Let's say I survey the class and ask "Did you leave Reed College to travel during Spring Break". Out of 23 students, 14 of them or 60.8% said yes. Is this consistent with a claim that half of Reed students travel over spring break?
infer code that would test this claim.infer code that compute a confidence interval for our statistic.springbreaktravel, which takes values yes and no.\[ SE_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}} \]
We swap in \(\hat{p}\) for \(p\).
Scientists predict that global warming may have big effects on the polar regions within the next 100 years. One of the possible effects is that the northern ice cap may completely melt. Would this bother you a great deal, some, a little, or not at all if it actually happened?
Are Reed Students different from a random sample of Americans?
GSS Survey data (2010)
| response | count |
|---|---|
| A great deal | 454 |
| Some | 124 |
| A little | 52 |
| Not at all | 50 |
| Total | 680 |
\[\hat{p}_{US} = 454/680 \approx 0.67\]
Difference between the proportions of all Reed students and all Americans who would be bothered a great deal by the northern ice cap completely melting.
\[p_{Reed} - p_{US}\]
Difference between the proportions of sampled Reed students and sampled Americans who would be bothered a great deal by the northern ice cap completely melting.
\[\hat{p}_{Reed} - \hat{p}_{US}\]
Details same as before:
\[ SE_{\hat{p}_1 - \hat{p}_2} = \sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}} \]
We swap in \(\hat{p}_1\) and \(\hat{p}_2\) for \(p_1\) and \(p_2\).