Learning Objectives
- State the various steps and elements in the process of statistical inference.
- Define simple random sampling and the type of population it is suited for.
- Describe how and why stratified random sampling is conducted.
- Determine if a particular sample is biased.
- Explain why statistics are random variables.
- Define what a sampling distribution is.
- State a condition under which the sampling distribution of the mean will be normal. Explain why the sampling distribution is normal under this condition
- Calculate a standard normal variable (Z) for any normal random variable.
- Describe what it means for a normal random variable to be standard/standardized.
- State the relationship between Z and the number of standard deviations.
- Discuss why normal random variables are standardized.
- Identify the various elements of the standard normal probability table.
- Determine the area/probability under the standard normal curve to the left of (or less than) a given value of z.
- Calculate the area/probability under the standard normal curve to the right of (or greater than) a given value of z.
- Calculate the area/probability under the standard normal curve between two given values of z.
- State in your own words what the Empirical Rule says.
- Describe in your own words what the Central Limit Theory says.
- State why the Central Limit is useful.
- Calculate a standardized variable (Z) for a normally distributed sample average.
- State which sample size n is relevant to the Central Limit Theorem (CLT).
- Describe what is meant by “sufficiently large” for the CLT to apply.
- Differentiate between use of the Z and T distributions.
- Calculate a random variable distributed according to the T distribution.
- State the conditions associated with use of the T distribution.
- State key properties of the T distribution.
- Contrast the Z and T distributions.
- Identify the various elements of the T probability table.
- Determine the critical value of T having a certain area/probability to the right or left of it for a particular degrees of freedom.
- Determine the area/probability under the T curve to the right or left of a particular critical value of t for a certain degrees of freedom.
- Calculate the area/probability under the T curve between two critical values of t for a given degrees of freedom.
- Calculate the area/probability under the T curve between two critical values of t for a given degrees of freedom.
- State key properties of the Chi-Squared distribution.
- Identify the various elements of the Chi-Squared probability table.
- Describe how to determine whether a particular critical value of the Chi-Squared distribution has a high probability of occurrence (or not).
- Determine the Chi-Squared critical value having a particular area/probability to the right or left of it under the curve for a given degrees of freedom.
- Determine the area/probability under the Chi-Squared curve to the right or left of a particular critical value for a given degrees of freedom.
- State key properties of the F distribution.
- Identify the various elements of the F probability table.
- Determine the critical value of F having a particular area/probability to the right or left of it under the curve for a given set of degrees of freedom.
- Apply Theorem 8.7 in the textbook to determine additional critical values of the F distribution.
Videos
Title: V6 – Sampling Distribution Theory (Inference & Sampling)
Summary: This video covers the steps of the process of statistical inference. It also covers simple random sampling, stratified random sampling, and biased samples.
Learning Objectives: 1) State the various steps and elements in the process of statistical inference. 2) Define simple random sampling and the type of population it is suited for. 3) Describe how and why stratified random sampling is conducted. 4) Determine if a particular sample is biased.
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Title: V7 – Sampling Distribution Theory (Sampling Distribution)
Summary: This video covers the concept of statistics as random variables and the definition of a sampling distribution.
Learning Objectives: 5) Explain why statistics are random variables. 6) Define what a sampling distribution is.
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Title: V8 – Sampling Distribution Theory (Shape of Sampling Distribution)
Summary: This video reviews the definition of a sampling distribution. It then discusses the shape of the sampling distribution of the mean when the population is normally distributed and why this shape occurs.
Learning Objectives: 7) State a condition under which the sampling distribution of the mean will be normal. Explain why the sampling distribution is normal under this condition.
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Title: V9 – Sampling Distribution Theory (Z Transformation)
Summary: This video describes how and why a Z Transformation, or standardization of a normal random variable, is done.
Learning Objectives: 8) Calculate a standard normal variable (Z) for any normal random variable. 9) Describe what it means for a normal random variable to be standard/standardized. 10) State the relationship between Z and the number of standard deviations. 11) Discuss why normal random variables are standardized.
