Question

A political pollster conducted a study to determine political party loyalty. To do so, he selected a random sample of 100 registered Democrats and a random sample of 100 registered Republicans. He determined the proportion of Democrats who plan to vote for the Democratic candidate in the upcoming election and the proportion of Republicans who plan to vote for the Republican candidate in the upcoming election. A) test of significance was conducted on the following hypotheses. H0: pD = pR Ha: pD ≠ pR where pD = the proportion of Democrats who plan to vote for the Democratic candidate in the upcoming election and pR = the proportion of Republicans who plan to vote for the Republican candidate in the upcoming election. The conditions for inference were met. This test resulted in a P-value of 0.0981.

(a) Interpret this P-value in the context of this study.
(b) Using a significance level of = 0.05, what conclusion should be made?
(c) Based upon your conclusion in part (b), what type of error (Type I error or Type II error) could have been made? Provide one potential consequence of this error.

Answer 1

Answer: (a)

P - Value = 0.0981 is high, this indicates stronger evidence that we should fail to reject the null hypothesis: H0: pD = pR (There is no significant difference between the proportion of Democrats who plan to vote for the Democratic candidate in the upcoming election and the proportion of Republicans who plan to vote for the Republican candidate in the upcoming election). P - Value = 0.0981 is the probability of obtaining results at least as extreme as the observed results of the Hypothesis Test, assuming that the null hypothesis is correct.

(b)

Since P - Value = 0.0981 is greater than \alpha = 0.05, the difference is not significant. Fail to reject null hypothesis.

(c)

Since in the Hypothesis Test, we have failed to reject null hypothesis, we could have made: Type II Error: Failure to reject a false null hypothesis. One potential consequence of this error is as follows:

Suppose in reality there is significant difference between the proportion of Democrats who plan to vote for the Democratic candidate in the upcoming election and the proportion of Republicans who plan to vote for the Republican candidate in the upcoming election. But the political pollster wrongly concludes that there is no significant difference between the proportion of Democrats who plan to vote for the Democratic candidate in the upcoming election and the proportion of Republicans who plan to vote for the Republican candidate in the upcoming election. Type II Error is committed in this situation. The consequence of this Type II Error is that the political pollstar will that the political parties are loyal and will not do any follow up work whereas in reality it is not so.

Explanation:

got this from chegg!!!