1. Why is the sample mean an unbiased estimator of the population mean?
2. Why does the standard error of the mean decrease as the sample size, n, increases?
3. Why is it true that for a given sample size, n, an increase in confidence is achieved by widening (and making less precise) the confidence interval?
4. Why is the sample size needed to determine the proportion smaller when the population proportion is 0.20 than when the population proportion is 0.50?
5. What is the difference between a one-tail and a two-tail hypothesis test?
6. How can a confidence interval estimate for the population mean provide conclusions for the corresponding two-tail hypothesis test for the population mean?
7. How do you evaluate the assumptions of regression analysis?
8. What is the interpretation of the Y intercept and the slope in the simple linear regression equation?
9. What is the difference between attribute control charts and variables control charts?
10. Suppose that you have been hired as a summer intern at a large amusement park. Every day, your task is to conduct 200 exit interviews in the parking lot when customers leave. You need to construct questions to address the cleanliness of the park and the customers' intent to return. When you begin to construct a short questionnaire, you remember the control charts you learned in a statistics course, and you decide to write questions that will provide you with data to graph on control charts. After collecting data for 30 days, you plan to construct the control charts.
a. Give a question that will allow you to develop a control chart of customers' perceptions of cleanliness of the park.
b. Give examples of common cause variation and special cause variation for the control chart.
c. If the control chart is in control, what does that indicate and what do you do next?
d. If the control chart is out of control, what does this indicate and what do you do next?
e. Repeat (a) through (d), this time addressing the customers' intent to return to the park.
f. After the initial 30 days, assuming that the charts indicate in-control processes or that the root sources of special cause variation have been corrected, explain how the charts can be used on a daily basis to monitor and improve the quality in the park.