Using the following data, calculate the χ2, the degrees of freedom, and the effect size.  Would the researcher accept or reject the null hypothesis and what can be said about the effect size?                         Gun Control Gender        Against       For          Total       Male             180             90           270Female           60             170          230                     240             260         500

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Asked Dec 6, 2019
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Using the following data, calculate the χ2, the degrees of freedom, and the effect size.  Would the researcher accept or reject the null hypothesis and what can be said about the effect size? 

                        Gun Control 

Gender        Against       For          Total       Male             180             90           270

Female           60             170          230

                     240             260         500                                                                 

 

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Expert Answer

Step 1

The appropriate Null and Alternative Hypotheses are given below:

 

Null hypothesis:

 

H0: The variables ‘Gender’ and ‘Gun control’ are independent.

 

Alternative hypothesis:

 

Ha: The variables ‘Gender’ and ‘Gun control’ are dependent.

 

From the given information,

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Against For Total Male 180 90 270 Female 170 60 230 Total 240 260 500

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Step 2
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Expected value( E,) Actual row total x column total value (0, - E. )* /E, (0, - E,) (0.) 270x 240 =129.6 19.6 180 2540.16 500 270x 260 =140.4 90 2540.16 18.0923 500 230x240 =110.4 60 2540.16 23.0087 500 230x 260 =119.6 170 2540.16 21.2388 500 (0, - E, Σ E; =81.9398

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Step 3
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(0,-E, * = E, = 81.9398 The value of x' is 81.9398.

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Hypothesis Testing

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