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

Answer:

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

Step-by-step explanation:

The null hypothesis is:

$H_{0} = 7.8$

The alternate hypotesis is:

$H_{1} \neq 7.8$

Our test statistic is:

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

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

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

$t = \frac{8.2 - 7.8}{\frac{0.6}{\sqrt{16}}}$

$t = 2.67$

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