46.9k views
0 votes
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.4 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 23 samples is 4.2 ppm with a standard deviation of 0.7. Does the data support the claim at the 0.01 level? Assume the population distribution is approximately normal. Step 1 of 5: State the null and alternative hypotheses.

User ITake
by
7.7k points

1 Answer

7 votes

Solution:

To test the hypothesis is that the mean ozone level is different from 4.40 parts per million at 1% of significance level.

The null hypothesis and the alternative hypothesis is :


$H_0: \mu = 4.40$


$H_a: \mu \\eq 4.40$

The z-test statistics is :


$z=(\overline x - \mu)/(\left( \sigma / \sqrt n \right)) $


$z=(4.2 - 4.4)/(\left(0.7 / √(23) \right)) $


$z =(-0.2)/(0.145)$

z = -1.37

The z critical value for the two tailed test at 99% confidence level is from the standard normal table, he z critical value for a two tailed at 99% confidence is 2.57

So the z critical value for a two tailed test at 99% confidence is ± 2.57

Conclusion :

The z values corresponding to the sample statistics falls in the critical region, so the null hypothesis is to be rejected at 1% level of significance. There is a sufficient evidence to indicate that the mean ozone level is different from 4.4 parts per million. The result is statistically significant.

User Aleks Tkachenko
by
8.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.