1)
Claim: The proportions fallings into each of the 2 categories are not the same for males and females.
The null and alternative hypothesis is
H0: The proportions fallings into each of the 2 categories are not the same for males and females.
H1: The proportions fallings into each of the 2 categories are the same for males and females.
Level of significance = 0.05
Test statistic is
O: Observed frequency
E: Expected frequency.
E = ( Row total*Column total) / Grand total
Usually | Rarely | Total | |
Male | 32 | 16 | 48 |
Female | 26 | 65 | 91 |
Total | 58 | 81 | 139 |
O | E | (O-E) | (O-E)^2 | (O-E)^2/E |
32 | 20.02878 | 11.97122 | 143.3102 | 7.155214 |
16 | 27.97122 | -11.9712 | 143.3102 | 5.123486 |
26 | 37.97122 | -11.9712 | 143.3102 | 3.774179 |
65 | 53.02878 | 11.97122 | 143.3102 | 2.702498 |
Total | 18.755 |
Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 2 - 1) * (2 - 1) = 1 * 1 = 1
Critical value = 3.841
( From chi-square table)
Test statistic > critical value we reject null hypothesis.
Conclusion:
The proportions fallings into each of the 2 categories are the same for males and females.
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