Question

A trucking firm suspects that the mean lifetime of a certain tire it uses is more than 30,000 miles. To check the claim, the firm randomly selects and tests 54 of these tires and gets a mean lifetime of 29,400 miles with a population standard deviation of 1200 miles. At ΅ = 0.05, test the trucking firm's claim. Justify your decision with work. Write a short parargraph about the results of the test and what you can conclude about the claim

Answer 1

Answer:

We conclude that the lifetime of tires is less than 30,000 miles.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 30,000 miles

Sample mean, $\bar{x}$ = 29,400 miles

Sample size, n = 54

Alpha, α = 0.05

Population standard deviation, σ =1200 miles

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 30000\text{ miles}\\H_A: \mu < 30000\text{ miles}$

We use One-tailed z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{29400 - 30000}{\frac{1200}{\sqrt{54}} } = -3.6742$

Now, $z_{critical} \text{ at 0.05 level of significance } = -1.64$

Since,  

$z_{stat} < z_{critical}$

We reject the null hypothesis and accept the alternate hypothesis.

Thus, we conclude that the lifetime of tires is less than 30,000 miles.