Question

A safety engineer records the braking distances of two types of tires. Each randomly selected sample has 35 tires. The results of the tests are shown in the table. At alphaαequals=0.10, can the engineer support the claim that the mean braking distance is different for the two types of tires? Assume the samples are randomly selected and that the samples are independent. Complete parts (a) through (e).

Type A
x overbar 1x1	equals=	41 feet
sigma 1σ1	equals=	4.5 feet
Type B
x overbar 2x2	equals=	44 feet
sigma 2σ2	equals=	4.2 feet

1. Find critical value(s)
2. Identify the Claim
3. Find rejection regions
4. Find the standardized test statistic z for μ1−μ2.
5. Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below
6. Interpret the decision in the context of the original claim

At the ____% significance level, there is _____ evidence to ­­­­____ the claim that the mean braking distance for Type A tires is ______the one for Type B tires.

Answer 1

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


t = -2.8833

Test Criteria :-
Reject null hypothesis if


DF = 67

Critical values   

Result :- Reject Null Hypothesis

Decision based on P value
P - value = P ( t > 2.8833 ) = 0.0053
Reject null hypothesis if P value < level of significance
P - value = 0.0053 < 0.1 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

At the __10__% significance level, there is __sufficient___ evidence to ­­­­__support__ the claim that the mean braking distance for Type A tires is ___different___the one for Type B tires.