 1: Null Hypothesis and Alternate Hypothesis are:

H0: No significant difference between the frequency distribution for males and females

H1: Significant difference between the frequency distribution for males and females

Step 2: For the given sample, degrees of freedom equals:

df=(R1)(C1)  where R equals number of rows and C equals columns=(21)(31)=2

With α=0.05 and df=2 , the critical value (CV)  is obtained from the χ2table as

χ2=5.991

Step 3: χ2statistics is calculated as:

χ2=(fofe)2fe

The formula to calculate expected frequency is:

fe=fcfrnwhere fr is row frequency and fc is column frequency

Substitute n=160 in the above formula and compute respective values of expected frequencies:

For the category boys, the expected frequencies are:

fe,low=30×80160fe,medium=96×80160fe,high=

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