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.
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.
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