Question

A research team is testing whether a fuel aditive increases a car's gas mileage. The maker of the additive claims that the additive will increase a car's gas mileage by at least 6 mpg. Among 25 cars that were treated with the additive, the average increase in mileage was 5.3 mpg with a standard deviation of 1.8 mpg. The research team found the z-score to be -1.94. Is there enough evidence to reject the company's evidence?

Answer 1

Yes there is sufficient evidence to reject the company's evidence

Explanation:

From the question we are told that

The sample size is n = 25

The mean is
`\= x = 5.3 \ mpg`

The standard deviation is
`\sigma = 1.8 \ mpg`

The z-score is z = -1.94

The null hypothesis is
`H_o : \mu = 6 \ mpg`

The alternative hypothesis is
`H_a : \mu \\e 6`

Generally the p-value is mathematically evaluated as

`p-value = 2 * P( Z <-1.94)`

From the z table the area under the normal curve to the left corresponding to -1.94 is

`P( Z <-1.94) = 0.02619`

=>
`p-value = 2 * 0.02619`

=>
`p-value = 0.052`

Let assume the level of significance is
`\alpha = 0.05`

Hence the
`p-value > \alpha` this mean that

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is sufficient evidence to reject the company's evidence