Exercise

# Compare with classical interval

In our example, if \(\bar y\) and \(se\) are the respective sample mean and standard error, then a standard 90 percent confidence interval for `M`

is given by

$$ (\bar y - 1.645 \times se, \bar y + 1.645 \times se). $$

For my data, we have `ybar`

= 275.9, and `se`

= 6.32, so my confidence interval is given by

```
c(275.9 - 1.645 * 6.32, 275.9 + 1.645 * 6.32)
```

Recall that Kathy's posterior curve was normal with mean 271.35 and standard deviation 5.34.

Now you can compare the 90% confidence interval with Kathy's probability interval for `M`

!

Instructions

**100 XP**

- Compute a vector
`C_Interval`

containing the 90% confidence interval. This is the interval obtained by using the frequentist method. - Find the length of the confidence interval using the
`diff()`

function. - Define a vector
`Posterior`

with the mean and standard deviation of Kathy's posterior. - Use the
`normal_interval()`

function to display a 90% probability interval. - Use
`qnorm()`

to compute the 90% Bayesian probability interval. Assign the result to`B_Interval`

. - Compute the length of the Bayesian interval using
`diff()`

once more.