Question

A polling company conducts an annual poll of adults about political opinions. The survey asked a random sample of 2190 adults whether they think things in the country are going in the right direction or in the wrong direction. 43​% 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 90% confidence.

b).  Explain what this margin of error means. Select the correct choice below and fill in the answer box within your choice.

A. We are 90​% confident that the observed proportion of adults that responded​ "wrong track" is within __ of the population proportion.

B.We are 90​% confident that the observed proportion of adults that responded​ "wrong track" is within __ of the sample proportion.

C.The probability that any given adult surveyed from the population will respond​ "wrong track" is __

D.The probability that any given adult surveyed from the sample responded​ "wrong track" is __

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.43

1 - = 1 - 0.43 = 0.57

Z/2 = Z0.05 = 1.645

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.645 (((0.43 * 0.57) / 2190 )

= 0.017

A. We are 90​% confident that the observed proportion of adults that responded​ "wrong track" is within 0.017 of the population proportion.