Suppose that the organizers of the Lagoon Summer Concert ser

Suppose that the organizers of the Lagoon Summer Concert series wish to estimate how many people attend one of their concerts. In order to do this, they hand out 150 t-shirts before the concert begins. Once the concert ends, they randomly select 467 people and find that 84 were given a t-shirt.
A) Find an estimate for the number of people that attended the concert.  
B) Find the 95% confidence interval for the number of people that attended the concert. ? to ?

Solution

a)
Point estimate = x/n
People were given a t-shirt (x)=84
Sample Size(n)=467
Point estimate = Sample proportion = x/n =0.18
b)
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Confidence Interval = [ 0.18 ±Z a/2 ( Sqrt ( 0.18*0.82) /467)]
= [ 0.18 - 1.96* Sqrt(0) , 0.18 + 1.96* Sqrt(0) ]
= [ 0.145,0.215]

the 95% confidence interval for the number of people that attended the concert. 14.5% to 21.5%