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Essentials of Statistics for the B...

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

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BuyFindarrow_forward

Essentials of Statistics for the B...

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

Research has demonstrated strong gender differences in teenagers’ approaches to dealing with mental health issues (Chandra & Minkovitz. 2006). In a typical study, eighth-grade students are asked to report their willingness to use mental health services in the event they were experiencing emotional or other mental health problems. Typical data for a sample of n = 150 students are shown in the following table.

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  1. a. Do the data show a significant relationship between gender and willingness to seek mental health assistance? Test with α = .05.
  2. b. Compute Cramér’s V to measure the size of the treatment effect.

a.

To determine

To check: Whether there is significant relationship between gender and willingness to seek mental health assistance for the given question.

Explanation

Given info:

A sample of 150 students was involved in a study based on “the willingness to use mental health services and gender”. Use α=0.05 to test the claim.

Calculations:

Step 1: Null Hypothesis and Alternate Hypothesis are:

H0: There is no significant relationship between gender and willingness to seek mental health assistance.

H1: There is a significant relationship between gender and willingness to seek mental health assistance.

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=200 in the above formula and compute respective values of expected frequencies:

For the category “males”, the expected frequencies are:

fe,prob.no=30×60150fe,yes=75×60150fe,prob.no=45×60150

Similarly, for the category “females”, the expected frequencies are:

fe,prob

b.

To determine

To Find: The value of Cramer’s V for the given question.

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