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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

Although the phenomenon is not well understood, it appears that people born during the winter months are slightly more likely to develop schizophrenia than people born at other times (Bradbury & Miller, 1985). The following hypothetical data represent a sample of 50 individuals diagnosed with schizophrenia and a sample of 100 people with no psychotic diagnosis. Each individual is also classified according to the season in which he or she was born. Do the data indicate a significant relationship between schizophrenia and the season of birth? Test at the .05 level of significance.

  Season of Birth  
  Summer Fall Winter Spring  
No Disorder 26 24 22 28 100
Schizophrenia 9 11 18 12 50
  35 35 40 40  

To determine

To Find: If there is a significant relationship between schizophrenia and the season of birth.

Explanation

Given info:

A sample of 150 participants were involved in a study. The distribution is given in the question. Use α=0.05 to test the claim.

  Summer Fall Winter Spring total
No disorder 26 24 22 28 100
schizophrenia 9 11 18 12 50
Total 35 35 40 40 150

Calculations:

Step 1: Null Hypothesis and Alternate Hypothesis are:

H0: There is no significant relationship between schizophrenia and the season of birth.

H1: There is significant relationship between schizophrenia and the season of birth.

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

df=(R1)(C1)   where R equals number of rows and C equals columns=(21)(41)=3

With α=0.05 and df=3, the critical value (CV)  is obtained from the χ2table as

χ2=7.815

Step 3: χ2-statistics 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=150 in the above formula and compute respective values of expected frequencies:

For the row 1, the expected frequencies are:

fe,no_summer=100×35150fe,no_fall=100×35150fe,no_winter=100×</

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