Question

A new design for the braking system on a certain type of car has been proposed. For the current system, the true average braking distance at 40 mph under specified conditions is known to be 120 ft. It is proposed that the new design be implemented only if sample data strongly indicates a reduction in true average braking distance for the new design.

(b) What is the P-value in this case? (Round your answer to four decimal places.) ......

(c) What is the probability that the new design is not implemented when its true average braking distance is actually 115 ft and the test from part (b) is used? (Round your answer to four decimal places.)

Answer 1

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  Solution 1) Null Hypothesis The average breaking system on a certain type of a car is 120 ft Alternative Hypothesis The average breaking system on a certain type of a car is not equal 120 ft The test statistic value is given as 117.2-120 36 Conclusion Use a significance level, a 0.05 Here, Z value is 1.53, which is less than the value of Zoo5 1.96 That is, F -53)Zo0 1.96) Therefore, by the rejection rule, do not reject the null hvpothesis Ho

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  Interpretation There is no evidence at level of significance a 0.05 That is, the average breaking system on a certain type of a car is 120 ft. Since it is two tailed test the p- value in this case is given as 2P(Z<-1.53)=2(0.06301 ) 0.12602 - 0.1260 Thus, the p value is 0.1260. 3) Null Hypothesis: The average breaking system on a certain type of a car is 120 ft. Alternative Hypothesis: The average breaking system on a certain type of a car is not equal 120 ft.

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  The test statistic value is given as 72 115-120 /36 --2.72 -2.72 Conclusion: Use a significance level, α-005 Here, Z value is 2.72, which is greater than the value of Z0s1.96 That is, F(-2.72)Z1.96) Therefore, by the rejection rule, reject the null hypothesis H Interpretation:

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  There is an evidence at level of significance α-0.05 That is, the average breaking system on a certain type of a car is not equal to120 ft. Since it is two tailed test the p value in this case is given as 2P(Z<-2.73) 2(0.00317) 0.00634 -0.0063 Thus, the p- value is 0.0063