A nationwide sample of influential Republicans and Democrats was asked as a part

Question

A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored lowering environmental standards so that high-sulfur coal could be burned in coal-fired power plants. The results were: State the decision rule foe .02 significance level: H_0: pi_d lessthanorequalto pi_r, H_1: pi_d > pi_r. Reject H_0 if z > Compute the value of the test statistic. Value of the test statistic Determine the p-value. p-value is Can we conclude that there is a larger proportion of Democrats in favor of lowering the standards? Use H_0. We conclude that there is a larger proportion of Democrats in favor of lowering the standards.

Explanation / Answer

1. Zcritical for alpha = 0.02 significance level and right tailed test

Zcritical = 2.055

2. Z - statistic

p* = (200 + 168)/ ( 1000 + 800) = 0.2044

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] } = sqrt {0.2044 * 0.7956 * (1/1000 + 1/800) } = 0.0191

Z = (p1 - p2 )/ SE = ( 0.21 - 0.20)/ 0.0191 = 0.5235

(3)The P-Value is 0.29719.

The result is not significant at p < 0.02

(4) Yes, We cannot reject the null hypothesis and we can not conclude that there islarger proportion of democrats in favour of lowering the standards.

Republicans Democrats Number sampled 1000 800 Number in favour 200 168 proportions 0.2 0.21

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