A restaurant in a certain state is under new management. While under the previou

Question

A restaurant in a certain state is under new management. While under the previousmanagement, 15%
of the customers rated their dining experiences as "unsatisfactory." Therestaurant's current managers would like to test their belief that this percentage is now lower due to new training procedures. Suppose 72
customers were randomly chosen and asked to rate their dining experiences. Using =0.05,
complete parts a through c below. Calculate the probability of a Type II error occurring if the actual proportion of unsatisfied customers is 10%.

Explanation / Answer

Z score = p - P / sqrt(PQ/n)

-1.645 = p - 0.15/sqrt(0.15*0.85/72)

=> p = 0.2192

Type II error = p [Z < 0.2192 - 0.1/sqrt(0.1*0.9/72)

= p[Z < 3.37]

= 0.9996

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