Question

A company with a large fleet of cars sets a goal of attaining a fleet average of at least 26 miles per gallon of gasoline. To see if that goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 25.02 mpg and a standard deviation of 4.83 mpg.

1. a) Is this a strong evidence that they have failed to attain their fuel economy goal? Assume significance level of 0.1.

2. b) Calculate the p-value and confirm that you get the same conclusion as in part (a).

Answer 1

Solution :

= 26

=25.02

=4.83

n = 50

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :    = 26

H_a : > 26

Test statistic = z

= ( - ) / / n

= (25.02-26) /4.83 / 50

= −1.43

Test statistic = z = −1.43

P(z > −1.43 ) = 1 - P(z < −1.43 ) = 1 -0.0764

P-value =0.9236

= 0.1

P-value >

0.9236 > 0.1

Fail to reject the null hypothesis .

There is not sufficient evidence to sclaim that the population mean μ is greater than 26, at the 0.1 significance level