Prior content: None
Previous Section: Combinations of Random Variables*
Next Section: Further Hypothesis Tests*
This whole chapter is A level only (not needed for AS Further Maths).
Contents
- Whole Topic Notes
- 5A Estimators, Bias and Standard Error*
- 5B Confidence Intervals*
- 5C Hypothesis Testing for the Difference Between Means*
- 5D Use of Large Sample Results for an Unknown Population*
- Whole Topic Summary Resources (Including Past Paper Questions)
Whole Topic Notes
Full Notes to Accompany Examples
Dr Frost
- Dr Frost Further Statistics 2 Estimation, Confidence Intervals and Tests Using a Normal Distribution Section
- Dr Frost Further Statistics 2 Estimation, Confidence Intervals and Tests Using a Normal Distribution Slides
5A Estimators, Bias and Standard Error*
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Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 871a: Understand the terms estimator, biased estimator and unbiased estimator.
- 871b: Determine an unbiased estimator S^2 of the population variance σ^2
- 871f: Calculate an updated value of s^2 given additional data points.
- 871c: Calculate the bias of an estimator for a value involved in the range of a continuous uniform distribution.
- 871d: Identify an unbiased estimator a value involved in the range of a continuous uniform distribution.
- 871e: Compare estimators involved in a continuous uniform distribution.
- 870a: Know the definition of standard error and understand why it is useful.
- 870b: Calculate the standard error of the mean (SEM).
- 870c: Calculate the standard error of a sampling distribution for a statistic where the population distribution is known.
- 871: Exam Practice: Estimators and bias
- 870: Exam Practice: Standard error
Worksheets
- Mathshelper (Jon Stone)
5B Confidence Intervals*
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Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 873a: Understand what is meant by the margin of error and calculate it for the mean μ of a population.
- 873b: Calculate the confidence interval for the mean μ of a population.
- 873c: Calculate the confidence interval for the mean μ of a population for multiple groups in the sample.
- 873d: Determine the sample size that will result in a percentage confidence of a given margin of error for the population mean.
- 873e: Determine the sample size that will result in a margin of error for the population mean with a given confidence level.
- 873: Exam Practice: Confidence intervals for a population mean
Activities
- Math = Love (Sarah Carter)
5C Hypothesis Testing for the Difference Between Means*
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Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 874a: Conduct a hypothesis test to determine evidence that μ_A > μ_B
- 874b: Conduct a hypothesis test to determine evidence that μ_A > μ_B + k
- 874c: Conduct a two-tailed hypothesis test to determine evidence that μ_A \ne μ_B
- 874e: Calculate the standard error for the difference of two means.
- 874: Exam Practice: z-tests for a difference of means
5D Use of Large Sample Results for an Unknown Population*
Textbook resources
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Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 872a: Understand the concept of z-tests and normalised test statistics, and how it compares to use of a p value.
- 872b: Conduct a z-test on the population mean.
- 874d: Conduct a hypothesis test for the difference of means using s^2 when the sample size is large.
- 872: Exam Practice: z-tests for the population mean
- 874: Exam Practice: z-tests for a difference of means