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

Question

contestada

Respuesta :

jlmpco jlmpco · Answer 1 · 2019-11-16T03:59:24+01:00

Answer:

B. 0.60

Step-by-step 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