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

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

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}{(\sigma)/(√(n)) }`

Putting all the values, we have

`z_(stat) = \displaystyle(29400 - 30000)/((1200)/(√(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.