Question

The figure to the right shows the results of a survey in which 3000 college graduates from the year 2016 were asked questions about employment.Construct 99% confidence intervals for the population proportion of college students who gave each response.

A table labeled "Employment, College students' responses to questions about employment" consists of five rows containing the following information from top to bottom, with row listed first and information listed second: Expect to stay at first employer for 3 or more years, 70 percent; Completed an apprenticeship or internship, 68 percent; Employed in field of study, 64 percent; Feel underemployed, 45 percent; Prefer to work for a large company, 13 percent.70%68%64%45%13%

The

99%

confidence interval for the proportion of college students that are employed in their field of study is

left parenthesis nothing comma nothing right parenthesisnothing,nothing.

​(Round to three decimal places as​ needed.)

Answer 1

Sol:

n=3000

z alpha/2 for 99%=2.576

Given Employed in field of study, 64 percent that is p^=0.64

99%

confidence interval for the proportion of college students that are employed in their field of study is

p^-z*sqrt(p^(1-p^)/n,p^+z*sqrt(p^(1-p^)/n

0.64-2.576*sqrt(0.64*(1-0.64)/3000),0.64+2.576*sqrt(0.64*(1-0.64)/3000

0.617,0.663

lower limit=0.617

upper imit=0.663

EXTRA INFO:

99%

confidence interval for the proportion of college students Expect to stay at first employer for 3 or more years is

p^-z*sqrt(p^(1-p^)/n,p^+z*sqrt(p^(1-p^)/n

0.70-2.576*sqrt(0.70*(1-0.70)/3000),0.70+2.576*sqrt(0.70*(1-0.70)/3000)

0.678,0.722

lower limit=0.678

upper limit=0.722

similarly it can be found for others

99%

confidence interval for the proportion Completed an apprenticeship or internship

0.68-2.576*sqrt(0.68*(1-0.68)/3000),0.68+2.576*sqrt(0.68*(1-0.68)/3000)

0.658,0.702

lower limit=0.658

upper limit=0.702

9%

confidence interval for the proportion who  Feel underemployed

=0.45-2.576*sqrt(0.45*(1-0.45)/3000),0.45+2.576*sqrt(0.45*(1-0.45)/3000)

=0.427,0.473

lower limit=0.427

upper limit=0.473