A restaurant in a certain state is under new management. While under the previou
ID: 3068991 • Letter: A
Question
A restaurant in a certain state is under new management. While under the previous management, 15% of the customers rated their dining experiences as unsatisfactory." The restaurant's current managers would like to test their belief that this percentage is now lower due to new training procedures. Suppose 75 customers were randomly chosen and asked to rate their dining experiences. Using -010, complete parts a through c below a. Explain how Type l and Type Il errors can occur in this hypothesis test. Choose the correct answer below A. A Type l error can occur if the proportion of unsatisfied customers is above or equal to 0.15 and the null hypothesis is not rejected. A Type II error can occur if the proportion of unsatisfied customers is below 0.15 and the null hypothesis is rejected B. A Type l error can occur if the proportion of unsatisfied customers is below 0.15 and the null hypothesis is rejected. A Type ll error can occur if the proportion of unsatisfied customers is above or equal to 0.15 and the null hypothesis is not rejected C. A Type l error can occur if the proportion of unsatisfied customers is above or equal to 0.15 and the null hypothesis is rejected. A Type Il error can occur if the proportion of unsatisfied customers is below 0.15 and the null hypothesis is not rejected D. A Type l error can occur if the proportion of unsatisfied customers is below 0.15 and the null hypothesis is not rejected. A Type ll error can occur if the proportion of unsatisfied customers is above or equal to 0.15 and the null hypothesis is rejected b. Calculate the probability of a Type II error occurring if the actual proportion of unsatisfied customers is 11% The probability of committing a Type Il error is (Round to three decimal places as needed.)Explanation / Answer
Ans:
b)Critical z value=normsinv(0.1)=-1.282
critical sample proportion=0.15-1.282*sqrt(0.15*(1-0.15)/75)=0.0972
Now,as true proportion is 0.11,so
z=(0.0972-0.11)/sqrt(0.11*(1-0.11)/75)
z=-0.355
Type II error=P(z>-0.355)=0.639