- 1. Define a parameter and contrast it with a statistic.
2. State examples of parameters that are estimated.
3. Describe how the classical method of estimation is done.
4. Define a point estimate and state the relationship between a point estimate and the parameter.
5. Explain why an interval estimate is preferable when doing estimation.
6. Determine zα/2 where α/2 represents an area/probability to the right of z. Likewise, determine -zα/2 where α/2 represents an area to the left of -z.
7. Transform a normally distributed sample mean to a Z variable.
8. State the conditions under which the sample mean will be normally distributed.
9. Calculate a random variable distributed according to the T distribution.
10. State the conditions associated with use of the T distribution.
11. Determine the critical value of T having a particular area/probability to the right of it for a given degree of freedom.
12. Define when two populations are independent and state an example of this.
13. Define when two populations are dependent.
14. Describe a “before and after” study as a dependent-populations study with the same two populations.
15. State examples of two dependent populations that are different but directly related and paired.
16. Transform a normally distributed difference in sample means (independent populations) to a Z random variable.
17. State the conditions under which the difference in sample means (independent populations) is normally distributed.
18. State the conditions under which the pooled estimate of the variance should be used.
19. Calculate the pooled estimate of the variance.
20. State why the pooled estimate of the variance is used.
21. Discuss why data are paired.
22. Identify the quantities and statistics that are calculated with a paired data setup.
23. Define binary data or a binary variable and state an example.
24. Define the mode or modal category.
25. Define a Bernoulli trial.
26. Calculate the sample proportion.
27. Describe the numerator of the sample proportion formula.
28. Define the denominator of the sample proportion formula.
29. Describe a binomial random variable.
30. State the distribution that approximates the Binomial and the conditions under which the approximation holds.
31. Calculate a random variable distributed according to the Chi-Squared distribution for estimating the population variance.
32. Determine critical values or areas from the Chi-Squared table of probabilities.
33. Calculate a random variable distributed according to the F distribution for estimating the ratio of population variances from independent populations.
34. Determine critical values or areas from the F table of probabilities.
Videos
Title: V18 – Estimation (Classical Method of Estimation)
Summary: This video defines and provides examples of a statistical parameter and describes the classical method of estimation. It also sets the stage for interval estimation (i.e., via confidence intervals) and why interval estimation is done.
Learning Objectives:
1) Define when two populations are independent and state an example of this.
2) Define when two populations are dependent.
3) Describe a “before and after” study as a dependent-populations study with the same two populations.
4) State examples of two dependent populations that are different but directly related and paired.
Annotated Slides: See the slides
Slides With Annotation: See the slides
Slides Without Annotation: See the slides
Title: V19 – Estimation (Review of Z and T distributions)
Summary: This video reviews both the Z and T distributions for use in confidence interval estimation. Simple math under the Z curve, standardization of the sample mean, and use of the Z probability table are reviewed. The T random variable and use of the T probability table are also reviewed for use in confidence interval estimation.
Learning Objectives:
5) Transform a normally distributed difference in sample means (independent populations) to a Z random variable.
6) State the conditions under which the difference in sample means (independent populations) is normally distributed.
7) State the conditions under which the pooled estimate of the variance should be used.
8) Calculate the pooled estimate of the variance.
9) State why the pooled estimate of the variance is used..
Transcript: Read the transcript
Annotated Slides: See the slides
Title: V20 – Estimation (Independent vs. Dependent Populations)
Summary: This video defines what it means for two populations or groups to be independent versus dependent. It covers “before and after measurements” and paired observations from directly related (but different) populations as data from dependent populations.
Learning Objectives:
1) Define when two populations are independent and state an example of this.
2) Define when two populations are dependent.
3) Describe a “before and after” study as a dependent-populations study with the same two populations.
4) State examples of two dependent populations that are different but directly related and paired.
Transcript: Read the transcript
Annotated Slides: See the slides
Slides With Annotation: See the slides
Title: V21 – Estimation (Topics related to estimating differences in independent means)
Summary: This video covers various topics related to estimating the difference in independent means, specifically standardization of the difference in sample means, normality of the difference in sample means, and the pooled estimate of the sample variance.
Learning Objectives:
5) Transform a normally distributed difference in sample means (independent populations) to a Z random variable.
6) State the conditions under which the difference in sample means (independent populations) is normally distributed.
7) State the conditions under which the pooled estimate of the variance should be used.
8) Calculate the pooled estimate of the variance.
9) State why the pooled estimate of the variance is used..
Annotated Slides: See the slides
Slides With Annotation: See the slides
Title: V22 – Estimation (Pairing of Data)
Summary: This video discusses why data are paired and covers the paired-data setup for statistical analysis.
Learning Objectives:
10) Discuss why data are paired.
11) Identify the quantities and statistics that are calculated with a paired data setup..
Transcript: Read the transcript
Annotated Slides: See the slides
Slides Without Annotation: See the slides
Summary: This video begins by describing binary data and the mode as a descriptive statistic for categorical data. The population proportion (parameter) and its point estimate based on Bernoulli trials are discussed, along with the definition of a Bernoulli trial. The relationship of the point estimate to the Binomial distribution is covered, along with approximating the Binomial distribution by the Normal distribution.
Learning Objectives:
12) Define binary data or a binary variable and state an example.
13) Define the mode or modal category.
14) Define a Bernoulli trial.
15) Calculate the sample proportion.
16) Describe the numerator of the sample proportion formula.
17) Define the denominator of the sample proportion formula.
18) Describe a binomial random variable.
19) State the distribution that approximates the Binomial and the conditions under which the approximation holds.
Transcript: Read the transcript
Annotated Slides: See the slides
Title: V24 – Estimation (Review of Chi-Squared and F Distributions)
Summary: This video reviews the Chi-Squared distribution, statistic, and table of critical values for use in confidence interval estimation. This video also reviews the F distribution, statistic, and table of critical values for use in confidence interval estimation.
Learning Objectives:
1) Calculate a random variable distributed according to the Chi-Squared distribution for estimating the population variance.
2) Determine critical values or areas from the Chi-Squared table of probabilities.
3) Calculate a random variable distributed according to the F distribution for estimating the ratio of population variances from independent populations.
4) Determine critical values or areas from the F table of probabilities.
Transcript: Read the transcript
Annotated Slides: See the slides
Slides without Annotation: See the slides