In a random sample of 978 students from a large public university, it was found

Question

In a random sample of 978 students from a large public university, it was found that 463 of the students changed majors during their college years.

(a) Give a 95% confidence interval for the proportion of students at this university who change majors. (Round your answers to four decimal places.) ,

(b) Express your results from(a) in terms of the percent of students who change majors. (Round your answers to two decimal places.) %, %

(c) University officials concerned with counseling students are interested in the number of students who change majors rather than the proportion. The university has 38,300 undergraduate students. Convert the confidence interval you found in (a) to a confidence interval for the number of students who change majors during their college years. (Round your answers to the nearest whole number.) students, students

Explanation / Answer

(a) Give a 95% confidence interval for the proportion of students at this university who change majors

p^=sample prop=x/n=463/978=0.473415

Z crit for 95%=1.96

95% confidence interval for population proportion of students at this university who change majors

=p^-zsqrt(p^*(1-p^)/n),p^+zsqrt(p^*(1-p^)/n)

=0.473415-1.96*sqrt(0.473415*(1-0.473415/978),0.473415+1.96*sqrt(0.473415*(1-0.473415/978)

=0.4421,0.5047

0.4421<p<0.5047

lower limit=0.4421

uper limit=0.5047

(b) Express your results from(a) in terms of the percent of students who change majors. (Round your answers to two decimal places.) %, %

0.4421*100=44.21%

0.5047*100=50.47%

Solutionc:

lower limit=0.4421*38300=16932

upper limit=0.5047*38300=19330

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