Question

estion

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

17

AAA batteries produced by this manufacturer lasted a mean of

9.4

hours with a standard deviation of

2.2

hours. Find a

99%

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 99% confidence interval?
What is the upper limit of the 99% confidence interval?

Answer 1

Solution :

degrees of freedom = n - 1 = 17 - 1 = 16

t/2,df = t0.005,16 = 2.921

Margin of error = E = t/2,df * (s /n)

= 2.921 * (2.2 / 17)

Margin of error = E = 1.559

The 99% confidence interval estimate of the population mean is,

  ± E  

= 9.4 ± 1.559

= ( 7.841, 10.959 )

lower limit = 7.841

upper limit = 10.959