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Title: V10 – Sampling Distribution Theory (Z Probability Table)
Summary: This video covers the Z Probability table, or the table of areas or probabilities under the standard normal curve. Examples of how to use the Z Probability table are given.
Learning Objectives: 1) Identify the various elements of the standard normal probability table. 2) Determine the area/probability under the standard normal curve to the left of (or less than) a given value of z.
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Title: V11 – Sampling Distribution Theory (Additional Examples with Z Table)
Summary: This video provides additional examples of using the Z table to determine & calculate probabilities or areas under the standard normal curve.
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Title: V12 – Sampling Distribution Theory (Empirical Rule of Normal Distribution)
Summary: This video covers the Empirical Rule, otherwise known as the 68-95-99.7% rule, of the Normal distribution.
Learning Objectives: 5) State in your own words what the Empirical Rule says.
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Title: V13 – Sampling Distribution Theory (Central Limit Theorem)
Summary: This video explains the Central Limit Theorem (CLT) and discusses its importance and the conditions under which it holds.
Learning Objectives: 6) Describe in your own words what the Central Limit Theory says. 7) State why the Central Limit is useful. 8) Calculate a standardized variable (Z) for a normally distributed sample average. 9) State which sample size n is relevant to the Central Limit Theorem (CLT). 10) Describe what is meant by “sufficiently large” for the CLT to apply.
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Title: V14 – Sampling Distribution Theory (T Distribution)
Summary: This video covers the T distribution, also known as Student’s T distribution, including its key properties. It also compares the T and Z distributions.
Learning Objectives: 11) Differentiate between use of the Z and T distributions. 12) Calculate a random variable distributed according to the T distribution. 13) State the conditions associated with use of the T distribution. 14) State key properties of the T distribution. 15) Contrast the Z and T distributions.
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Title: V15 – Sampling Distribution Theory (Probability Table for T distribution)
Summary: This video covers the probability table for the T distribution, also known as the table of critical values of the T distribution. Specifically, this video covers how to use T table and contains practice examples with this table.
Learning Objectives: 16) Identify the various elements of the T probability table. 17) Determine the critical value of T having a certain area/probability to the right or left of it for a particular degrees of freedom. 18) Determine the area/probability under the T curve to the right or left of a particular critical value of t for a certain degrees of freedom. 19) Calculate the area/probability under the T curve between two critical values of t for a given degrees of freedom.
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Title: V16 – Sampling Distribution Theory (Probability Table for Chi-Squared Distribution)
Summary: This video covers the Chi-Squared distribution, its key properties, and the Chi-Squared probability table. This table is also known as the table of critical values of the Chi-Squared distribution. This video describes how to use this table and provides practice examples using it.
Learning Objectives:
State key properties of the Chi-Squared distribution.
Identify the various elements of the Chi-Squared probability table
Describe how to determine whether a particular critical value of the
Chi-Squared distribution has a high probability of occurrence (or not).
Describe how to determine whether a particular critical value of the
Chi-Squared distribution has a high probability of occurrence (or not).
Determine the Chi-Squared critical value having a particular
area/probability to the right or left of it under the curve for a given
degrees of freedom.
Determine the area/probability under the Chi-Squared curve to the
right or left of a particular critical value for a given degrees of
freedom.
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Title: V17 – Sampling Distribution Theory (Probability Table for F Distribution)
Summary: This video covers the F distribution, its key properties, and the F probability table. This table is also known as the table of critical values of the F distribution. This video describes how to use this table and provides practice examples using it.
Learning Objectives: 6) State key properties of the F distribution.7) Identify the various elements of the F probability table. 8) Determine the critical value of F having a particular area/probability to the right or left of it under the curve for a given set of degrees of freedom. 9) Apply Theorem 8.7 in the textbook to determine additional critical values of the F distribution.
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