Question

Government regulations restrict the amount of pollutants that can be released into the atmosphere through industrial smokestacks. REM industries claims that their smokestacks release an average number of pollutants of 5 parts per billion. To test this claim, the government collects a sample from 81 smokestacks and finds that the mean pollutant level is 4.79 parts per billion. Suppose the standard deviation is known to be 1.08 parts per billion. Is there enough evicence to suggest that the average number of pollutants is different from the claim at the .05 level of significance? Use the p-value approach to make your decision.

Answer 1

Solution

Given,

Claim to be tested is "smokestacks release an average number of pollutants of 5 parts per billion" vs "the average number of pollutants is different from the claim"

So, the hypothesis can be written as

H0: μ=μ0=5 vs   H1: μ ≠ 5

n = 81

= 4.59

= 1.08

= 0.05

Since the population SD() is known , we use z test

The test statistic z is given by

z =   

= (4.79 - 5)/(1.08/81)

= -1.75

Now , ≠ sign in H1 indicates that the test is two tailed

p value = 2 * P(Z < -1.75)

= 2 * 0.0401

= 0.0802

We observe that , p value = 0.0802 is greater than = 0.05

So, we fail to reject the null hypothesis at 0.05 level.

There is NOT enough evidence to suggest that the average number of pollutants is different from the claim at the .05 level of significance