Question

Canada has much stronger gun control laws than the United States, and Canadians support gun control more strongly than do Americans. A sample survey asked a random sample of 1505 adult Canadians, Do you agree or disagree that all firearms should be registered?

Of the 1505 people in the sample, 1288 answered either Agree strongly or Agree somewhat.

Nonetheless, act as if we have an SRS from adults in the Canadian provinces.
Give a 95% confidence interval for the proportion who support registration of all firearms.

(A) 0.8460 to 0.8656
(B) 0.8325 to 0.8791
(C) 0.7324 to 0.9792
(D) 0.8381 to 0.8736

Answer 1

Option D) 0.8381 to 0.8736

Explanation:

We are given the following in the question:

Sample size, n = 1505

Number of people who answered, x = 1288

`\hat{p} = (x)/(n) = (1288)/(1505) = 0.8558`

Confidence interval:

`\hat{p}\pm z_(stat)\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}`

`z_(critical)\text{ at}~\alpha_(0.05) = 1.96`

Putting the values, we get:

`0.8558\pm 1.96(\sqrt{(0.8558(1-0.8558))/(1505)}) = 0.8558\pm 0.0177\\\\=(0.8381,0.8736)`

Option D) 0.8381 to 0.8736