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Answer:
We conclude that there is an equal or larger proportion of Republicans in favor of lowering the standards.
Step-by-step explanation:
<u>The complete question is</u>: 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:
Number sampled: 1,000 (republican) , 800 (democrats)
Number in favor: 200 (republican) , 168 (democrats)
At the 0.02 level of significance, can we conclude that there is a larger proportion of Democrats in favor of lowering the standards? Determine the p-value.
Let = <u><em>proportion of Republicans in favor of lowering the standards</em></u>.
= <u><em>proportion of Democrats in favor of lowering the standards</em></u>.
SO, Null Hypothesis, :
{means that there is an equal or larger proportion of Republicans in favor of lowering the standards}
Alternate Hypothesis, :
{means that there is a larger proportion of Democrats in favor of lowering the standards}
The test statistics that would be used here <u>Two-sample z-test for</u> <u>proportions</u>;
T.S. = ~ N(0,1)
where, = sample proportion of Republicans in favor of lowering the standards =
= 0.20
= sample proportion of Democrats in favor of lowering the standards =
= 0.21
= sample of Republicans = 1000
= sample of Democrats = 800
So, <u><em>the test statistics</em></u> =
= -0.52
The value of z test statistics is -0.52.
<u>Now, P-value of the test statistics is given by the following formula; </u>
P-value = P(Z < -0.52) = 1 - P(Z 0.52)
= 1 - 0.6985 = 0.3015
Now, at 0.02 significance level, the z table gives a critical value of -2.054 for left-tailed test.
Since our test statistic is more than the critical value of z as -0.52 > -2.054, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <em><u>we fail to reject our null hypothesis</u></em>.
Therefore, we conclude that there is an equal or larger proportion of Republicans in favor of lowering the standards.