In a random sample of 980 students from a large public university, it was found
ID: 3131405 • Letter: I
Question
In a random sample of 980 students from a large public university, it was found that 465 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 36,300 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)
Note that
p^ = point estimate of the population proportion = x / n = 465/980 = 0.474489796
Also, we get the standard error of p, sp:
sp = sqrt[p^ (1 - p^) / n] = 0.015951112
Now, for the critical z,
alpha/2 = 0.025
Thus, z(alpha/2) = 1.959963985
Thus,
Margin of error = z(alpha/2)*sp = 0.031263606
lower bound = p^ - z(alpha/2) * sp = 0.44322619
upper bound = p^ + z(alpha/2) * sp = 0.505753402
Thus, the confidence interval is
( 0.44322619 , 0.505753402 ) [ANSWER]
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b)
In percent,
( 44.322619% , 50.5753402% ) [ANSWER]
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c)
Multiplying the proportions by 36300,
( 0.44322619*36300 , 0.505753402*36300 )
= (16089, 18359) [ANSWER]
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