Question

A person wants to estimate the population mean gas price in a county. The population standard deviation is $0.05. A sample of 59 gas stations is collected and the sample mean price is $2.06

(a) What is the population ? What is the sample?

(b) Construct a 99% confidence interval.

Answer 1

Solution :

Given that,

a) population mean = unknown

sample mean = = 2.06

b) Population standard deviation =    = 0.05

Sample size = n = 59

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z_{0.005 =} 2.576

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

= 2.576 * ( 0.05 /  59 )

= 0.017

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

  ± E

2.06 ± 0.017

( $ 2.043, $ 2.077 )