Question

To compare two kinds of bumper guards, 6 of each kind were mounted on a certain kind of compact car. Then each car was run into a concrete wall at 5 miles per hour, and the following are the costs of the repairs (in dollars)

Bumper guard 1:         107      148      123      165      102            119

Bumper guard 2:         134      115      112      151      133            129 Use the 0.01 level of significance to test whether the difference between the two sample means is significant.   

Answer 1

Guard 1	Guard 2
127.33	129.00	mean
24.45	14.21	std. dev.
6	6	n

To Test :-

H0 :- µ1 = µ2
H1 :- µ1 ≠ µ2

Test Statistic :-
t = (X̅1 - X̅2) / SP √ ( ( 1 / n1) + (1 / n2))

Sp = 19.998

t = - 0.14

P value = 2 * P ( t > 0.14 ) = 0.8881

Reject null hypothesis if P value < α = 0.01 level of significance
P - value = 0.8881 > 0.01, hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is no sufficient evidence to conclude that the difference is significant.