Download Chapter 11 Statistics

Chapter 8 The Binomial and Geometric Distributions pp. 510 – 559
Case Closed Psychic probability p. 511 and pp. 554-555
Section 8.1 Objectives – The Binomial Distributions
1. Describe the conditions that need to be present to have a binomial setting.
2. Define a binomial distribution.
3. Explain when it might be all right to assume a binomial setting even thought the independence condition is not
satisfied.
4. Explain what is meant by the sampling distribution of a count.
5. State the mathematical expression that gives the value of a binominal coefficient. Explain how to find the value
of that expression. State the mathematical expression used to calculate the value of binomial probability..
6. Evaluate a binomial a probability by using the mathematical formula for P(X=k).
7. Explain the difference between binompdf(n,p,X) and binomcdf(n,p,X).
8. Use your calculator to help evaluate a binomial probability.
9. If X is B(n,p), fin
and
(that is, calculate the mean and variance of a binomial distribution).
10. Use a Normal approximation for a binomial distribution to solve questions involving binomial probability.
Section 8.2 Objectives – The Geometric Distributions
11. Describe what is meant by a geometric setting.
12. Given the probability of success, p, calculate the probability of getting the first success on the nth trial.
13. Calculate the mean (expected value) and the variance of a geometric random variable.
14. Calculate the probability that it takes more than n trials to see the first success for a geometric random variable.
15. Use simulation to solve geometric probability problems.
Chapter 9 Sampling Distributions pp. 560 – 609
Case Closed Building Better Batteries p. 561 and pp. 604 – 605
Section 9.1 Objectives – Sampling Distributions
1. Compare and contrast parameter and statistic.
2. Explain what is meant by sampling variability.
3. Define the sampling distribution of a statistic.
4. Explain how to describe a sampling distribution.
5. Define an unbiased statistic and an unbiased estimator.
6. Describe what is meant by the variability of a statistic.
7. Explain how bias and variability are related to estimating with a sample.
Section 9.2 Objectives – Sample Proportions
8. Describe the sampling distribution of a sampling distribution of a sample proportion.(Remember: “describe”
means tell about shape, center, and spread.)
9. Compute the mean and standard deviation for the sampling distribution of .
10. Identify the “rule of thumb” that justifies the use of the recipe for the standard deviation of .
11. Identify the conditions necessary to use a Normal approximation to the sampling distribution of .
12. Use a Normal approximation to the sampling distribution of to solve probability problems involving .
Section 9.3 Objectives – Sample Means
13. Given the mean and standard deviation of a population, calculate the mean and standard deviation for the
sampling distribution of a sample mean.
14. Identify the shape of the sampling distribution of a sample mean drawn from a population that has a Normal
distribution.
15. State the central limit theorem.
16. Use the central limit theorem to solve probability problems for the sampling distribution of a sample mean.
Chapter 10 Estimating with Confidence pp. 614 – 683
Case Closed Need help? Give us a call! p.615 and p. 677
Introduction Objectives:
1. Explain what is meant by statistical inference.
2. Explain how probability is used to make conclusions in statistical inference.
Section 10.1 Objectives – Confidence Intervals: The Basics
3. List the (six) basic steps in the reasoning of statistical estimation.
4. Distinguish between a point estimate and an interval estimated.
5. Identify the basic form of all confidence intervals.
6. Explain what is meant by margin of error.
7. State in nontechnical language what is meant by a “level C confidence interval.”
8. State the three conditions that need to be present in order to construct a valid confidence interval.
9. Explain what it means by the “critical p critical value” of the standard Normal distribution.
10. For a known population standard deviation σ, construct a level C confidence interval for a population mean.
11. List the four necessary steps in the creation of a confidence interval (see Inference Toolbox).
12. Identify three ways to make the margin of error smaller when constructing a confidence interval.
13. Once a confidence interval has been constructed for a population value, interpret the interval in the context of
the problem.
14. Determine the sample size necessary to construct a level C confidence interval for a population mean with a
specified margin of error.
15. Identify as many of the six “warnings” about constructing a confidence interval.
16. Once a confidence interval has been constructed for a population vale, interpret the interval in the context of
the problem.
