Question

A chemical plant is required to maintain ambient sulfur levels in the working environment atmosphere at an average level of no more than 12.50. The results of 15 randomly timed measurements of the sulfur level produced a sample mean of Y = 14.82 and a sample standard deviation of s = 2.91.

Required:
Is there evidence that the chemical plant is in violation of the working code?

Answer 1

Since the calculated value of z= 3.101 falls in the critical region it is concluded that average level of the chemical is greater than 12.50. The null hypothesis is rejected. There is evidence that the chemical plant is in violation of the working code.

Explanation:

Here

The population mean = u= 12.50

The sample mean = x`= 14.83

The sample size= n= 15

Sample standard deviation= 2.91

Let the null and alternate hypotheses be

H0 : u ≤ 12.50 against the claim that Ha: u > 12.50

Applying z- test

z= x`-u/s/√n

Z= 14.83-12.5/ 2.91/√15

Z= 2.33/ 0.751

z= 3.101

The significance level is chosen to be 0.05

The critical value of z at 0.05 > 1.645 for one tailed test

Since the calculated value of z= 3.101 falls in the critical region it is concluded that average level of the chemical is greater than 12.50. The null hypothesis is rejected. There is evidence that the chemical plant is in violation of the working code.