# Two Sample T-Test Essay

962 Words Apr 3rd, 2015 4 Pages
Defensive backs (DBs) have become more important every year in the NFL because of the increase in the passing game. DBs are being drafted more often in the first round with height as one of the most important specs to defend Wide Receivers (WRs). My research question: Is the average DB taller than the average WR? My expectation is that there will not be a significant difference between the two.
The Populations used to support my hypothesis are three starting (NFL) DBs from each team in the American Football Conference (AFC) and three starting WRs from each team in the National Football Conference (NFC). The variable used is height in inches. For example 5’11” = 71 inches and 6’0” = 72 inches. The data collected is from Athlon Sports 2014
The standard deviation, how far away the typical observation is from the mean, for DBs is 1.60 and 2.69 for WRs. The 5-number summary for DBs is 69, 70, 71, 73, and 76. For WRs it is 68, 72, 74, 76, and 80. The five-number summary gives information about the location (from the median), spread (from the quartiles) and range (from the sample minimum and maximum) of the observations (Wikipedia 2014). The chart below shows the columns computed for a 5-number summary, Mean, and Standard Deviation. To begin this experiment, I will first check that the conditions for this experiment are valid and then use a two-sample t-test to compare the difference of means of the populations with a .05 level of significance and 95% confidence interval.
The first condition is met because the samples are random and the observations are independent. Meaning the knowledge of the DBs height tells nothing about the WRs height. The heights entered are random because the heights were not specifically chosen. The population was chosen by player names (starters) not height. The second condition is met because the populations, like the observations, are independent of each other. The value of DBs tells nothing about the value of the WRs. Condition three is met because the populations are both normal and both population sizes are 25 or more. I expected the population distributions to be normally distributed because the gender is male only. If women were to play there

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