Question

In a survey of 628 males ages 18-64, 394 say they have gone to the dentist in the past year. oportion n er re the results and compare he wa ns onstruct 90% and 95% confidence intervals or the population The 90% confidence interval for the population proportion p is ( Round to three decimal places as needed.) The 95% confidence interval for the population proportion p is (Round to three decimal places as needed.) Interpret your results of both confidence intervals. e com ence te vas. com enen use echnology construct he con encenter as O A. With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is not between the endpoints of the given confidence interval OB. With the given confidence,it can be said that the sample proportion of males ages 18-64 who say they have gone to the dentistin the past year is between the endpoints of the given confidence interval O C. With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interva Which intervalis wider? O The 90% confidence interval The 95% confidence interval

Answer 1

n = 628

p = 394 / 628 = 0.627

a) Z for 90% confidence interval = Z_0.05 = 1.65

confidence interval $=(p \pm Z_{0.05}*\sqrt{\frac{p*(1-p)}{n}})$

                               $=(0.627 \pm 1.65*\sqrt{\frac{0.627*(1-0.627)}{628}})$

                               $=(0.627 \pm 0.032)$

                               = (0.595 , 0.659)

b) Z for 95% confidence interval = Z_0.025 = 1.96

confidence interval $=(p \pm Z_{0.025}*\sqrt{\frac{p*(1-p)}{n}})$

                               $=(0.627 \pm 1.96*\sqrt{\frac{0.627*(1-0.627)}{628}})$

                               $=(0.627 \pm 0.038)$

                               = (0.589 , 0.665)

c) Option-C)

d) Option-B) the 95% confidence interval is wider