1. How is the central limit theorem related to normal distribution?
Ans: According to the central limit theorem, when you take samples with enough observations (sample size greater than 30), the shape of a distribution of sample means approaches normal.
Learning Objective: 8-1 What is the standard error?
Cognitive Domain: Comprehension
Answer Location: The Distribution of Sample Means Revisited
2. Briefly describe the hypothesis testing procedure.
Ans: The first step in hypothesis testing procedure is to state your null and research hypothesis, then set a decision criterion for making a decision about the hypothesis. Next, you would collect your data and calculated statistics. Finally, you make decision about the hypothesis.
Learning Objective: 8-3: What are the steps in hypothesis testing?
Cognitive Domain: Knowledge
Answer Location: Logic of Hypothesis Testing
3. Is it possible for a researcher to avoid making Type 1 and Type 2 errors? Explain your answer.
Ans: There is no way for a researcher to avoid making Type 1 and Type 2 errors. If the researcher rejects the null hypothesis, the researcher could be making a Type 1 error. If the researcher fails to reject the null hypothesis, the researcher could be making a Type 2 error. Because these decisions are based on the probability, one can never be sure if the decision is correct.
Learning Objective: 8-5: What types of errors exist in our hypothesis-testing procedure?
Cognitive Domain: Application
Answer Location: Types of Hypothesis-Testing Errors