Question

Eric randomly surveyed 150 adults from a certain city and asked which team in a contest they were rooting​ for, either North High School or South High School. From the results of his​ survey, Eric obtained a​ 95% confidence interval of​ (0.52,0.68) for the proportion of all adults in the city rooting for North High. What proportion of the 150 adults in the survey said they were rooting for North High​ School?

A. 0.646

B. 0.60

C. Somewhere between 0.52 and 0.68, but the exact proportion cannot be determined.

D. This information cannot be determined from the information given in the problem

Answer 1

B. 0.60

Explanation:

Let be

X = adults in the survey said they were rooting for North High School

µ = mean

σ = standard deviation

let be

X1 = 0.52

X2 = 0.68

We know that a 95% confidence interval correspond to z values of -1.96 and 0.96

Now we have two equations to find µ and σ

-1.96 = (0.52 –µ)/σ ….. equation 1

1.96 = (0.68 –µ)/σ ….. equation 2

Dividing equation 1 and equation 2

-1.0 = (0.52 –µ)/ (0.68 –µ)

-1.0 (0.52 –µ) = (0.68 –µ)

-0.52 + µ =0.68 - µ

µ + µ = 0.68 + 0.52

2 µ = 1.2

µ = 0.6