Question
Asked Nov 24, 2019
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Listed below are data from a survey conducted recently where Males and Females responded to their happiness with their supervisor (this is fictitious data). 

Response

Male

Female

Total

Not at all

23

25

48

Somewhat

13

22

35

Very

26

16

42

Total

62

63

125

 

Is there significance evidence that a difference exists between the actual males and female responses in this sample and the expected male/female responses in the population?  YES OR NO

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Expert Answer

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Step 1

The null and the alternative hypotheses for the given scenario are shown below:

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H There is no significane difference between the actual males and female responses and the expected male/female responses in the population Ha There is a significane difference between the actual males and female responses and the expected male/female responses in the population

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Step 2

The expected frequency is calculated as follows:

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Row total x Column total E Grand total Response Male Female Total Not at all 23 25 48 Somewhat 13 22 35 26 Very 16 42 Total 62 63 125 Expected frequencies are given below: 48x 62 125 = 23.81 48 x 63 125 =24.19

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Step 3

Similarly, the remaining expected frequencies are calculated and the values are 23.81, 24.19, 17...

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(Observed frequency O-Expected frequency E) Expected frequency E The calculation for the test statistic is given below: E (O-Ey 2/E 23.81 23 0.028 25 24.19 0.027 13 17.36 1.095 22 17.64 1.078 26 20.83 1.283 16 21.17 1.263 4.77 Thus, the chi-square test statistic is 4.77.

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