# 3/27/2023

## Confidence intervals for a population mean - see handout

• When the population standard deviation is known (VERY UNREALISTIC)
• When the population standard deviation is unknown (WIDELY USED - Section 7.1)

## Relationship between normal and t-distributions

• There is a different t distribution for each sample size.
• The degrees of freedom for this statistic comes from the standard deviation s.
• t distributions are very similar to the N(0,1) distribution. The major difference is that t distributions have more area in the tails than the N(0, 1) distribution.
• As the sample size increases, t distributions get closer to the N(0, 1) distribution.

## In class exercises

1. Complete Example 4 on the hypothesis testing handout (spectrophotometer data) using RStudio and without assuming that the standard deviation is known. See Spectro.R
2. Textbook exercises - 7.1, 7.3, and 7.11. Tip: use use the RStudio commands qt and pt to find the quantiles and probability for a t distribution with (n-1) degrees of freedom. You may also use the pdist("t", value, df) command to illustrate the probability calculations.