Chapter 11: Inference for Distributions
§ standard error
§ t distribution
§ degrees of freedom
§ z statistic
§ one-sample t statistic
§ two-sample t statistic
§ normalpdf (X)
§ tpdf (X, df)
§ ShadeNorm (leftendpoint, rightendpoint)
§ Shade_t (leftendpoint, rightendpoint, df)
11.1 Inference for the Mean of a Population (pp.616-647)
1. Under what assumptions is s a reasonable estimate of s?
2. In general, what is meant by the standard error of a statistic?
3. What is the standard deviation of the sample mean ?
4. What is the standard error of the sample mean ?
5. Describe the similarities between a standard normal distribution and a t distribution.
6. Describe the differences between a standard normal distribution and a t distribution.
7. How do you calculate the degrees of freedom for a t distribution?
8. What happens to the t distribution as the degrees of freedom increase?
9. How would you construct a level C confidence interval for m if s is unknown?
10. The z-Table gives the area under the standard normal curve to the left of z. What does the t-Table give?
11. In a matched pairs t procedure, what is m, the parameter of interest?
12. Samples from normal distributions have very few outliers. If your data contains outliers, what does this suggest?
13. If the size of the SRS is less than 15, when can we use t procedures on the data?
14. If the size of the SRS is at least 15, when can we use t procedures on the data?
15. If the size of the SRS is at least 40, when can we use t procedures on the data?
11.2 Comparing Two Means (pp.648-680)
1. How are two-sample problems different than one-sample problems?
2. Describe two different types of two-sample problems.
3. In a two-sample problem, what assumptions must be made for comparing two means?
4. In a two-sample problem, must/should the two sample sizes be equal?
5. In a two-sample problem, what is the null hypothesis for comparing two means?
6. Explain how to standardize if and are unknown.
7. What assumption must you check if the sample sizes are small? How would you check?
8. If the two sample distributions for a two-sample problem are clearly skewed, how large should the samples be in order to use t procedures?