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

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