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:

Hint: For the calculations, assume the Democrats as the first sample.

1. State the decision rule for 0.02 significance level: H0: d r ; H1: d > r. (Round your answer to 2 decimal places.)

2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

3. Determine the p-value. (Round your answer to 4 decimal places.)

4. Can we conclude that there is a larger proportion of Democrats in favor of lowering the standards? Use the 0.02 significance level.

Republicans Democrats Number sampled 1,000 800 Number in favor 200 168

Explanation / Answer

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 > 0

Hypothesis test results:

Hence,

1. Decision Rule: Reject Ho if z > 2.05

2. z = 0.52

3. p - Value = 0.3006

4. Since p - Value > 0.02, do not reject Ho.

There is not sufficient evidence to conclude that there is a larger proportion of Democrats in favor of lowering the standards.

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 168 800 200 1000 0.01 0.019129965 0.52274011 0.3006

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