What is statistical inference?

A formal process that uses information from a sample to draw conclusions about a population.

What does statistical inference provide?

A statement of how much confidence can be placed in the conclusion.

What are conclusions made using in statistical inference?

Statistics

What is the sampling distribution of a statistic?

The distribution of values taken by the statistic in all possible samples of the same size from the same population.

What mean and standard deviation does the sampling distribution of a sample means have?

Mean μ Standard deviation ^{σ}/_{√n}

What can x̄ be thought of as?

An unbiased estimator of μ

What does it mean that x̄ is an unbiased estimator of μ?

In repeated sampling, will sometimes fall above the true value of the parameter and sometimes below. There is no systematic tendency to overestimate or underestimate the parameter.

What is a point estimate?

A single number, calculated from available sample data, that is used to estimate the value of an unknown population parameter.

What does the accuracy of a point estimate depend on?

The sample size and variability of the population

What does a confidence interval provide?

An upper and lower bound for a specific unknown population parameter.

What is the standard error of the mean a measure of?

The reliability or precision of x̄ as a point estimate of μ

When we estimate σ with s, what is this called?

A quantity called the standard error of the mean SE_{x̄}=^{s}/_{√n}

Describe the estimate of a confidence interval

The estimate is a sample statistic and the margin of error represents the accuracy of our guess for the parameter.

What is 1-α?

The probability that a value will fall within the confidence interval

What is the variable way to represent the range outside of the confidence interval?

There is ^{a}/_{2} above and below the 1-α confidence interval range.

What is the Z range for a 90% confidence interval?

Plus-minus 1.645

What is the Z range for a 95% confidence interval?

Plus-minus 1.96

What is the Z range for a 99% confidence interval?

Plus-minus 2.58

What is the variable that represents the upper and lower confidence interval values?

Z_{α/2}

What is the formula for confidence interval?

x̄ ± Z_{α/2}(^{σ}/_{√n})

How do you organise a statistical problem?

Using the State/Formulate/Solve/Conclude method.

What does "state" encompass in the State/Formulate/Solve/Conclude method of organising a statistical problem?

What is the practical question, in the context of the real world setting?

What question should you ask yourself for the "formulate" part of the State/Formulate/Solve/Conclude method of organising a statistical problem?

What specific statistical operations does the problem call for?

What does "solve" encompass in the State/Formulate/Solve/Conclude method of organising a statistical problem?

Make the graphs and carry out the calculations needed for this problem.

What does "conclude" encompass in the State/Formulate/Solve/Conclude method of organising a statistical problem?

Give your practical conclusion in the setting of the real-world problem.

What is a student t distribution used for?

To find critical values needed for interval estimation when σ is not known.

What does a student t distribution look like?

The standard Normal distribution but it has thicker ‘tails’.

What does the added variability in a student t distribution come from?

The fact that we use a sample standard deviation in place of the population standard deviation.

What does the student t distribution vary depending on?

Degrees of freedom n–1.

What is the formula for a student t distribution?

x̄ ± t_{α/2}(^{s}/_{√n})