# 3/27/2023

## Discussion of Quiz #3

## Complete discussion of Chi-squared tests

## 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)

- 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

- Complete Example 4 on the hypothesis testing handout (spectrophotometer data) using RStudio and without assuming that the standard deviation is known. See Spectro.R
- 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.

## Please read Section 7.2 for class on Wednesday.

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