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 Ha: 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? Group of answer choices

Answer 1

Larger sample size gives less std error and hence test statistic is larger.

Explanation:

Given that 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

Group I II

Success 640 64

Total 1200 120

p 0.533333333 0.533333333

q 0.466666667 0.466666667

se 0.014401646 0.045542003

p diff 0.033333333 0.033333333

Z 2.314550249 0.731925055

p 0.01 0.233

we find that though p is the same, std error is very small for larger sample size thus making z statistic much bigger. So we get p value less than 0.05 whereas for 120 sample size, std error is large so Z statistic is small thus making p value to accept null hypothesis