Question

A small company involved in​ e-commerce is interested in statistics concerning the use of​ e-mail. A poll found that 36​% of a random sample of 1084 ​adults, who use a computer at their​ home, work, or​ school, said they do not send or receive​ e-mail. Complete parts a through e. ​a) Find the margin of error for this poll if we want 99​% confidence in our estimate of the percent of American adults who do not use​ e-mail. MEequals 34 ​(Round to three decimal places as​ needed.) ​b) Explain what that margin of error means. A. The margin of error is the width of the confidence interval that contains the true proportion of adults who do not use​ e-mail. B. The margin of error​ (as a​ percent) is the value that should be subtracted from the 99​% confidence level to obtain the​ pollsters' true confidence level. C. The pollsters are 99​% confident that the margin of error contains the true proportion of adults who do not use​ e-mail. D. The pollsters are 99​% confident that the true proportion of adults who do not use​ e-mail is within the margin of error​ (as a​ percent) of the estimated 36​%. ​c) If we want to be 95​% ​confident, will the margin of error be larger or​ smaller? A. A 95​% confidence interval leads to a smaller margin of error. In order to decrease ​confidence, the interval must be narrower. B. A 95​% confidence interval leads to a smaller margin of error. In order to decrease ​confidence, the interval must be wider. C. A 95​% confidence interval leads to a larger margin of error. In order to increase ​confidence, the interval must be narrower. D. A 95​% confidence interval leads to a larger margin of error. In order to increase ​confidence, the interval must be wider. ​d) Find that margin of error. MEequals 34 ​(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 involve greater or less confidence in the​ interval? Smaller margins of error will be the result of more confident intervals. Smaller margins of error will be the result of less confident intervals.

Answer 1

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