7. A pollster has been hired by a media outlet to take a random sample of Albert

Question

7. A pollster has been hired by a media outlet to take a random sample of Alberta voters to determine the percentage that would vote for the current premier should a provincial election be held in the near future. A poll conducted a month ago indicated that 20% of Alberta voters would cast a vote for the party that the current premier is the leader of. (a) If the pollster wished to be 95% confidence that the results of the sample are 'off' by at most four percentage points, how many Alberta voters should the pollster randomly sample? 2 (b) From the sample size determined in (a), the number of Alberta voters indicating they would vote for the current premier should a provincial election be held in the near future found to be 190. From this result, find a 95% confidence interval for the proportion of Alberta voters that would vote for the current premier. (c) In the last provincial election, the current premier's party received 42% of the vote. Does the interval in (b) suggest that current premier is less popular now compared to the last provincial election? Explain your answer.

Explanation / Answer

A) Margin of error = 0.04

Or, z0.025 * sqrt (P * (1 - P )/n) = 0.04

Or, 1.96 * sqrt(0.2 * 0.8/n) = 0.04

Or, sqrt(n) = 1.96 * sqrt(0.2 * 0.8)/0.04

Or, sqrt(n) = 19.6

Or, n = 384

B) p = 190/384 = 0.49

The Confidence interval is

p +/- z0.025 * sqrt(p * (1 - p)/n)

= 0.49 +/- 1.96 * sqrt(0.49 * 0.51/384)

= 0.49 +/- 0.05

= 0.44, 0.54

C) The Confidence interval for 42% of vote is

0.42 +/- 1.96 * sqrt(0.42 * 0.58/384)

= 0.42 +/- 0.049

= 0.371, 0.469

As the confidence interval for current premier is more wider than provincial election, so it isn't less popular compared to the last provincial election.

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