Confidence intervals for means and differences of means

Learning objectives

Explain why a t-distribution is used when the population standard deviation is unknown and is replaced by s, and describe how the shape of a t-distribution changes with its degrees of freedom

Identify a one-sample t-interval as the procedure for a population mean, or for a population mean difference when the data are paired, define the parameter in context, and check the conditions: random data, the 10% condition, and a normal population, a large sample or a graph of the data showing no strong skew or outliers

Calculate the standard error s/√n, the margin of error and the interval x̄ ± t* × s/√n with n − 1 degrees of freedom, and interpret the interval and the confidence level in context

Recognize paired data, calculate the differences and construct a one-sample t-interval for the mean difference, explaining why a two-sample procedure would be wrong

Check the conditions for a two-sample t-interval for a difference between two population means, and calculate it, stating the degrees of freedom used

Justify a claim from a confidence interval for a mean, a mean difference or a difference of means, and describe how the sample size and the confidence level affect its width