Question

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.5 parts/million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 24 samples is 7.8 ppm with a standard deviation of 0.7. Assume the population is normally distributed. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to three decimal places.

Answer 1

The value of the test statistic is
`t = 2.1`

Explanation:

Our test statistic is:

`t = (X - \mu)/((\sigma)/(√(n)))`

In which X is the sample mean,
`\mu` is the expected value,
`\sigma` is the standard deviation and n is the size of the sample.

The level of ozone normally found is 7.5 parts/million (ppm).

This means that
`\mu = 7.5`

The mean of 24 samples is 7.8 ppm with a standard deviation of 0.7.

This means that
`X = 7.8, \sigma = 0.7, n = 24`

Test Statistic:

`t = (X - \mu)/((\sigma)/(√(n)))`

`t = (7.8 - 7.5)/((0.7)/(√(24)))`

`t = 2.1`

The value of the test statistic is
`t = 2.1`