A polling company conducts an annual poll of adults about political opinions. Th
ID: 3060793 • Letter: A
Question
A polling company conducts an annual poll of adults about political opinions. The survey asked a random sample of 455 adults whether they think things in the country are going in the right direction or in the wrong direction. 64% said that things were going in the wrong direction. Complete parts a and b below.
a) Calculate the margin of error for the proportion of all adults who think things are going in the wrong direction for 95% confidence.
ME=___(round to 3 decimal places)
b) Would the margin of error be larger or smaller for 99% confidence? Choose one.
A. To be more confident, the interval needs to contain the true proportion more often, so the margin of error would be larger.
B. To be more confident, the interval needs to contain the true proportion less often, so the margin of error would be larger.
C. To be more confident, the interval needs to contain the true proportion more often, so the margin of error would be smaller.
D. To be more confident, the interval needs to contain the true proportion less often, so the margin of error would be smaller.
Explanation / Answer
a) At 95% confidence interval the critical value is z0.025 = 1.96
Margin of error = z0.025 * sqrt(p * (1 - p)/n)
= 1.96 * sqrt(0.64 * 0.36/455)
= 0.044
b) Option A is correct.