Question

A random sample of 650 attendees of the 2019 Country Fest concert at Gillette Stadium indicated that 230 of them thought that Jason Aldean was their favorite performer.
a. (3pts.) Find the point estimate for the population proportion p of attendees that thought Jason Aldean was their favorite performer.
b. (4 pts.) Find the 90% confidence interval for the population proportion p of attendees that thought Jason Aldean was their favorite performer.
c. (3 pts.) Interpret your results in the context of this problem.

Answer 1

Given,

n = 650

x = 230

1) p= x/n = 230/650

p = 0.3538

2) now calculate 90% of confidence interval is

CI = p z*((p*(1-p))/n)

z value 90% of confidence interval is 1.645

CI = 0.3538 1.645*((0.3538*(1-0.3538))/650)

= 0.3538 0.0309

CI = 0.3538 - 0.0309 and CI = 0.3538 +0.0309

= 0.323 and CI = 0.385

Therefore 90% of confidence interval is (0.323,0.385)