Question

2) A trucking firm suspects that the mean lifetime of a certain tire it uses is less than 40,000 miles. To check the claim, the firm randomly selects and tests 54 of these tires and gets a mean lifetime of 39,460 miles with a population standard deviation of 1200 miles. At = 0.05, test the trucking firm’s claim.

Answer 1

Hypothesis test Ho : 112 40000 Ha : μ < 40000 (Null Hypothesis, Ho : μ-40000 is also correct) (Alternative Hypothesis, also called H1 This is lower tailed test i-39460 ơ-1200 n 54 Significance Level, a -0.05 --μ 39460-40000 Test statistic z*-- ะ-3.306811 ะ-3.31 Test Statistic, z-3.31 P-value is in direction of Alternative hypothesis Since Ha : μ < 40000. P-value= P(Z <-3.31) P-value is Area to the left of test statistic-3.31 P-value 0.0005 test statistic =-3.31 P-value P(Z<-3.31) 0.0005(from z-table) P-value0.0005 Rejection Rule: Reject H0 if p-value < α Using excel function normdist(((39460-40000)/(1200/sqrt(54))),0,1, TRUE) or TI's function normalcdfE-99, ( (39460- 40000)/(1200/sqrt (54) answer is: 0.0004718224 Decision: Since 0.00050.05, we reject the null hypothesis Hence at 5% significance level, we have sufficient evidence to conclude that μ is less than 40000