Learning Objectives
After completing this pre-class module, you should be able to:
Video 25
5) Describe (at a high level) how hypothesis testing proceeds.
6) State and define the two types of hypotheses.
7) Write an example of a null and alternative hypothesis using symbols and numbers.
8) State the two possible conclusions in hypothesis testing.
9) Explain why a null hypothesis is rejected or not rejected.
10) Describe how a proof by contradiction works.
Video 26
11) Calculate the appropriate test statistic for inference on µ, depending on the knowledge of the population variance, the distribution of the population or sample mean, and the size of the sample.
12) Explain in your own words how a null hypothesis for µ is related to a confidence interval.
13) Explain why the Z distribution should be used when the sample size is large, even if the population variance is unknown.
Video 27
1) Calculate the appropriate test statistic for inference on two independent means, depending on knowledge of the population variances, the distribution of the populations or sample means, and size of the samples.
Video 28
1) Calculate the appropriate test statistic for inference on two independent means when the population variances are unknown and the sample sizes are small.
2) Explain in your own words how a null hypothesis for a difference in independent means (µ1 – µ2) is related to a confidence interval.
Video 29
3) Identify when two sets of data are dependent or paired.
4) Calculate the appropriate test statistic for inference on two dependent or paired means, depending on knowledge of the population variance, the distribution of the population or sample mean, and size of the sample.
5) Explain in your own words how a null hypothesis for a difference in dependent means (µD) is related to a confidence interval.
Video 30
6) Calculate the sample proportion.
7) Describe the numerator of the sample proportion formula.
8) Define the denominator of the sample proportion formula.
9) State the distribution that approximates the Binomial and the conditions under which this approximation holds.
10) Calculate the test statistic for inference on a population proportion using the Normal approximation to the Binomial distribution.
11) Ensure the assumptions for using the Normal approximation are met in the case of inference on a proportion.
12) Explain in your own words how a null hypothesis for p is related to a confidence interval.
Video 31
13) Calculate the test statistic for inference on two independent population proportions using the Normal approximation to the Binomial distribution.
14) Ensure the assumptions for using the Normal approximation are met in the case of inference on two proportions.
15) Explain in your own words how a null hypothesis for a difference in two proportions (p1 – p2) is related to a confidence interval.
Video 32
1) Calculate the test statistic for inference on the population variance using the Chi-Squared distribution.
2) Identify the critical value of the Chi-Squared distribution based on an area/probability to the left or right of it for a certain degrees of freedom.
3) Calculate the test statistic for inference on the ratio of two independent population variances using the F distribution.
4) Identify the critical value of the F distribution based on an area/probability to the left or right of it for a certain set of degrees of freedom.
Video 33
5) Describe specifically what a Goodness of Fit test is used for.
6) Discuss the expected frequencies associated with a discrete uniform distribution, such as the toss of a fair die.
7) Discuss observed versus expected frequencies in relation to a Goodness of Fit test.
Video 34
8) Define and describe a contingency table.
9) Define and calculate a marginal total or frequency in a contingency table.
10) Calculate a marginal probability in a contingency table.
11) Calculate the probability that two independent events both occur.
12) Calculate a cell probability within a contingency table.
Video 35
1) Discuss how normality can be visually assessed using a normal Q-Q plot.
2) Define what an empirical distribution is.
3) Describe a Cumulative Frequency Graph and how it is constructed.
4) Generate an empirical cumulative distribution function (ECDF) for a set of observed data.
Videos
Title: V25 – Hypothesis Testing (Null & Alternative Hypotheses, Two Conclusions, & Proof by Contradiction)
Summary: This video introduces hypothesis testing by describing what it is used for and its high-level steps. The two types of hypotheses (null vs. alternative) are discussed, along with the two possible conclusions in hypothesis testing. The steps involved in a proof by contradiction, which is used in hypothesis testing, are reviewed.
Learning Objectives:
5) Describe (at a high level) how hypothesis testing proceeds.
6) State and define the two types of hypotheses.
7) Write an example of a null and alternative hypothesis using symbols and numbers.
8) State the two possible conclusions in hypothesis testing.
9) Explain why a null hypothesis is rejected or not rejected.
10) Describe how a proof by contradiction works.
Transcript: Read the transcript
Slides with Annotation: See the slides
Title: V26 – Hypothesis Testing (Z. vs. T for Inference on Mean, Proof by Contradiction, & CI)
Summary: This video reviews the various cases for inference on the mean involving the Z and T distributions in preparation for hypothesis testing. The application of proof by contradiction is shown, and the relationship of a confidence interval to a hypothesis test is explained.
Learning Objectives:
11) Calculate the appropriate test statistic for inference on µ, depending on the knowledge of the population variance, the distribution of the population or sample mean, and the size of the sample.
12) Explain in your own words how a null hypothesis for µ is related to a confidence interval.
13) Explain why the Z distribution should be used when the sample size is large, even if the population variance is unknown.
Transcript: Read the transcript
Annotated Slides: See the slides
Slides without Annotation: See the slide
Title: V27 – Hypothesis Testing (Use of Z for difference in 2 independent means)
Summary: This video reviews the use of the Z distribution for inference on the difference in two means from independent populations in preparation for hypothesis testing.
Learning Objectives:
1) Calculate the appropriate test statistic for inference on two independent means, depending on knowledge of the population variances, the distribution of the populations or sample means, and size of the samples.
Transcript: Read the transcript
Annotated Slides: See the slides
Title: V28 – Hypothesis Testing (Use of T for Difference in 2 Independent Means)
Summary: This video reviews the use of the T distribution for inference on the difference in two means from independent populations in preparation for hypothesis testing.
