1. A mayoral election in North Bay, Ontario, has twocandidates. Exactly half the residents currently prefereach candidate.

(a) For a random sample of 600 voters, 290 voted for a particular candidate. Are you willing to predict the winner?Why?

(b) For a random sample of 60 voters, 29 voted for a particularcandidate. Would you be willing to predict the winner? Why?

2. Mary and Joe separately conduct studies to testHo:?= 300 against Ho:??300, each with n = 800.

Mary gets?= 219.5, with se = 5 Joe gets?= 219.7,with se = 8

(a) Calculate the test statistic and P -value for both.

(b) Using a = 0.050, for each study indicate whether theresult is " statistically significant. "

3. The table below summarizes responses from General social Surveys in 1980 and in 2016 to the statement "is much better for everyone involved if the man is theachiever outside the home and the woman takes catthe home and family. " Let?₁denotethe population proportion who agreed with this statement in 1980, and let?₂denote the population proportion in 2016.

(a)Calculatethe95 % confidence interval.

b) Explain how results would differ for comparing the proportions who did not agree in the two years

TABLE

YearAgreeDisagreeTotal

19807964861282

201645611151571

5. At a major credit card company, the percentages ofpeople who historically apply for the Silver, Gold, andPlatinum cards are 60 %, 30 %, and 10 %, respectively. Ina recent sample of customers responding to a promotion,of 200 customers, 110 applied for Silver, 55 for Gold, and35 for Platinum. We are interested in whether the percentages for this promotion are different from the historicalpercentages.

a) What is the expected number of customers applying foreach type of card in this sample if the historical proportions are still true?

b) Compute the?²statistic.

c) How many degrees of freedom does the?²statistichave?

6.

4. The table below summarizes the number of hours spent in housework per week by gender, based on a recent survey. (a) Estimate the difference between the population means for women and men. (b) Find the estimated standard error of the sample difference. Interpret. (c) Find a 99 % confidence interval for the difference. Interpret Housework hours Gender Sample size Mean Standard deviation Men 245 7.8 8.5 Women 367 11.5 10.86. A European manufacturer of automobiles claims that its cars are preferred by the younger generation and would like to target university students in its next ad campaign. Suppose we test the manufacturer's claim with student lot and the staff lot at a large university classified the brands by country of origin, as seen in the following table. Are there differences in the national origins of cars driven by students and staff? a) Write appropriate hypotheses. b) Compute the x statistic and find the P - value of your test. c) State your conclusion and analysis. Origin Driver Student Staff American 107 105 European 33 12 Asian 55 47 Attach File