A consumer products company is formulating a new shampoo and is interested in fo

Question

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 H0: mu = 175 mm versus HA : mu > 175 mm, using the results of n = 16 samples with a sample mean of -x = 185. Find the value of the boundary of the critical region (that is, find C) if the type | error probability is 0.05. Using n = 16 and the critical region found in part (a), find the type II error probability if the true mean foam height is 195 mm.

Explanation / Answer

H0: µ = 14 H1: µ < 14 a) The statistic is Zc=(X-mean0)/(dev/vn) Zc=(X-14)/(0.3/v16) Error I = 0.05 P(Z P(Z using the table --> Zc= -1.6449 -1.6449 = (X-14)/(0.3/v16) X-14 = -1.6449*(0.3/v16) X=14 -1.6449*(0.3/v16) X=13.8766

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