Question

Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

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 alpha = 0.05, test the trucking firm’s claim.

Answer 1

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.

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
`\mu` = mean lifetime of a certain tire.

SO, Null Hypothesis,
`H_0` :
`\mu \geq` 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,
`H_A` :
`\mu` < 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. =
`(\bar X -\mu)/((\sigma)/(√(n) ) )` ~ N(0,1)

where,
`\bar X` = sample mean lifetime of 54 tires = 39,460 miles

`\sigma` = population standard deviation = 1200 miles

n = sample of tires = 54

So, test statistics =
`(39,460-40,000)/((1200)/(√(54) ) )`

= -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.