Question

3) (15 points) In a survey of 2,328 adults, 1,950 reported that e-mails are easy to misinterpret, but only 1,239 reported that telephone conversations are easy to a. Construct a 95% confidence interval estimate for the population proportion of b. Construct a 95% confidence interval estimate for the population proportion of c. Compare the results of (a) and (b). Which of the following statements regarding t than the number misinterpret adults who report that e adults who report that telephone conversations are easy to misinterpret. the implications of the information found in (a) and (b) is correct? Pick one. -mails are easy to misinterpret. i. More adults believe that e-mails are easy to misinterpre ii. More adults believe that telephone conversations are easy to misinterpret iii. The number of adults that believe that e-mails are easy to misinterpret and that believe that telephone conversations are easy to misinterpret. than the number that believe that e-mails are easy to misinterpret. the number of adults that believe that telephone conversations are easy to misinterpret are roughly the same. iv. The information cannot be compared because it is derived from two different opinions.

Not: solve without ti calculator please

Answer 1

Solution :

(a) 95% confidence interval is given by-

$\dpi{100} \hat{p} \pm Z_{.025} * \sqrt{\frac{\hat{p}*(1-\hat{p})}{n}}$

where observed proporrion of people who said that e mails are easy to misinterpret = $\hat{p} =$ 1950/2328 = 0.8376 , and n = 2328

then putting the values we get following confidence interval-

( 0.8226 , 0.8526 )

(b) 95% confidence interval is given by-

$\dpi{100} \hat{p} \pm Z_{.025} * \sqrt{\frac{\hat{p}*(1-\hat{p})}{n}}$

where observed proporrion of people who said that telephone conversations are easy to misinterpret = $\hat{p} =$ 1239/2328 = 0.5322 , and n = 2328

then putting the values we get following confidence interval-

( 0.5119 , 0.5525 )

(c) Option A is correct. As both limits of the confidence interval in part (a) are higher than that in part (b)

Answer

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