Respuesta :
Answer:
We conclude that the mean lifetime of a certain tire it uses is less than 40,000 miles which means that the trucking firm’s claim was correct.
Step-by-step explanation:
We are given that 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.
Let [tex]\mu[/tex] = mean lifetime of a certain tire.
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 40,000 miles {means that the mean lifetime of a certain tire it uses is more than or equal to 40,000 miles}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 40,000 miles {means that the mean lifetime of a certain tire it uses is less than 40,000 miles}
The test statistics that will be used here is One-sample z test statistics as we know about the population standard deviation;
T.S. = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean lifetime of 54 tires = 39,460 miles
[tex]\sigma[/tex] = population standard deviation = 1200 miles
n = sample of tires = 54
So, test statistics = [tex]\frac{39,460-40,000}{\frac{1200}{\sqrt{54} } }[/tex]
= -3.307
Hence, the value of test statistics is -3.307.
Now at 0.05 significance level, the z table gives critical value of -1.6449 at for left-tailed test. Since our test statistics is less than the critical value of t as -3.307 < -1.6449, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the mean lifetime of a certain tire it uses is less than 40,000 miles which means that the trucking firm’s claim was correct.
