In a random sample of 989 students from a large public university, it was found

Question

In a random sample of 989 students from a large public university, it was found that 464 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.) (________ %, _________ %) University officials concerned with counseling students are interested in the number of students who change majors rather than the proportion. The university has 38, 100 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)

estimate proportion p=464/989=0.469

std error of mean =(p(1-p)/n)1/2 =0.0159

for 95% CI, z=1.96

hence confidence interval =0.4381 ; 0.5003

b)confidence interval =43.81 ; 50.03

c)confidence interval =0.4381*38100 ; 0.5003*38100 =16690 ; 19060

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