Question

A random sample of 27 Exxon customers used an average of 15 gallons to fill their vehicles with a sample standard deviation of 5.4 gallons. 99% confidence interval for this sample is (_________ ,___________ ). Assume that the gas usage of Exxon customers is normally distributed.

Round your answers to the nearest whole number

Answer 1

Solution :

Point estimate = sample mean = = 15

sample standard deviation = s = 5.4

sample size = n = 27

degrees of freedom = n - 1 = 27 - 1 = 26

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = t_0.005,26 = 2.779

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

= 2.779 * (5.4 / 27)

Margin of error = E = 3

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

  ± E

= 15  ± 3

= ( 12, 18 )