Question

Dalize kept careful records of the fuel efficiency of her car. After filling the car tank 20 times, she
found that a tank covered 600km on average with a sample standard deviation of R50 km.
Create a 95% confidence interval for the average distance covered on one tank.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 600

sample standard deviation = s = 50

sample size = n = 20

Degrees of freedom = df = n - 1 = 20 - 1 = 19

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,19 = 2.093

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

= 2.093 * (50 / 20)

= 23.4

The 95% confidence interval estimate of the population mean is,

- E < < + E

600 - 23.4 < < 600 + 23.4

576.6 < < 623.4

(576.6 , 623.4)