Question

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.

Answer 1

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.