Question

a manufacturer claims that his tires last at least 40,000 miles. a test on 25 tires reveals that the mean life of a tire is 39,750 miles, with a standard deviation of 387 miles. test the manufacturers claim at α = .01. what is the t score for the sample?

Explanation:

Step1: Recall the t - score formula

The formula for the t - score in a one - sample t - test is \(t=\frac{\bar{x}-\mu}{s/\sqrt{n}}\)

Given that \(\bar{x} = 39750\) (sample mean), \(\mu=40000\) (population mean), \(s = 387\) (sample standard deviation), and \(n = 25\) (sample size)

Step2: Substitute the values into the formula

First, calculate the denominator \(s/\sqrt{n}=\frac{387}{\sqrt{25}}=\frac{387}{5}=77.4\)

Then, calculate the numerator \(\bar{x}-\mu=39750 - 40000=- 250\)

Now, find the t - score: \(t=\frac{-250}{77.4}\approx - 3.23\)

Answer:

\(t\approx - 3.23\)