Question

a random sample of the price of gasline from 40 gas stations in a region gives the statistic below.

ÿ=$3.49 s=$0.29

find the 95% confidence interval.

Answer 1

Here the parameters we have are:                                                                                                                           Sample Mean, Ȳ = $3.49 ; Standard deviation, s = $0.29 and sample size, n = 40

95% confidence interval for population mean is given by:

Ȳ ± Z*(s/ √ n) ,

where the value of Z is calculated by using standard normal table. The value of Z for 95% confidence interval is 1.96

Now the calculation of 95% confidence interval is:

3.49 ± 1.96* (0.29/√ 40)

3.49 ± 1.96*(0.046)

3.49 ± 0.090

(3.49 - 0.090) , (3.49 + .090)

3.4 , 3.58

Therefore the lower limit is $3.4 and the upper limit is $3.58