)A new design for the braking system on a certain type of car has been proposed.
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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 122 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.
a. Suppose braking distance for the new system is normally distributed with = 11. Let x¯ denote the sample average braking distance for a random sample of 30 observations. What is the significance level for the rejection region R:{x¯:x¯116.17}?
b. How would you change the region to obtain a test with =0.05
R:{x¯:x¯
c. For the rejection region in part (a),what is the probability that the new design is not implemented when its true average braking distance is actually 115 ft?
Explanation / Answer
a)
Test statistic, z = (116.17 - 122)/(11/sqrt(30)) = -2.9029
p-value = 0.0018
Significance level for the rejection has to be greater than or equal to 0.0018
b)
z-value for 0.05 significance level is -1.645
xbar = mean + z*sigma
xbar = 122 - 1.645*11/sqrt(30)
xbar = 118.6963201
c)
Xcritical values 128.61
requried probability is 0.0000
mu0 (hypothesised mean) 122 sigma 11 n 30 alpha 0.001 sample/true mean 115 Std. Error. SE = sigma/sqrt(n) 2.0083 Zcritical -3.291Related Questions
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