6.32 Punxsutawney Phil. In the United States, Groundhog Day is celebrated on Feb

Question

6.32 Punxsutawney Phil. In the United States, Groundhog Day is celebrated on February 2. ruary 2, Punxsutawney Phil, a mythical groundhog in Punxsutawney, PA, On Feb emerges from his home and if he sees his shadow and returns to his hole, he has predicted six more weeks of winter-like weather. How accurate is Phil? We have data for 113 years (up to 2013) indicating whether Phil saw his shadow and average temperature in March. It is not clear what constitutes "six more weeks of winter-like weather," so here we define it to occur if the average temperature for March is not above the historical average. The results are: 52 years where Phil saw his shadow and the average March temperature was not above the historical average, 46 years where Phil saw his shadow and the average March temperature was above the historical average, 5 years where Phil did not see his shadow and the average March temperature was not above the historical average, and 10 years where Phil did not see his shadow and the average March temperature was above the historical average.16 (a) Make a two-way table of "Phil saw his shadow or not" against "above historical average temperatures in March or not." (b) What do the data tell us about Phil as a weather forecaster?

Explanation / Answer

Below is the two way table for above given problem

B) The above data Shows that :

Phil was successful in telling the weather approx half of the time i.e 54.87%

also if there are two events with equall likelyhood of happening they a natural probability of 50%

so Phil is not a very good weather observer but just using statistics in predicting weather almost approx half of the Time .

Temprature in March Above Historical Average Temprature in March Below Historical Average Total Phil Saw His Shadow 46 52 98 Phil Does Not Saw His Shadow 10 5 15 Total 56 57 113

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