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

Answer:

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

Step-by-step explanation:

Our test statistic is:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

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:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$t = \frac{7.8 - 7.5}{\frac{0.7}{\sqrt{24}}}$

$t = 2.1$

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