The new purification method requires significant investments in installations in the sea before it can be used there. It is therefore desirable to be sure that it is genuinely better than today's technology which gives an expected emission of μ = 21.6 mg / l.

c) Formulate this as a hypothesis testing problem and perform the test. Use level α = 0.01. Calculate the p-value of the test.
d) Calculate the strength of the test in point c) for μ = 20.
Calculate how many measurements must be taken if the test in point c) has a strength of at least 0.90 for μ = 20.

Certain properties of the cleaning method mean that there is reason to suspect that the standard deviation σ is also different when using the new cleaning method. We shall therefore now assume that σ is also unknown. From the 16 measurements that yielded an average of 19.8, a sample standard deviation of s = 1.9 was obtained.

e) Find a 95% confidence interval for σ
Finally, retest the test from point c) under the new prerequisites. Explain why we are reaching a different conclusion now.