Question

A poll taken this year asked 1010 adults whether they were fans of a particular sport and 47​% said they were. Last​ year, 46​% of a​ similar-size sample had reported being fans of the sport. Complete parts a through e below.

​a) Find the margin of error for the poll taken this year if one wants 95​% confidence in the estimate of the percentage of adults who are fans of the sport. MEequals nothing ​(Round to three decimal places as​ needed.) ​

b) Explain what that margin of error means.

A. One is 95​% confident that this sample proportion is within plus or minusME of the true proportion of adults who are fans of the sport.

B. One is 95​%plus or minusME confident that the true proportion of adults who are fans of the sport is equal to this sample proportion.

C. In 95​% of samples of​ adults, the proportion who are fans of the sport will be within plus or minusME of the sample proportion.

D. There is a 95​% chance that the true proportion of adults who are fans of the sport is within plus or minusME of this sample proportion.

​c) If one wanted to be 99​% confident instead of 95​% ​confident, would the margin of error be larger or​ smaller?

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 more ​often, so the margin of error would be smaller.

C. To be more ​confident, the interval needs to contain the true proportion less ​often, so the margin of error would be larger.

D. To be more ​confident, the interval needs to contain the true proportion less ​often, so the margin of error would be smaller.

​

d) Find the margin of error for the poll taken this year if one wants 99​% confidence in the estimate of the percent of adults who are fans of the sport. ME= ____________ ​(Round to three decimal places as​ needed.) ​

e) In​ general, if all other aspects of the situation remain the​ same, will smaller margins of error produce greater or less confidence in the​ interval?

Less confidence or greater confidence?

Answer 1