Question

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.8 parts/million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 16 samples is 8.2 ppm with a standard deviation of 0.6. Assume the population is normally distributed. A level of significance of 0.01 will be used. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

The value of the test statistic is
`t = 2.67`

Explanation:

The null hypothesis is:

`H_(0) = 7.8`

The alternate hypotesis is:

`H_(1) \\eq 7.8`

Our test statistic is:

`t = (X - \mu)/((\sigma)/(√(n)))`

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

In this problem, we have that:

`X = 8.2, \mu = 7.8, \sigma = 0.6, n = 16`

Then

`t = (X - \mu)/((\sigma)/(√(n)))`

`t = (8.2 - 7.8)/((0.6)/(√(16)))`

`t = 2.67`

The value of the test statistic is
`t = 2.67`