Question

A survey of 30 adults found that the mean age of a person's primary vehicle is 5.6 years. Assuming the standard deviation of the population is 0.8 year, find the 99% confidence interval of the population mean.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 5.6

Population standard deviation =    = 0.8
Sample size = n =30

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576   ( Using z table )

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

=2.576 * (0.8 / 30)

= 0.3762

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

- E < < + E

5.6-0.3762 < < 5.6+ 0.3762

5.2238< <5.9762

(5.2238,5.9762 )