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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

The data from problem 13 show no significant relation-ship between the type of game and helping behavior. To construct the following data, we simply doubled the sample size from problem 13 so that all of the individual frequencies are twice as big. Notice that the sample proportions have not changed.

  Prosocial Violent Neutral  
Helped 24 14 16 54
Did not Help 6 16 14 36
  30 30 30  
  • a. Test for a significant relationship using α = .05. How does the decision compare with the decision in problem 13? You should find that a larger sample increases the likelihood of a significant result.
  • b. Compute the phi-coefficient for these data and compare it with the result from problem 13. You should find that the sample size has no effect on the strength of the relationship.

a.

To determine

To Find: If there is significant relationship between the type of game played and helping behavior

Explanation

Given info: A sample of 90 participants were involved in a study. The distribution is given in the question. Use α=0.05 to test the claim.

  Prosocial Violent Neutral Total
Helped 24 14 16 54
Didn’t help 6 16 14 36
Total 30 30 30 90

Calculation:

Step 1: Null Hypothesis and Alternate Hypothesis are:

H0: There is no significant relationship between the two groups.

H1: There is significant relationship between the two groups.

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=fcfrn...where fr is row frequency and fc is column frequency

Substitute n=54 in the above formula and compute respective values of expected frequencies:

For the row 1, the expected frequencies are:

fe,helped_pro=30×5490fe,helped_violent=

b.

To determine

To Find: The value of phi-coefficient for the given question.

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