Question

Question 1 : Angus Reid Strategies regularly surveys Canadians as to whether they prefer an elected head of state instead of a monarch. The percentage preferring an elected head of state was 43% in November 2009, 30% in July 2010 and 40% in in April 2013 based on surveys of 1005 Canadian Adults each year. Test whether support for an elected head of state in 2013 was more than 5% higher than it had been in 2010 at the 5% level of significance and interpret the results.

Question 2 : British Columbia introduced carbon tax in 2008. In 2011 Environics surveyed 1025 British Columbians about the tax and found that 54% supported it. In 2013, Environics surveyed 250 British Columbians and found that 52% supported the tax. Has the support gone down by more than 1% between 2011 and 2013 at the 10% significance level.

Question 3 : An Angus Reid survey of 1003 Canadian adults and 1980 British adults found that 59% of the Canadian sample and 56% of the British sample thought that homosexuality is something people are born with as opposed to being preference they have chosen. Does a smaller percentage of Britons hold this view than Canadians. Do a complete hypothesis test.

Question 4 : Suppose a professional survey of 1016 Canadian Adults (assume a 50/50 split between men and women) found that 65% of men and 45% of women support scrapping the nickel. Do more Canadian men support scrapping nickel than Canadian women ? Conduct a hypothesis test.

Answer 1

(Q 3)

Data:

Let 1 denote the British sample and 2 denote the Canadian sample    

n1 = 1980   

n2 = 1003   

p1 = 0.56   

p2 = 0.59   

Hypotheses:    

Ho: p1 ≥ p2    

Ha: p1 < p2    

Decision Rule:    

α = 0.05   

Lower Critical z- score = -1.644853627   

Reject Ho if z < -1.644853627   

Test Statistic:    

Average proportion, p = (n1p1 + n2p2)/(n1 + n2) = (1980 * 0.56 + 1003 * 0.59)/(1980 + 1003) = 0.570087161

q = 1 - p = 1 - 0.570087160576601 = 0.429912839

SE = √[pq * {(1/n1) + (1/n2)}] = √(0.570087160576601 * 0.429912839423399 * ((1/1980) + (1/1003))) = 0.019186882

z = (p1 - p2)/SE = (0.56 - 0.59)/0.0191868819203916 = -1.563568282

p- value = 0.058959494   

Decision (in terms of the hypotheses):    

Since -1.563568282 > -1.644853627 we fail to reject Ho

Conclusion (in terms of the problem):    

There is no sufficient evidence that a smaller percentage of Britons hold this view than Canadians.

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