Math 227 Fal 2017 Homework: 6.3 Score: 0 of 1 pt 6.3.27 11 01 1 1 (gcomplete) HW
ID: 3359198 • Letter: M
Question
Math 227 Fal 2017 Homework: 6.3 Score: 0 of 1 pt 6.3.27 11 01 1 1 (gcomplete) HW Score: 7 In a survey of 1023 adults, 804 disapprove of the job the legislature is doing Use technology to construct A 90% confidence interval for the population proportion is (LM 90%, 95%, and 99% confidence intervals for the population proportion Interpret the results and compare th e widths of the confidence intervals. (Round to three decimal places as needed.) Enter your answer in the edit fields and then click check Answed 6 remaining partsExplanation / Answer
Solution:-Given that n = 1023, x = 804
=> p = x/n = 804/1023 = 0.786 , q = 0.214
a) z = 1.645 for 90% confidence interval
90% confidence interval for the population proportion = P ± Z * sqrt((p*q)/n)
= 0.786 ± 1.645 sqrt((0.786*0.214)/1023)
= 0.786 ± 0.021
= (0.765 , 0.807)
A 90% confidence interval for the population proportion is (0.765 , 0.807)
b) z = 1.96 for 95% confidence interval
95% confidence interval for the population proportion = P ± Z * sqrt((p*q)/n)
= 0.786 ± 1.96 *sqrt((0.786*0.214)/1023)
= 0.786 ± 0.025
= (0.761 , 0.811 )
A 95% confidence interval for the population proportion is (0.761 , 0.811)
c) z = 2.58 for 99% confidence interval
95% confidence interval for the population proportion = P ± Z * sqrt((p*q)/n)
= 0.786 ± 2.58 *sqrt((0.786*0.214)/1023)
= 0.786 ± 0.033
= ( 0.753 , 0.819)
A 99% confidence interval for the population proportion is (0.753 , 0.819)