4 (a) A manager wants to determine the average time it takes a robot-arm to pain

Question

4

(a) A manager wants to determine the average time it takes a robot-arm to paint a UV, and he wants to be able to assert with 90% confidence that the mean of his sample is off by at most 2 min. If the manager can presume from past experience that standard deviation is 8 min, how large a sample will he have to take at? (b) A tire manufacturer claims that the average lifetime of certain tires is 28,000 miles. A trucking firm suspects the claim. To check the claim, the firm puts 40 of these tires on its trucks and gets a mean lifetime of 27, 463 miles with a standard deviation of 1, 348 miles. What can it conclude if the probability of a type-1 error (a) is to be at most 0.01?

Explanation / Answer

a) std deviation =8

margin of error E =2

for 90% CI, z=1.645

hence sample size =(z*std deviaiton/E)2 =~44

b)here std error of mean =std deviaiton/(n)1/2 =213.1375

from above test stat z=(X-mean)/std error =(27463-28000)/213.1375=-2.5195

for 0.01 level critical value =-/+ 2.7079

as test stat z is less then critical value we can not reject null hypothesis that mean is 28000 miles

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