A newspaper is conducting a statewide survey concerning the race for governor.The newspaper will take a simple random sample of n registered voters and determine X = the number of voters that will vote for the Democratic candidate.Is there evidence that a clear majority of the population will vote for the Democratic candidate? To answer this,they will test the hypotheses H₀: p = 0.50 versus H_a: p 0.50.Consider the two scenarios,where in Scenario 1,n = 1200 and X = 640.In Scenario 2,n = 120 and X = 64.Even though the values for are the same in the two scenarios,we come to opposite decisions (we reject H₀ in one scenario and we do not in the other).What is the reason for these contrasting decisions? A)When the sample size is larger,the margin of error is larger.This may cause the results to be biased. B)The 64 people in the small sample must also be part of the 640 people in the big sample.This means we are counting them twice,causing the results of the test with the larger sample to be wrong. C)The sample size in the first scenario is much larger,leading to a test with higher power. D)We must have made a mistake.With equal values of ,we must come to equal decisions.

Question

A newspaper is conducting a statewide survey concerning the race for governor.The newspaper will take a simple random sample of n registered voters and determine X = the number of voters that will vote for the Democratic candidate.Is there evidence that a clear majority of the population will vote for the Democratic candidate? To answer this,they will test the hypotheses H₀: p = 0.50 versus H_a: p > 0.50.Consider the two scenarios,where in Scenario 1,n = 1200 and X = 640.In Scenario 2,n = 120 and X = 64.Even though the values for are the same in the two scenarios,we come to opposite decisions (we reject H₀ in one scenario and we do not in the other).What is the reason for these contrasting decisions? A)When the sample size is larger,the margin of error is larger.This may cause the results to be biased. B)The 64 people in the small sample must also be part of the 640 people in the big sample.This means we are counting them twice,causing the results of the test with the larger sample to be wrong. C)The sample size in the first scenario is much larger,leading to a test with higher power. D)We must have made a mistake.With equal values of ,we must come to equal decisions.

Quizplus · Accepted Answer

The sample size in Scenario 1 is much larger, which gives a higher power to the test. This means that we are more likely to detect a true difference in proportions, leading to the rejection of the null hypothesis. In Scenario 2, the smaller sample size reduces the power of the test, making it less likely to detect a true difference in proportions. Therefore, we do not reject the null hypothesis. Option A is incorrect because as the sample size increases, the margin of error decreases. Option B is incorrect because we cannot count the same people twice in different scenarios. Option D is incorrect because with equal values and different sample sizes, the decision can still differ due to the power of the test.

A Newspaper Is Conducting a Statewide Survey Concerning the Race