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Chapter 6   Estimating Parameters

6.1   Populations and samples

6.1.1   Distinction between populations and samples

The exercise on this page asks whether three statements describe populations or samples.

6.1.2   Distinction between parameters and estimates

This exercise asks whether three statements describe parameters or estimates.

6.2   Standard error

6.2.1   Standard error of mean

The exercise on this page shows a data set with the sample mean and st devn. The standard error of the mean must be calculated.

6.2.2   Standard error vs standard deviation

This exercise states the value of either the standard deviation or the standard error or the mean. The question asks for an interval containing about 95% of the values or an interval with 95% confidence of including the popn mean.

6.2.3   Factors affecting the standard deviation and standard error

This exercise asks 3 questions about the effect of sample size and spread of sample values on the sd and se, and about the interpretation of the se and sd.

6.3   Confidence interval for mean

6.3.1   Confidence interval from standard error

This exercise displays an estimate and standard error and asks for an approximate 95% confidence interval. Various different types of parameters are estimated (not just means).

6.3.2   95% confidence interval, known sigma

This exercise gives practice with the calculations for finding the 95% confidence interval for a mean when the population standard deviation is known.

6.3.3   95% confidence interval, unknown sigma

This exercise is similar to the previous one but requires use of a t distribution since the population standard deviation is unknown.

6.3.4   Other confidence levels, known sigma

In this exercise, confidence intervals are requested with a mixture of 90%, 95% and 99% confidence levels, but with known population standard deviation.

6.3.5   Mixture of levels, known & unknown σ

In this exercise, the questions involve a mixture of types with known and unknown population standard deviation and with 90%, 95% and 99% confidence levels.

6.3.6   Factors affecting width of CI

This exercise asks how the sample size, sample standard deviation and confidence level affect the width of a CI for the mean.

6.3.7   Interpreting a 95% confidence interval

In this exercise, you must choose which of four statements correctly interprets the meaning of a 95% confidence interval.

6.4   Estimating proportions

6.4.1   Standard error of proportion

A template is provided in this exercise to help evaluate the standard error of a sample proportion.

6.4.2   95% confidence interval for probability

This exercise gives practice at evaluating an approximate 95% confidence interval for a probability.

6.4.3   Other confidence levels

This exercise requests a mixture of 90%, 95% and 99% confidence intervals for a probability. A normal density can be used to find the relevant z-score and a template helps evaluate the 'plus-minus' value.

6.4.4   Factors affecting width of confidence interval

This exercise asks how the sample size, confidence level and population probability affect the width of a CI for the probability.

6.4.5   Interpreting a 95% confidence interval

This exercise presents 3 different statements about a 95% confidence interval and asks which is correct.