A political candidate feels that she performed particularly well in the most recent debate against her opponent. Her campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500 likely voters after the debate. The 95% confidence interval for the true difference (post-debate minus pre-debate) in proportions of likely voters who would vote for this candidate was (-0.014, 0.064). What was the difference (pre- debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate? 0.064 +(-0.014) 2 = 0.025 0.064 - (-0.014) = 0.039 2 O 0.064 + (-0.014) = 0.050 O 0.064 – (-0.014) = 0.078 %3D

A recent study looked at the relationship between condom use and the spread of AIDS, by following heterosexual couples in which one partner was infected with HIV. The couples were classified by their condom use. Of the 98 couples who always used condoms, 4 partners became infected with HIV. Of the 67 couples who did not always use condoms, 11 partners became infected. Test whether the proportions of partners who became infected with HIV are different for each group, using a 5% level of significance. Give each of the following: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. You MUST show your work

In a recent poll, 410 people were asked if they liked dogs, and 44% said they did. Find the margin of error of this poll, at the 95% confidence level.

A political researcher takes a survey of 310 randomly selected registered voters in Orlando, and each person was asked who they plan on voting for in the 2024 presidential election. 110 said they plan on voting for Candidate A, 185 said they plan on voting for Candidate B, and 15 were unsure or plan to vote for another candidate. The researcher wants to construct a 95% confidence interval for the proportion of all registered voters in Orlando who plan to vote for Candidate B. What is the point estimate? Round final answer to 3 decimal places.

A telephone service representative believes that the proportion of customers completely satisfied with their local telephone service is different between the South and the Midwest. The representative's belief is based on the results of a survey. The survey included a random sample of 11601160 southern residents and 12601260 midwestern residents. 43%43% of the southern residents and 56%56% of the midwestern residents reported that they were completely satisfied with their local telephone service. Find the 80%80% confidence interval for the difference in two proportions. Step 3 of 3 :   Construct the 80%80% confidence interval. Round your answers to three decimal places.

The last poll of 144 voters in Iowa shows that 19% of voters will vote for him in the Iowa Presidential Caucus.  What is the 99% confidence interval of his support level in Iowa?

A statistics student wants to conduct a study to determine the proportion of workers in Cititon who commute to another town for work. If the student wants a 90% confidence interval with a margin of error of 2%, how many workers should be in her sample?