Question

2. [13 marks] Forum Research is a Canadian market research and polling firm that conducted opinion polls leading up to the 2015 Canadian Federal Election (which the Liberal Party and Justin Trudeau won). On August 19th, 2015 (two months before the election), the company polled 1473 people asking them which party they would vote for if the election were held that day. The results were as follows:

Party		Liberal	Conservative	NDP	Other
People’s Choice		412	427	501	133

(a) Rounding results to 3 decimals, construct a 95% confidence interval for the true proportion of people voting for the Liberal Party in the election.

(b) Rounding results to 3 decimals, construct a 90% confidence interval for the true proportion of people voting for a party other than the Liberal Party in the election.

(c) Perform a hypothesis test at the α =0.01 significance level to determine whether the sample above provided evidence that the true proportion of people who would vote for the Liberal Party would be less than 35% (alternate hypothesis). Be sure to state the null and alternate hypotheses and show your calculations of the test statistic (to 3 decimals) and critical region.

Null Hypothesis H0:                                            Alternate Hypothesis Ha:

Observed test statistic:

Critical Region:

Conclusion:

Concluding Statement:

(d) How many people from the sample of 1473 would have needed to respond with a vote for the Liberal Party in order for the outcome in the hypothesis test in part (c) to change?

(e) As it turned out, the Liberal Party received 39.5% of the popular vote and won the election. In the context of this problem, what type of error occurred in the test in part (c)? Determine the probability of making such a mistake in this case.

Answer 1

(a)

(b)

(c)

Conclusion: We can conclude that the sample above provided evidence that the true proportion of people who would vote for the Liberal Party would be less than 35%.

(d)

If we take number of respondents who vote for Liberal Party 474, then the p-value is less than 0.01 while for 475 it is greater than 0.01. That is for 475 decision will be changed.

Answer: 475

(e)

That is null hypothesis is true. Since we reject the true null hypothesis so type II error is possible.