Question

Shipments of coffee beans are checked for moisture content. High moisture content indicates possible water contamination, leading to rejection of shipment. The µ indicate the mean moisture content (in percent by weight) in shipment, and more than 10% will be rejected and standard deviation is known to be 2%.

(a) If 10 measurements will be made on beans chosen, at α = 0.05, what is the power of test if the true moisture content is 12%?

(b) If we want to want to achieve 85% of power in (a), what is the necessary sample size?

Answer 1

a) Rejection region :

Standard deviation: %

Significance level:

We will fail to reject the null (commit a Type II error) if we get X critical value ( X critical)less than 10%

So I will incorrectly fail to reject the null as long as a draw a sample mean that greater that is less than 10%. To complete the problem what I now need to do is compute the probability of drawing a sample mean less than 10% given µ = 12%.

Thus, the probability of a Type II error is given by

The power of the test = 1- probability of type II error = 1- 0.0008 = 0.9992

b) Sample size formula