Question

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.5 parts/million (ppm). A researcher believes that the current ozone level is at an excess level. The mean of 980 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? a) State the null and alternative hypothesis. b) test statistic c) One tailed or two tailed? d) What is the P-value of the test statistic? e)Identify the level of significance for the hypothesis test. f) Reject or fail to reject the null hypothesis?

Answer 1

Solution :

Given that,

a)

The null and alternative hypothesis is,  

Ho: 7.5

Ha: 7.5

b)

The test statistics,

Z =( - )/ (/n)

= ( 7.6 - 7.5 ) / ( 1.1 / 980 )

= 2.85

c)

This a right (One) tailed test.

d)

P-value = P(Z > z )

= 1 - P(Z < z )

= 1 - P(Z < 2.85 )

= 1 - 0.9978

= 0.0022

e)

The p-value is p = 0.0022, and since p =0.0022 < 0.02 , it is concluded that the null hypothesis is rejected.

f)

Reject the null hypothesis.