(1) Point and Interval Estimates. One question on a recent General Social Survey asked, "Do you think that it should be the government's responsibility to reduce income differences between the rich and the poor?" Those answering yes included 90 out of the 142 subjects who called themselves strong Democrats in political party identification and 26 of the 102 who called themselves strong Republicans. (5 total points, 2.5 points for each part)

a.Find the point estimate of the population proportion who would answer yes for each group.

b.The 95% confidence interval for the population proportion of yes responses is (0.55, 0.71) for strong Democrats and (0.17, 0.34) for strong Republicans. Explain how to interpret the intervals.

(2) Confidence Interval for a Proportion. When the GSS most recently asked whether human beings developed from earlier species of animals, 53.8% of 1095 respondents answered that this was probably or definitely not true. Find a 99% confidence interval for the corresponding population proportion, and indicate whether you can conclude that a majority of Americans felt this way. (2.5 points)

(3) Confidence Interval for a Mean. In response to the GSS question in 2014 about the number of hours daily spent watching TV, the responses by the seven subjects who identified themselves as being raised Islamic were 1, 1, 1, 2, 2, 3, 6. (5 total points, 2.5 points for each part)

a.Estimate the mean, standard deviation, and standard error.

b.Construct a 95% confidence interval for the population mean, specifying its assumptions. Interpret.

(4) Choice of Sample Size. A 2011 poll in Canada indicated that 41% of Canadians favored bringing back the death penalty for convicted murderers. (The United States is the only Western democracy that has it.). A report by Amnesty International on this and related polls (www.amnesty.ca) did not report the sample size but states, "Polls of this size are considered to be accurate within 2.5 percentage points 95% of the time." If this is the case, about how large was the sample size? (2.5 points)

(5) The Five Parts of a Significance Test. You want to know whether adults in your country think the ideal number of children is equal to 2, or higher or lower than that. (7.5 total points, 2.5 points for each part)

a.Define notation and state the null and alternative hypotheses for studying this.

b.For responses in a recent GSS to the question "What do you think is the ideal number of children to have?" software shows results:

Test of mu = 2.0 vs mu not = 2.0

Variablen MeanStDevSE MeanT P-value

Children13022.4900.8500.023620.800.0000

Report the test statistic value, and show how it was obtained from other values reported in the table.

c.Explain what the P-value represents, and interpret its value.