17. Determine the sample size necessary to construct a level C confidence interval for a population mean with a
specified margin of error.
18. Identify as many of the six “warnings” about constructing confidence intervals as you can. (For example, a nice
formula cannot correct for bad data.)
Section 10.2 Objectives – Estimating a Population Mean
19. Identify the three conditions that must be present before estimating a population mean..
20. Explain what is meant by the standard error of a statistic in general and by the standard error of the sample
mean in particular.
21. List three important facts about the t distributions. Include comparisons to the standard Normal curve.
22. Use Table C to determine critical t value of a given level C confidence interval for a mean and a specified number
of degrees of freedom.
23. Construct a one-sample t confidence interval for a population mean (remembering to use the four-step
procedure).
24. Describe what is meant by paired t procedures.
25. Calculate a level C t confidence interval for a set of paired data.
26. Explain what is meant by a robust inference procedure and comment on the robustness of t procedures.
27. Discuss how sample size affects the usefulness of t procedures.
Section 10.3 Objectives – Estimating a Population Proportion
28. Given a sample proportion, , determine the standard error of
29. List the three conditions that must be present before constructing a confidence interval for an unknown
population proportion.
30. Construct a confidence interval for a population proportion, remembering to use the four-step procedure (see
the Inference Toolbox, p. 631).
31. Determine the sample size necessary to construct a level C confidence interval for a population proportion with
a specified margin of error.
Chapter 11 Testing a Claim pp. 684 – 739
Case Closed I’m getting a headache! p. 685 and p. 734
Section 11.1 Objectives – Significance Tests: The Basics
1. Explain why significance testing looks for evidence against a claim rather than in favor of the claim.
2. Define null hypothesis and alternative hypothesis.
3. Explain the difference between a one-sided hypothesis and a two-sided hypothesis.
4. Identify the three conditions that need to be present before doing a significance test for a mean.
5. Explain what is meant by a test statistic. Give the general form of a test statistic.
6. Define P-value.
7. Define significance level.
8. Define statistical significance (statistical significance at level α).
9. Explain the difference between the P-value approach to significance testing and the statistical significance
approach.
Section 11.2 Objectives – Carrying Out Significance Tests
10. Identify and explain the four steps involved in formal hypothesis testing.
11. Using the Inference Toolbox, conduct a z test for a population mean.
12. Explain the relationship between a level α two-sided significance test for μ and a level 1 – α confidence interval
for μ.
13. Conduct a two-sided significance test for μ using a confidence interval.
Section 11.3 Objectives – Use and Abuse of Tests
14. Distinguish between statistical significance and practical importance.
15. Identify the advantages and disadvantages of using P-values rather than a fixed level of significance.
Section 11.4 Objectives – Using Inference to Make Decisions
16. Define what is meant by a Type I error.
17. Define what is meant by a Type II error.
18. Describe, given a real situation, what constitutes a Type I error and what the consequences of such an error
would be.
19. Describe, given a real situation, what constitutes a Type II error and what the consequences of such and error
would be.
20. Describe the relationship between significance level and a Type I error.
21. Define what is meant by the power of a test.
22. Identify the relationship between the power of a test and a Type II error.
23. List four ways to increase the power of a test.
24. Explain why a large value for the power of a test is desirable.
Chapter 12 Significance Tests in Practice pp. 772 – 777
Case Closed Do you have a fever? p. 741 and pp. 773 – 774
Section 12.1 Objectives – Tests about a Population Mean
1. Define the one-sample t statistic.
2. Determine critical values of t (t*), from a “t table” given the probability of being to the right or left of t*.
3. Determine the P-value of a t statistic for both a one- and two-sided significance test.
4. Conduct a one-sample t significance test for a population mean using the Inference Toolbox.
5. Conduct a paired t test for the difference between two population means.
Section 12.2 Objectives – Tests about a Population Proportion
6. Explain why
, rather that , is used when computing the standard error of
in a significance test for a
population proportion.
7. Explain why the correspondence between a two-tailed significance test and a confidence interval for a
population proportion is not as exact as when testing for a population mean.
