Question

In: Statistics and Probability

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level...

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.7 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 870 samples is 7.6 ppm. Assume a population standard deviation of 1.1. Does the data support the researcher's claim at the 0.02 level?

Step 1 of 6: State the null and alternative hypotheses.

H0
Ha

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Step 4 of 6: Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6: Identify the level of significance for the hypothesis test.

Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

Solutions

Expert Solution

Solution :

= 7.7

= 7.6

= 1.1

n = 870

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :   = 7.7

Ha :    7.7

Test statistic = z

= ( - ) / / n

= (7.6- 7.7) /1.1 / 870

= -2.68

Two tailed test

P(z < -2.68  ) = 0.0073

P-value = 0.0073

= 0.02

The critical value for a two-tailed test is zc​=2.33.

p= 0.0073 < 0.02, it is concluded that the null hypothesis is rejected.

Reject the null hypothesis .

There is enough evidence to claim that the population mean μ is different than 7.7, at the 0.02 significance level.


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