Question

A sample of 148 mothers of infants found that the average amount of sleep they got was 6.85 hours with a standard deviation of 2.12 hours.

(a) Construct and interpret a 90% confidence interval for the average amount of sleep mothers of infants get.

(b) In your interpretation, you probably (hopefully) said, “I am 90% confident...”. What does that mean?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 6.85

Population standard deviation =    = 2.12

Sample size = n =148

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E = Z/2 * ( /n)

= 1.645* (2.12 /  148 )

= 0.287
At 90% confidence interval
is,

- E < < + E

6.85 - 0.287 <   < 6.85+ 0.287

(6.563 , 7.137 )

b.

I am 90% confident that sample mean lies between lower bound and upper bound

(lower bound 6.563

upper bound = 7.137 )