Question

In a laboratory, a new purification method is being tested that focuses on reducing the three dominant sources of oil concentrations in the production water. 16 independent samples of the oil concentration are taken using this purification method and these samples are found to have an average of 19.8 mg / l. It can be assumed that the measurements are independent and normally distributed with unknown expectation μ and known standard deviation σ = 3.4 mg / l.
b) Find a 95% confidence interval for μ.
How many measurements would one have to take to obtain a confidence interval of maximum 2 mg / l?
The new purification method requires significant investment on the 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 the number of measurements that must be taken if the test in point c) has a strength of at least 0.90 for μ = 20.

Answer 1

Hence there is sufficient evidence to conclude that it is genuinely better than today's technology .