Atrucking 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

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, = 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

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

Formula:

Putting all the values, we have

Now,

Since,  

We reject the null hypothesis and accept the alternate hypothesis.

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