Question

A company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining an average gas mileage of at least 29 mpg. To see if the goal is being met, they check the gasoline usage for 56 company trips chosen at random, finding a mean of 25.722 mpg and a standard deviation of 8.888 mpg. Does the sample provide convincing evidence the mean gas mileage is less than the goal set? Use a significance level of 0.10 to test the appropriate claim.

• H_{o_______________}
• H_A= ____________
• Aploha= _________
• Test statistic= t= ________
• probability= _____________
• decision=_______________
• At the 0.01 level, there ________significant evidence to conclude the mean gas mileage for this fleet of cars is _________________mpg.

Answer 1

solution

The null and alternative hypothesis is ,

H₀ :   = 29

H_a : >29

Test statistic = t

= ( - ) / s / n

= (25.722- 29) / 8.888 / 56

= −2.76

P-value = 0.0039

= 0.01

P-value >

0.0039<0.01, it is concluded that the null hypothesis is rejected.

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean is greater than 29, at the 0.01 significance level.