A consumer products company is formulating a new shampoo and is interested in foam height (in mm). Foam height is approximately normally distributed and has a standard deviation of 20 mm. The company wishes to test H_{0} : \mu=175H 0:μ=175mm versus H_{1} : \mu>175 mm, H 1:μ>175mm, using the results of n = 10 samples. (a) Find the P-value if the sample average is \overline{x}=185 x =185
(b) What is the probability of type II error if the true mean foam height is 200 mm and we assume that \alpha = 0.05?α=0.05?
(c) What is the power of the test from part (b)?