Question

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 5.5 parts/million (ppm). A researcher believes that the current ozone level is at an excess level. The mean of 6 samples is 5.9 ppm with a variance of 0.49. Does the data support the claim at the 0.05 level? Assume the population distribution is approximately normal.

Step 2 of 5 : Find the value of the test statistic. Round your answer to three decimal places.

Specify if the test is one-tailed or two tailed

Determine the decision rule for rejecting the null hypothesis.

Make the decision to reject or fail to reject the null hypothesis

Answer 1

Solution: Here the given information are as below

n=6, =5.9, Variance==0.49, We use standard deviation =s=0.7

The level of ozone normally found is 5.5 parts/million (ppm) = =5.5

Test statistic:

t=

=

t =1.399

The given test is one tailed test because A researcher believes that the current ozone level is at an excess level.

Decision rule :

Critical value=tc = = = -2.015 (left tailed test)-----------(from t table)

Since it is observed that t=1.399 tc=-2.015.it is then concluded that the null hypothesis is not rejected.

Conclusion:

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ is less than 5.5, at the 0.05 significance level.