In a survey of 2566 adults in a recent year, 1420 say they have made a New Year's resolution. Construct 90% and 95% confidence intervals for the popul

cistG 2020-11-22 Answered
In a survey of 2566 adults in a recent​ year, 1420 say they have made a New​ Years
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SchepperJ
Answered 2020-11-23 Author has 96 answers

Step 1 Given : n=2566 x=1420 Sample proportion: wide p^=xn
p^=14202566
wide p^=0.553 a) The​ 90% confidence interval for the population proportion p α=0.10
zc=zα2
zc=0.05
zc=1.645 Confidence interval: CI=p^±zc×p^×(1p^)n
CI=0.553±1.645×0.553×(10.553)2566

Step 2 CI=0.553±0.0161
CI=(0.5369,0.5691) 90% confidence interval for the population proportion p is lies between ( 0.5369, 0.5691 ) b) The​ 95% confidence interval for the population proportion p α=0.05
zc=zα2
zc=0.025
zc=1.96 Confidence interval: CI=p^±zc×p^×(1p^)n
CI=0.553±1.96×0.553×(10.553)2566
CI=0.553±0.0192
CI=(0.5338,0.5722) 95% confidence interval for the population proportion p is lies between ( 0.5338, 0.5722 ) Hence the 95% confidence interval is wider.

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