The Truth About Temperature
Do teams score more points in warmer weather than colder weather?
A game in cold weather is satisfied if the temperature of the game is played in 32 degrees or less.
A game in warmer weather is satisfied if the temperature of the game is played in 70 degrees or greater.
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Do teams score more points in warmer weather than colder weather?
Null Hypothesis: H=C
Alternate Hypothesis: HA:H>C
H= the mean number of points scored by teams from 70 degrees or more
C= the mean number of points scored by teams from 32 degrees or less
Conditions of Colder Weather
Random Sampling Condition: Random Sample of 40 NFL games in “cold” weather from 2012-2018 seasons.
Independent: the score of one game does not affect the score of other games nor does it affect games in the future weeks
Large Enough Condition: 40≥40
Conditions of Hot Weather
Random Sampling Condition: Random Sample of 100 NFL games in “hot” weather from 2012-2018 seasons.
Independent: the score of one game does not affect the score of other games nor does it affect games in the future weeks
Success/Failure Condition: 100>40
Therefore games from cold and hot weather are independent and can be modelled with Student’s T model.
t=(xH-xC)-(H-C)SH2nH+SC2nC
xH= 45.25203252
xC= 51.14516129
SH = 13.2878556
SC= 15.70094158
nH= 100
nC= 40
Range of degrees of freedom: 39 df 138
Alpha = .05
T = -2.09284
P= .02021
Because the p value (.02021) is less than the alpha value (.05), the null hypothesis is rejected. In other terms, the probability that teams score more points in warmer temperatures than in colder temperatures most likely did not occur to chance. According to this sample, it highly suggests that teams score more points in colder weather than in warmer weather.
In this sample, teams scored more points in colder weather than in warmer weather. However, this does not conclude that all teams, most of the time score more points in colder weather. If we were to truly investigate whether teams score more points in colder weather we would have to conduct dozens of samples that would have to support our previous conjecture.
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A correctly formatted version of the test can be found here. It also includes the original test using proportions instead of mean values.