Question

In a study of distances traveled by buses before the first major engine failure, a sample of 191 buses results in a mean of 96,700 miles and a population standard deviation 37,500 miles. Calculate the appropriate test statistic to test the claim that the mean distance traveled before a major engine failure is more than 90,000 miles.

Answer 1

The test statistics is
`z = 2.47`

Explanation:

From the question we are told that

The sample size is n = 191 \ buses

The sample mean is
`\= x = 96 700 \ miles`

The population standard deviation is
`\sigma = 37 500 \ miles`

The null hypothesis is
`H_o : \mu = 90 000`

The alternative hypothesis is
`H_a : \mu > 90 000`

Generally the test statistics is mathematically represented as

`z = (\= x - \mu )/( (\sigma )/(√(n) ) )`

=>
`z = (96700 - 90 000 )/( (37500)/(√(191) ) )`

=>
`z = 2.47`