Question

A tire manufacturing company claims that their tires can be used for at least 150,000 km before they start to wear out. A consumer organization performs a test on the tires. After testing 60 sets, they conclude that the average amount of km the tires can be used, without showing signs of being worn out, is 146,000 km, with a calculated standard deviation of 2000 km. The consumer organization wants to prove that the tires cannot be used for the amount of km that the manufacturer claims. State the hypotheses that need to be tested. Which test should be used? Explain the principle of an ANOVA. That means, what is the theoretical foundation upon which it is based.

Answer 1

The manufacturer claims that their tires can be used for at least 150000 kms before wearing out. We will perform a one-sample t-test to check the same.

Ho: mu <= 150,000

Ha: mu > 150,000

The sample size is 60 sets, n = 60

df = n - 1 = 59

Hence, critical value at df = 59 and alpha = 0.05 is 1.671

t = (X - mu)/(s/√n)

t = (146,000 - 150,000)/(2000/√60)

t = -2√60 = -15.49

As the t-value < +1.671 (one-tailed test), we fail to reject the null hypothesis. We conclude that the manufacturer claim is incorrect.

The principle of ANOVA is to test the differences among the means of two and more populations. The theoretical foundation is that we examine the amount of variation within each of the different samples we have, relative to the amount of variation between the samples.