In Exercise 30.7, we investigated whether snorers are more likely to have nightmares than non-snorers. We suspected there was no relationship between snoring and nightmares. Now that we’ve studied variance, we have the tools to investigate this pressing question in more depth.

The sample data revealed that 11 out of 93 snorers suffered from nightmares, while 12 out of 86 non-snorers did.

Note that this is the probability that snorers have nightmares, not the probability that they are nightmares.

Construct approximate 95% confidence intervals for the nightmare probability of snorers and non-snorers respectively. By comparing the intervals, say whether the data indicate a systematic difference between the nightmarish tendencies of snorers and non-snorers.