8. Explain why the test for a population proportion is sometimes called a large sample test.
9. Conduct a significance test for a population proportion using the Inference Toolbox.
10. Discuss how significance tests and confidence intervals can be used together to help draw conclusions about a
population proportion.
Chapter 13 Comparing Two Population Parameters pp. 778 – 831
Case Closed Fast-food frenzy! p. 779 and pp. 825 – 826
Section 13.1 Objectives – Comparing Two Means
1. Identify situations in which two-sample problems might arise.
2. Describe the three conditions necessary for doing inference involving two population means.
3. Clarify the difference between the two-sample z statistic and the two-sample t statistic.
4. Identify the two practical options for using two-sample t procedures and how they differ in terms of computing
the number of degrees of freedom.
5. Conduct a two-sample significance test for the difference between two independent means using the Inference
Toolbox.
6. Compare the robustness of two-sample procedures with that of one-sample procedures. Include in your
comparison the role of equal sample sizes.
7. Explain what is meant by “pooled two-sample t procedures,” when pooling can be justified, and why it is
advisable not to pool.
Section 13.2 Objectives – Comparing Two Proportions
8. Identify the meant and standard deviation of the sampling distribution of
9. List the conditions under which the sampling distribution of
10. Identify the standard error of
1
-
2
1
-
2
1
-
2.
is approximately Normal.
when constructing a confidence interval for the difference between two
population proportions.
11. Identify the three conditions under which it is appropriate to construct a confidence interval for the difference
between two population proportions.
12. Construct a confidence interval for the difference between two population proportions using the four-step
Inference Toolbox for confidence intervals.
13. Explain why, in a significance test for the difference between two proportions, it is reasonable to combine (pool)
your sample estimates to make a single estimate of the difference between the proportions.
14. Explain how the standard error of
1
-
2
differs between constructing a confidence interval for
performing a hypothesis test for
and
.
15. List the three conditions that need to be satisfied in order to do a significance test for the difference between
two proportions.
16. Conduct a significance test for the difference between two proportions using the Inference Toolbox.
Chapter 14 Inference for Distributions of Categorical Variables: Chi-Square Procedures pp. 832 – 885
Case Closed Does acupuncture promote pregnancy p. 833 and p. 880
Section 14.1 Objectives – Test for Goodness of Fit
1. Describe the situation for which the chi-square test for goodness of fit is appropriate.
2. Define the X2 statistic, and identify the number of degrees of freedom it is based on, for the
goodness of fit
test.
3. List the conditions that need to be satisfied in order to conduct a
4. Conduct a
test for goodness of fit.
test for goodness of fit.
5. Identify three main properties of the chi-square density curve.
6. Use technology to conduct a
test for goodness of fit.
7. If a X2 statistic turns out to be significant, discuss how to determine which observations contribute the most to
the total value.
Section 14.2 Objectives – Inference for Two-Way Tables
8. Explain what is meant by a two-way table.
9. Given a two-way table, compute the row or column conditional distributions.
10. Define the chi-square (X2) statistic.
11. Using the words populations and categorical variables, describe the major difference between homogeneity of
populations and independence.
12. Identify the form of the null hypothesis in a
test for homogeneity of populations.
13. Identify the form of the null hypothesis in a
test of association/independence.
14. Given a two-way table of observed counts, calculate the expected counts for each cell.
15. List the conditions necessary to conduct a
16. Use technology to conduct a
test of significance for a two-way table.
test of significance for a two-way table.
17. Discuss techniques of determining which components contribute the most to the value of X2.
18. Describe the relationship between a X2 statistic for a two-way table and a two-proportion z statistic.
Chapter 15 Inference for Regression pp. 887 – 918
Case Closed Three-pointers in college basketball p. 887 and pp. 911 – 912
Chapter Objectives:
1. Identify the conditions necessary to do inference for regression.
2. Given a set of data, check that the conditions for doing inference fro regression are present.
3. Explain what is meant by the standard error about the least-squares line.
4. Compute a confidence interval for the slope of the regression line.
5. Conduct a test of the hypothesis that the slope of the regression line is 0 (or that the correlation is 0) is the
population.