How do you answer in excel using excel 53, The National Center for Education Sta

Question

How do you answer in excel using excel 53, The National Center for Education Statistics reported that 47% of college students work to pay for tuition and living expenses. Assume that a sample of 450 college students was used in the study. a. Provide a 95% confidence interval for the population proportion of college students who work to pay for tuition and living expenses. Provide a 99% confidence interval for the population proportion of college students who work to pay for tuition and living expenses. what happens to the margin of error as the confidence is increased from 95% to 99%? b. c,

Explanation / Answer

Ans:

Point estimate for p=0.47

n=450

a)alpha=1-0.95=0.05

alpha/2=0.025

critical z value=normsinv(0.025) or normsinv(0.975)=+/-1.96

95% confidence interval for population proportion

=0.47+/-1.96*sqrt(0.47*(1-0.47)/450)

=0.47+/-0.046

=(0.424, 0.516)

b)alpha=1-0.99=0.01

alpha/2=0.005

critical z value=normsinv(0.005) or normsinv(0.995)=+/-2.58

99% confidence interval for population proportion

=0.47+/-2.58*sqrt(0.47*(1-0.47)/450)

=0.47+/-0.061

=(0.409, 0.531)

c)

Margin of error has increased from 0.046 to 0.61 as confidenec is increased from 95% to 99%.

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