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

solution:-

given that n = 650 , x = 230

a. point estimate p = x/n = 230/650 = 0.354

b. confidence interval

the value of 90% confidence from z table is 1.645

confidence interval formula

=> p +/- z * sqrt(p*(1-p)/n)

= 0.354 +/- 1.645 * sqrt(0.354*(1-0.354)/650)

= (0.323 , 0.385) (rounded to three decimals)

c. Interpret your results in the context of this problem

there is 90% chance that the interval is one the intervals contains the proportion for Jason Aldean was their favorite performer