Question

During a natural gas shortage, a gas company randomly sampled residential gas meters in order to monitor daily gas consumption. On a particular day, a sample of 100 meters showed a sample mean of 250 cubic feet and a sample standard deviation of 50 cubic feet. Provide a 90% confidence interval estimate of the mean gas consumption for the population.

Answer 1

Solution :

Given that,

= 250

s = 50

n = 100

Degrees of freedom = df = n - 1 = 100 - 1 = 99

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t _/2,df = t_0.05,99 =1.660

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

= 1.660 * (50 / 100) = 8.3

The 90% confidence interval estimate of the population mean is,

- E < < + E

250 - 8.3 < < 250 + 8.3

241.7 < < 258.3

(241.7, 258.3 )