Exercise

# Question 8

If you decided the conditions for inference are reasonable, you can now construct the interval by hand. It is possible to do this either by calculating the standard error and constructing the interval by hand, or by allowing the `inference()`

function to do it for us.

```
inference(us12$response, est = "proportion",
type = "ci", method = "theoretical",
success = "atheist")
```

Note that since the goal is to construct an interval estimate for a proportion, it's necessary to specify what constitutes a "success", which here is a response of atheist. Although formal confidence intervals and hypothesis tests don't show up in the report, suggestions of inference appear at the bottom of page 7: "In general, the error margin for surveys of this kind is \(\pm\) 3-5% at 95% confidence."

Use the `inference()`

function in the console (it's already loaded). Keep in mind that the `inference()`

function is a bit on the heavy side, it may take a while to run.

**Based on the R output, what is the margin of error for the estimate of the proportion of atheists in US in 2012?**