Question

Lifetimes of AAA batteries are approximately normally distributed. A manufacturer wants to estimate the standard deviation of the lifetime of the AAA batteries it produces. A random sample of 23 AAA batteries produced by this manufacturer lasted a mean of 10.1 hours with a standard deviation of 2.2 hours. Find a 90% confidence interval for the population standard deviation of the lifetimes of AAA batteries produced by the manufacturer. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places. (If necessary, consult a list of formulas.)

What is the lower limit of the 90% confidence interval?

What is the upper limit of the 90% confidence interval?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 10.1

Population standard deviation = = 2.2

Sample size = n =23

At 90% confidence level

= 1-0.90% =1-0.90 =0.10

/2 =0.10/ 2= 0.05

Z/2 = Z0.05 = 1.645

Z/2 = 1.645  
Margin of error = E = Z/2 * ( /n)

= 1.645 * (2.2 /  23 )

=0.7545

At 90 % confidence interval estimate of the population mean is,

- E < < + E

10.1 - 0.7545 <   < 101 + 0.7545

9.50 <   < 10.85

(9.50 ,10.85 )

The lower limit of the 90% confidence interval is = 9.50

The upper limit of the 90% confidence interval = 10.85