Chapter 11: Inference for Distributions

Key Vocabulary:

§ standard error

§ t distribution

§ degrees of freedom

§ t(k)

§ z statistic

§ one-sample t statistic

§ two-sample t statistic

§ robust

§ power

§ pooled

Calculator Skills:

§ normalpdf (X)

§ tpdf (X, df)

§ ShadeNorm (leftendpoint, rightendpoint)

§ Shade_t (leftendpoint, rightendpoint, df)

§ TInterval

§ T-Test

§ 2-SampTTest

§ 2-SampTInt

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?