Question

A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to test if the mean foam height is higher that 175 millimeters using the results of n = 10 samples.
a) Determine the probability that the test will incorrectly indicate that the mean foam height is higher that 175 millimeters, if a critical value of 185 millimeters is used.
b) If the true mean foam height is 185 millimeters, determine the probability that the test will indicate that the mean foam height is higher that 175 millimeters, if a critical value of 185 millimeters is used.

Answer 1