Question

A survey was conducted that asked 1004 people how many books they had read in the past year. Results indicated that x overbarequals12.5 books and sequals16.6 books. Construct a 95​% confidence interval for the mean number of books people read. Interpret the interval.

Answer 1

Explanation:

Given that a survey was conducted that asked 1004 people how many books they had read in the past year.

Results are:

x bar =12.5

s = 16.6

n = 1004

Std error of sample =
`(s)/(√(n-1) ) =(16.6)/(√(1003) )\\=0.524152\\=0.524`

Since population std dev is not known t critical value can be used for confidence interval.

df = 1004-1 =1003

t critical = 1.96

Margin of error
`= 1.96(std error) =1.027`

Confidence interval lower bound
`= 12.5-1.027 = 11.473`

Upper bound
`= 12.5+1.027 = 13.527`