10 years ago the University administration was concerend about the quality of the Cafeteria. They did a survey of several hundred students and asked them the question "How do you rate the food in the Cafeteria, on a scale of 1 to 10, 10 meaning the food is great?". The survey resulted in a mean score of 4.76. This was considered low, so the University made and implemented a "10 Year Master plan" for improving the Cafeteria. The 10 years are up, and they want to see whether the plan worked. So they are planning to repeat the survey to see whether the attitudes of the students have gone up. After the survey is done the University statisticians will carry out a hypothesis test with
1) a = 0.05
2) H0: m=4.76
3) Ha: m>4.76
Answer the following questions:
1) In your own words, what does "m=4.76" mean?
2) In your own words, what does "m>4.76" mean?
3) In your own words, what is the type I error here? Find three possible consequences of the type I error.
4) In your own words, what is the type II error here? Find three possible consequences of the type II error.
5) Say they interview 150 students, and the standard deviation turns out to be 1.35. If it were true that today m=5.02, what would be the power of the test? Use the Calc > Power and Sample Size > 1-sample t command. Explain in your own words what your answer means.
6) Using the same numbers as in part 5) (except the 5.02), what would the mean score today have to be so that the type II error probability b=0.05? Play around with the Calc > Power and Sample Size > 1-sample t command to answer this question
7) If in fact m=5.02, what sample size would be needed so that b=0.05? Again play around with the Calc > Power and Sample Size > 1-sample t command to answer this question