Learning Objectives:
1) Calculate the appropriate test statistic for inference on two independent means when the population variances are unknown and the sample sizes are small.
2) Explain in your own words how a null hypothesis for a difference in independent means (µ1 – µ2) is related to a confidence interval.
Transcript: Read the transcript
Slides with Annotation: See the slides
Title: V29 – Hypothesis Testing (Use of T and Z for Difference in 2 Dependent Means)
Summary: This video first reviews pairing of data from dependent populations and its advantages. The video then reviews the use of the T and Z distributions for inference on the difference in two means from dependent populations in preparation for hypothesis testing.
Learning Objectives:
3) Identify when two sets of data are dependent or paired.
4) Calculate the appropriate test statistic for inference on two dependent or paired means, depending on knowledge of the population variance, the distribution of the population or sample mean, and size of the sample.
5) Explain in your own words how a null hypothesis for a difference in dependent means (µD) is related to a confidence interval.
Transcript:Read the transcript
Slides with Annotation: See the slides
Title: V30 – Hypothesis Testing (Use of Z for One Proportion)
Summary: This video reviews the calculation of a sample proportion, which is used in hypothesis testing on the population proportion. The video then reviews use of the Z distribution (Normal approximation to the Binomial) in preparation for hypothesis testing on the proportion.
Learning Objectives:
6) Calculate the sample proportion.
7) Describe the numerator of the sample proportion formula.
8) Define the denominator of the sample proportion formula.
9) State the distribution that approximates the Binomial and the conditions under which this approximation holds.
10) Calculate the test statistic for inference on a population proportion using the Normal approximation to the Binomial distribution.
11) Ensure the assumptions for using the Normal approximation are met in the case of inference on a proportion.
12) Explain in your own words how a null hypothesis for p is related to a confidence interval.
Transcript: Read the transcript
Slides with Annotation: See the slides
Title: V31 – Hypothesis Testing (Use of Z for Two Proportions)
Summary: This video reviews use of the Z distribution (Normal approximation to the Binomial) for inference on the difference in two proportions from independent populations in preparation for hypothesis testing.
Learning Objectives:
13) Calculate the test statistic for inference on two independent population proportions using the Normal approximation to the Binomial distribution.
14) Ensure the assumptions for using the Normal approximation are met in the case of inference on two proportions.
15) Explain in your own words how a null hypothesis for a difference in two proportions (p1 – p2) is related to a confidence interval.
Transcript: Read the transcript
Annotated Slides: See the slides
Slides without Annotation: See the slides
Title: V32 – Hypothesis Testing (Use of Chi-Squared & F distributions for inference on Variance)
Summary: This video reviews the Chi-Squared distribution and test statistic in preparation for hypothesis testing on the population variance or standard deviation. This video also reviews the F distribution and test statistic in preparation for hypothesis testing on the ratio of two variances (or two standard deviations) from independent populations.
Learning Objectives:
1) Calculate the test statistic for inference on the population variance using the Chi-Squared distribution.
2) Identify the critical value of the Chi-Squared distribution based on an area/probability to the left or right of it for a certain degrees of freedom.
3) Calculate the test statistic for inference on the ratio of two independent population variances using the F distribution.
4) Identify the critical value of the F distribution based on an area/probability to the left or right of it for a certain set of degrees of freedom.
Transcript: Read the transcript
Slides with Annotation: See the slides
Slides without Annotation: See the slides
Title: V33 – Hypothesis Testing (Goodness of Fit Test)
Summary: This video introduces the Goodness of Fit Test, which tests for the fit, or alignment, between an observed distribution of data and a particular theoretical or hypothesized distribution, such as the Discrete Uniform (or other) distribution. An example involving the Discrete Uniform distribution is presented.
Learning Objectives:
5) Describe specifically what a Goodness of Fit test is used for.
6) Discuss the expected frequencies associated with a discrete uniform distribution, such as the toss of a fair die.
7) Discuss observed versus expected frequencies in relation to a Goodness of Fit test.
Transcript: Read the transcript
Slides with Annotation: See the slides
Title: V34 – Hypothesis Testing (Contingency Table)
Summary: This video introduces a contingency table, which is used in a Test of Independence of two categorical variables. The marginal frequencies or totals of the contingency table are defined, and calculation of a marginal probability is shown. Calculation of the various cell probabilities of the contingency table for use in a Test of Independence are demonstrated.
Learning Objectives:
8) Define and describe a contingency table.
9) Define and calculate a marginal total or frequency in a contingency table.
10) Calculate a marginal probability in a contingency table.
11) Calculate the probability that two independent events both occur.
12) Calculate a cell probability within a contingency table.
Transcript: Read the transcript
Slides with Annotation: See the slides
Slides without Annotation: See the slides
Title: V35 – Hypothesis Testing (Q-Q Plot and ECDF)
Summary: This video introduces the Q-Q Plot, or Quantile-Quantile plot, which is used to visually assess whether an observed (or empirical) distribution of data follows a particular theoretical distribution, such as the Normal distribution. The steps involved in calculating the Empirical Cumulative Distribution Function (ECDF), which is used in testing an observed distribution for goodness of fit to a theoretical distribution, are presented.
Learning Objectives:
1) Discuss how normality can be visually assessed using a normal Q-Q plot.
2) Define what an empirical distribution is.
3) Describe a Cumulative Frequency Graph and how it is constructed.
4) Generate an empirical cumulative distribution function (ECDF) for a set of observed data.
Transcript: Read the transcript
Annotated Slides: See the slides
Slides without Annotation: See the slides