Question

You are an assistant director of the alumni association at a local university. You attend a presentation given by the university’s research director and one of the topics discussed is what undergraduates do after they matriculate. More specifically, you learn that in the year 2018, a random sample of 216 undergraduates was surveyed and 54 of them (25%) decided to continue school to pursue another degree, and that was up two percentage points from the prior year. The Dean of the College of Business asks the research director if that is a statistically significant increase. The research director says she isn’t sure, but she will have her analyst follow up. You notice in the footnotes of the presentation the sample size in the year of 2017 was 200 undergraduates, and that 46 of them continued their education to pursue another degree.
There is a short break in the meeting. Take this opportunity to answer the dean’s question using a confidence interval for the difference between the proportions of students who continued their education in 2018 and 2017. (Use 95% confidence level and note that the university has about 10,000 undergraduate students).

Answer 1

Answer:

(0.102, -0.062)

Step-by-step explanation:

sample size in 2018 = n1 = 216

sample size in 2017 = n2 = 200

number of people who went for another degree in 2018 = x1 = 54

number of people who went for another degree in 2017 = x2 = 46

p1 = x1/n1 = 0.25

p2 = x2/n2 = 0.23

At 95% confidence level, z critical = 1.96

now we have to solve for the confidence interval =

$p1 -p2 ± z*\sqrt{((1-p1)*p1)/n1 + ((1-p2)*p2/n2}$

$0.25 -0.23 ± 1.96*\sqrt{((1 - 0.25) * 0.25)/216 + ((1 - 0.23) *0.23/200}$

= 0.02 ± 1.96 * 0.042

= 0.02 + 0.082 = 0.102

= 0.02 - 0.082 = -0.062

There is 95% confidence that there is a difference that lies between  - 0.062 and 0.102 on the proportion of students who continued their education in the years, 2017 and 2018.

There is no significant difference between the two.