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Social ScienceListed below are data from a survey conducted recently where Males and Females responded to their happiness with their supervisor (this is fictitious data). ResponseMaleFemaleTotalNot at all232548Somewhat132235Very261642Total6263125 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
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
Expert Answer
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
The expected frequency is calculated as follows:
Image Transcriptionclose
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
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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