The National Football League (NFL) combine is a forum in...

The National Football League (NFL) combine is a forum in which players who want to play in the NFL demonstrate various skills. One skill that is measured is the 40-yard dash. Go to www.pearsonhighered.com/sullivanstats to obtain the data file $13_{-} 1_{-} 23$ using the file format of your choice for the version of the text you are using. (a) What type of variable is 40 -yard dash time? (b) Excluding quarterback (QB), the skill positions are cornerback (CB), safety (S), running back (RB), and wide receiver (WR). Suppose we want to know whether there is a difference between the 40 -yard dash times for these positions. What would be the null and alternative hypotheses? (c) Assuming we treat the players as a random sample of all players in each position, explain why we may use a one-way ANOVA to determine if there is a significant difference between 40 -yard dash times for these positions. How many means are being compared? (d) Does the evidence suggest a difference exists for the 40 -yard dash times for the skill positions (except quarterback)? Use the $\alpha=0.05$ level of significance. (e) Draw boxplots of the 40 -yard dash times for the skill positions (except quarterback) to support the results from part (d).

The National Football League (NFL) combine is a forum in which players who want to play in the NFL demonstrate various skills. One skill that is measured is the 40-yard dash. Go to www.pearsonhighered.com/sullivanstats to obtain the data file $13_{-} 1_{-} 23$ using the file format of your choice for the version of the text you are using.
(a) What type of variable is 40 -yard dash time?
(b) Excluding quarterback (QB), the skill positions are cornerback (CB), safety (S), running back (RB), and wide receiver (WR). Suppose we want to know whether there is a difference between the 40 -yard dash times for these positions. What would be the null and alternative hypotheses?
(c) Assuming we treat the players as a random sample of all players in each position, explain why we may use a one-way ANOVA to determine if there is a significant difference between 40 -yard dash times for these positions. How many means are being compared?
(d) Does the evidence suggest a difference exists for the 40 -yard dash times for the skill positions (except quarterback)? Use the $\alpha=0.05$ level of significance.
(e) Draw boxplots of the 40 -yard dash times for the skill positions (except quarterback) to support the results from part (d).

Key Concepts

Box Plot Comparison

A box plot is a graphical tool used to depict the distribution of numerical data through their quartiles, highlighting the median, spread, and potential outliers. By drawing box plots for each group (skill positions, excluding quarterback), one can visually compare the central tendencies and variability of the 40-yard dash times across groups, providing clear evidence regarding the presence of any differences among them.

One-Way Analysis of Variance (ANOVA)

One-way ANOVA is a statistical method used to compare the means of three or more independent groups to determine if at least one of them is statistically significantly different from the others. It achieves this by analyzing the variance within and between groups. Here, the technique is applicable since we are comparing the 40-yard dash times across several skill positions, and the number of means compared corresponds to the number of positions included in the analysis.

Quantitative Continuous Variable

This concept refers to a variable that is measured on a continuous scale and results in a numerical value. It encompasses measurements such as time, distance, and weight, where the differences between values are meaningful and can be computed. In the context of the 40-yard dash, the time recorded is a continuous numerical measure indicating performance.

Null and Alternative Hypotheses

These are formal statements used in statistical hypothesis testing. The null hypothesis generally posits that there is no effect or difference—in this case, it suggests that the means of the 40-yard dash times for the different skill positions are equal. The alternative hypothesis specifies that there is at least one difference among these group means, reflecting a potential effect of the player’s position on performance.

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