Chapter 4 of TSATN gives a brief summary on the state of weather forecasting. A few years ago, when Hurricane Irene had New Jersey in its sites, I overheard a conversation surrounding weather prediction and meteorology. "They don't know anything" someone said. Well, actually, they know quite a bit and their models keep getting better. Meteorology is a mathematically rich science. The error rate in hurricane eye track forecasting has narrowed to as small as a 100 mile radius as far out as 3 days before landfall. That gives plenty of time for people to take the necessary precautions (evacuate!).
Yet, people still mistrust weather forecasts when they regularly get their predictions from local news outlets. And mistrust them they should. Local affiliates tend to grossly exaggerate the chances for rain occurring. This leads to a 'boy who cried wolf' mentality when it comes to actual threats such as hurricanes. What happened in New Orleans in 2005 is an unfortunate example of this. People just didn't believe it would be a big deal and thousands lost their lives. Technology has afforded us a way to save lives from menacing natural disasters, but it can only do so if you listen and respond to the warnings.
Lesson 11 of ST095 continued with t-distributions and gave us some practice with conducting t-tests for independent samples. The topics included pooled variance $\left(S^2_p =\frac{SS_x+SS_y}{df_x+df_y}\right)$, standard error $\left(S_{\bar{x}-\bar{y}}=\sqrt{\frac{S^2_p}{n_x}+\frac{S^2_p}{n_y}}\right)$, $t=\frac{\bar{x}-\bar{y}}{S_{\bar{x}-\bar{y}}}$ and a few assumptions.
- X and Y should be random samples from two independent populations
- Populations are approximately normal
- Sample data can estimate population variances
- Population variances are roughly equal
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