Question

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 6.5 parts/million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 27 samples is 6.9 ppm with a variance of 1.21. Assume the population is normally distributed. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to three decimal places.

Answer 1

Answer:  t = 1.890

Step-by-step explanation:

Let $\mu$ be the population mean amount of ozone in the upper atmosphere.

As per given , we have

$H_0:\mu=6.5\\\\ H_a: \mu\neq6.5$

Sample size : n= 27

Sample mean = $\overline{x}=6.9$

Sample variance = $\sigma^2=1.21\\\\\Rightarrow\ \sigma=\sqrt{1.21}=1.1$

Since population standard deviation is now given , so we use t-test.

Test statistic : $t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}$

$t=\dfrac{6.9-6.5}{\dfrac{1.1}{\sqrt{27}}}\\\\ t=\dfrac{0.4}{0.211695}\\\\ t=1.8895108528\approx1.890$

Hence, the value of the test statistic : t = 1.890