Question

In 10 test runs, a truck operated for 8, 10, 10, 7, 9, 12, 10, 8, 7, and 9 miles with one gallon of a certain gasoline. Is this evidence at the 0.05 level of signifcance that the truck is not operating at an average of 11.5 miles per gallon with this gasoline? What assumptions must be satised in order for the procedure you used to analyze these data to be valid?

Answer 1

let the null hypothesis H0: =11.5 against alternative hypothesis H1: 11.5

Test statistic,

t =

Xi	Xi-Xbar	(Xi-Xbar)2
8	-1	1
10	1	1
10	1	1
7	-2	4
9	0	0
12	3	9
10	1	1
8	-1	1
7	-2	4
9	0	0
90		22

Let = = 90/10 = 9

s²== 22/9 = 2.4444

t=

t= -3.2341

=3.2341

= level of significance= 0.05

degrees of freedom= n-1 = 9

critical value= t_{9, 0.05} = 2.2621    ...... Table of t distribution

Decision Rule- t₉ > t_9,0.05

Reject H0 at 5% level of significance.

Or

P value= 0.01025334

p value < 0.05

Reject H0 at 5% level of significance.

Conclusion:The truck may not be operating at an average of 11.5 miles per gallon with this gasoline.