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Questions: 1/Suppose that the data resulted from classifying each person in a random sample of 48 male students and each pers2/The following table gave the information on the age distribution of adults who purchase lottery tickets in California: 15%

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Answer #1

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

\chi ^{2}=\sum \frac{(O-E)^{2}}{E}

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

\chi ^{2}=\sum \frac{(O-E)^{2}}{E}=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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