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 7.0 parts/million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 1000 samples is 6.9 ppm. Assume a population standard deviation of 1.2. Does the data support the researcher's claim at the 0.02 level?

Step 1 of 5 : State the null and alternative hypotheses.

Step 2 of 5 :  Find the value of the test statistic. Round your answer to two decimal places.
Step 3 of 5 : Specify if it is one tailed or two tailed
Step 4 of 5 :  Find the P-value of the test statistic. Round your answer to four decimal places.
Step 5 of 5 : Make the decision to reject or fail to reject the null hypothesis.

Solutions

Expert Solution

Solution :

Given that,

Step 1 of 5

The null and alternative hypothesis is,  

Ho: 7.0

Ha: 7.0

Step 2 of 5 :

The test statistics,

Z =( - )/ (/n)

= ( 6.9 - 7 ) / ( 1.2 / 1000 )

= -2.64.

Step 3 of 5 :

This a right (One) tailed test.

Step 4 of 5 :

P- Value = P(Z > z )

= 1 - P(Z < -2.63 )

= 0.9957

Step 5 of 5 :

The p-value is p = 0.9957, and since p = 0.9957 > 0.02, it is concluded that fail to reject the null hypothesis.


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