(a) Suppose a survey determines the political orientation of 60 men in a certain

Question

(a) Suppose a survey determines the political orientation of 60 men in a certain community: Left Right Middle 18 350 60 Men 12 Among these men, calculate the proportion belonging to each political category. Then show that a Chi-squared Test of the null hypothesis of equal proportions Ho: Left IMen Mid Men Right l Men leads to its rejection at the a .05 significance level. Conclusion (b) Suppose the survey also determines the political orientation of 540 women in the same community Left Middle Right 108 270 162 Women 540 Among these women, calculate the proportion belonging to each political category. How do these proportions compare with those in (a)? Show that a Chi-squared Test of the null hypothesis of equal proportions Ho: T Left l women Mid Women Right l Women leads to its rejection at the a .05 significance level. Conclusion? (c) Suppose the two survey results are combined: Left Middle Right 12 18 30 60 Men 108 162 270 Women 540 180 300 600 120

Explanation / Answer

a)

Test Statistic, X^2: 8.4000
Critical X^2: 5.991471
P-Value: 0.0150

Here P-value < alpha 0.05, we reject H0

b)

From the given data

Test Statistic, X^2: 75.6

Critical X^2: 5.991471
P-Value: 0.0000

Here P-value =0 < alpha 0.05, we reject H0

c)

The observed frequencies are calculated as follows

The chisquare test statistic is calculated as follows

Test Statistic, X^2: 0.0000
Critical X^2: 5.991471
P-Value: 1.0000

Here P-value > alpha 0.05, we accept H0

Observed Expected frequencies Proportions frequencies (Oi-Ei)^2/Ei 12 0.33333333 20 3.2 18 0.33333333 20 0.2 30 0.33333333 20 5 Total: 8.4

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