Question

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

H_a

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.

Answer 1

Solution :

= 7.7

= 7.6

= 1.1

n = 870

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 7.7

H_a :    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 z_c​=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.