In: Statistics and Probability
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?
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 )