According to a recent NY Times article: (http://www.nytimes.com/2010/07/07/nyreg

Question

According to a recent NY Times article: (http://www.nytimes.com/2010/07/07/nyregion/07heat.html), ‘With the temperature reaching 103 degrees in Central Park at 3:11 p.m., breaking the former record high of 101 degrees for the day set in 1999 Con Edison officials braced for the greatest demand for power they had ever had to supply. … The heat broke several records in the Northeast, as Boston, Providence and Philadelphia all saw temperatures in the 100s that eclipsed previous highs’. Could this be the result of some random fluctuations? The average maximum temperature for New York (historically) is listed at 85 F, while the minimum temperature is listed at 68F (according to http://www.ny.com/general/weather.html). Set up a test of hypothesis and present
your conclusion in terms of p-values.

Explanation / Answer

The hypothesis would be that the high temperature was just due to chance (null hypothesis). The z score of the 103 heat would be (103-85)/4.25= 4.2. Standard deviation of 4.25 was estimated by the range rule of thumb (range)/4 (85-68)/4. P value of 4.2 standard deviations from mean would be very small (less than .01), thus we would reject the null hypothesis that the high temperature was just due to chance.

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