Question

Incinerators can be a source of hazardous emissions into the atmosphere. Stack gas samples were collected from a sample of 50 incinerators in a major city and compared against the environmental standard. Part a Of the 50 samples, only 18 passed the environmental test. Can it be concluded that fewer than half of the incinerators in the city meet the standard?

Answer 1

Yes, we can conclude that fewer than half of the incinerators in the city meet the standard

Explanation:

The null and alternative hypothesis are stated as;

H0: p = 0.5

H0: p < 0.5

The significance level is 0.05

The sample proportion of incinerators is;

p' = 18/50

p' = 0.36

The formula for the z-value of the test statistic of the hypothesis test can be calculated from;

z = (p' - p)/√[p(1 - p)/n]

z = (0.36 - 0.5)/√[0.5(1 - 0.5)/50]

z ≈ -1.98

So the test statistic value is - 1.98

From the table i attached the p value is gotten from P(z < -1.98) because tail of the test is left tailed that is tested here.

Thus, p-value = 0.0238

Conclusion:

The significance level is 0.05 and the p-value is 0.0238. The p-value is less than the significance level and thus, we reject the null hypothesis.

We can now say, that fewer than half of the incinerators in the city meet the standard