Questions on Descriptive and Inferential Statistics

The questions listed below are designed for discussion and preparation. When reviewing these questions, try to illustrate your points with specific examples/cases from what we have seen in class.

1. Why do we make distinctions between samples and populations in statistics?
2. Discuss the use of exploratory data analysis. Illustrate with an example.
3. Why do we care about the distribution of their data?
4. What are outliers? What impact do they have on how you describe your data?
5. What is a robust statistic? Why would you choose to use it?
6. What is variability? Discuss measures of variability. What are their strengths and weaknesses? In a operations setting, what is the relation of variability to the quality of the product/service?
7. Why do we standardise data? What does a Z-score tell you, i.e., how do you interpret one? How do you convert a raw score to a Z-score?
8. What is the Normal distribution? What is the Standard Normal distribution?
9. How do you use the Normal distribution table to find the percentage of the population that is expected to fall between two points or beyond or below one point in the distribution?
10. What does the Central Limit Theorem tell us?
11. Discuss the differences between descriptive and inferential statistics. Is one better than the other? Are they competitive or complementary? Illustrate the kind of situation in which each approach is appropriate.
12. What are the steps involved in hypothesis testing?
13. What does specifying the null hypothesis mean? What about the alternative hypothesis? What is the benefit of being so specific about the hypotheses?
14. With inferential statistics, the goal is to reject the null hypothesis. What does this mean? Do we conclude that the alternative hypothesis is correct? Why or why not?
15. Why is the standard error of the mean, based on many samples, going to be smaller than the standard deviation of a single sample? In explaining your answer, be sure to describe the interpretation of a standard error of the mean.
16. What types of error can occur when making decisions based on test of hypothesis? Be specific.
17. Why are observations that are more than 3 or less than -3 standard deviations from the mean often considered outliers by some researchers?
18. What does it mean if a researcher sets her \(\alpha = 0.01\), and rejects the null hypothesis? How does this differ from setting the alpha at \(\alpha = 0.05\) and rejecting the null? In which case is the researcher going to be most likely to reject the null hypothesis?
19. What is the difference between a one-tailed (directional) and a two-tailed (non-directional) test? When would you use each of them?
20. What is meant when a researcher says that a finding is statistically significant?