20.40 Kicking a helium-filled football. Does a football filled with helium travel farther than one filled with ordinary air? To test this, the Columbus Dispatch conducted a study. Two identical footballs, one filled with helium and one filled with ordinary air, were used. A casual observer was unable to detect a difference in the two footballs. A novice kicker was used to punt the footballs. A trial consisted of kicking both footballs in a random order. The kicker did not know which football (the helium-filled or the air- filled football) he was kicking. The distance of each punt was recorded. Then another trial was conducted. A total of 39 trials were run. Here are the data for the 39 trials, in yards that the footballs traveled. The difference (helium minus air) is the response variable. 22 Helium 25 16 25 14 23 29 25 26 22 26 Air 25 23 18 16 35 15 26 24 24 28 Difference -7 7 -2 -12 14 -1 -2 -2 Helium 12 28 28 31 22 29 23 26 35 24 Air 25 19 27 25 34 26 20 22 33 29 Difference -13 1 6 -12 3 3 4 2 -5 Helium 31 34 39 32 14 28 30 27 33 11 Air 31 27 22 29 28 29 22 31 25 20 Difference 17 3 -14 -1 8 -4 8 -9 Helium 26 32 30 29 30 29 29 30 26 Air 27 26 28 32 28 25 31 28 28 Difference -1 6 2 -3 2 4 -2 2 -2 (a) Examine the data. Is it reasonable to use the t procedures? (b) If your conclusion in part (a) is "Yes," do the data give convincing evidence that the helium-filled football travels farther than the air-filled football?

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.