Clearly show how Ipsos Reid obtained the margin of error quoted in the third par

Question

Clearly show how Ipsos Reid obtained the margin of error quoted in the third paragraph. Remember that pollsters use the "worst case" choice of p in their margin of error calculation. Construct a 99% confidence interval for the percentage of adult British Columbians who think that the Canadian military mission in Afghanistan has been "very effective" so far. In your answer: - check the conditions, - show the details of your CI construction, and - interpret your interval. Suppose that you wanted to investigate student opinion regarding the effectiveness of the Canadian military mission in Afghanistan by taking a random sample of students. You want your estimate of the percentage of students rating the mission "very effective" to be within 2% at a 90% confidence level. How large a random sample would you need? In your calculation, clearly indicate your thinking on your choice of values for pq.

Explanation / Answer

Answer:

a).

p value for worst case =0.5

z values for 95% ( 19 out of 20) 1.96

margin of error= z*se

=1.96*sqrt(0.5*0.5/550) =0.04178

Or 4.2%

b).

p=0.1, n=550

Both np and n(1-p) > 10, conditions holds.

Z value for 99% = 2.576

Lower limit = 0.1-2.576*sqrt(0.1*0.9/550) =0.067

upper limit = 0.1+2.576*sqrt(0.1*0.9/550) =0.133

99% CI = (6.7% to 13.3%)

we are 99% confident that percentage of adult British Colombians think that Canadian military mission in Afghanistan is effective falls in the interval (6.7% to 13.3%).

c).

Sample size calculation

p=1/10=0.1

For 90%, z=1.645

d=0.02

Sample size = (z2*p*(1-p))/d2

= (1.6452*0.1*0.9)/0.022

=608.8

The sample size required= 609

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