---
title: "Lec 01 code"
format: html
---

## Example

Here is some data and the normal QQ plot:

```{r}
wt <- c(41,34,40,44,33,42,52,38,32,31,31,35,
39,44,42,42,35,33,40,48,51,32,41,35,
38,48,37,35,42,41,40,47,40,46,33,38,
51,39,40)
qqnorm(wt)
```

Here we construct a confidence interval for the mean which assumes $\sigma = 5$ is known.
```{r}

n <- length(wt)
xbar <- mean(wt)
alpha <- 0.05
za2 <- qnorm(1-alpha/2)
sigma <- 5


lo <- xbar - za2 * sigma / sqrt(n)
up <- xbar + za2 * sigma / sqrt(n)
```

The sample mean is $\bar X_n =  `r xbar`$.

The confidence interval is $[`r lo`,`r up`]$.


Now we construct a confidence interval without assuming $\sigma$ is known.
```{r}

sn <- sd(wt)
ta2 <- qt(1-alpha/2,n-1)
lot <- xbar - ta2 * sn/sqrt(n)
upt <- xbar + ta2 * sn/sqrt(n)
```

This confidence interval is $[`r lot`, `r upt`]$.