In a random sample of 979 students from a large public university, it was found

Question

In a random sample of 979 students from a large public university, it was found that 467 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 37,000 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

here p = 467/979 = 0.477
n = 979
SE = sqrt(0.477 * 0.523/979) = 0.016

for 95% CI, z-value = 1.96

lower limit = p - z*SE = 0.477 - 1.96*0.016 = 0.4456
upper limit = p + z*SE = 0.477 + 1.96*0.016 = 0.5084

Hence the 95% CI of the proportion of students at this university who change major is (0.4456, 0.5084)

This means 44.56% to 50.84% students of the university change their major.

Out of 37000 undergraduate students at the university around 37000*0.4456=16489 to 37000*0.5084=18809 students changed their major

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