Question

A trucking firm is suspicious of the claim that the average lifetime of certain tires is at least 28,000 miles. To check the claim, the firm puts 40 of theses on its trucks, and gets a mean lifetime of 27,463 miles with a standard deviation of 1,348 miles. Test the claim using 0.01?

Answer 1

Answer:

There is not enough evidence to support the claim that the average lifetime of certain tires is at least 28,000 miles.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 28,000 miles

Sample mean, $\bar{x}$ = 27,463 miles

Sample size, n = 40

Alpha, α = 0.01

Sample standard deviation, s =  1,348 miles

First, we design the null and the alternate hypothesis

$H_{0}: \mu \geq 28000\text{ miles}\\H_A: \mu < 28000\text{ miles}$

We use one-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{27463 - 28000}{\frac{1348}{\sqrt{40}} } = -2.519$

Now,

$t_{critical} \text{ at 0.05 level of significance, 9 degree of freedom } = -2.4258$

Since, the calculated test statistic is less than the the critical t value, we fail to accept the null hypothesis and accept the alternate hypothesis.  

We conclude that there is not enough evidence to support the claim that the average lifetime of certain tires is at least 28,000 miles.