In a random sample of 990 students from a large public university, it was found

Question

In a random sample of 990 students from a large public university, it was found that 461 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 36, 400 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.)

Explanation / Answer

Solution:-

Given,

In a random sample of 990 students, 461 changed majors.

Proportion of students those who changed majors = 461/990 = 0.4657

(a)

95% confidence interval:-

Lower limit = 0.4348

Upper limit = 0.4968

(b) In percentage

Lower limit = 43.48%

Upper limit = 49.68%

(c) If the university has 36,400 undergraduates,

Lower limit = 43.48% of 36400 = 15826.72 or 15827

Upper limit = 49.68% of 36400 = 18083.52 or 18084

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