Question

Compare the mean 40-yard dash times for the three positions: wide receiver (WR); cornerback (CB); and safety (SAF). Do the three positions have the same population mean time? Present a graph to compare the 40-yard dash times for the three positions, and state your visual conclusions based on the graph. Also conduct a formal test to compare the population mean times across the three positions, giving the test statistic and P-value of your test. General Manager Jones of the Cowboys wants a 0.10 significance level for this inference, while General Manager Dimitroff of the Falcons wants a 0.05 significance level. As their statistical consultant, what conclusions should you report to each of Jones and Dimitroff? [Summary statistics for the three groups are given below.]

	Sample Size	Sample Mean	Sample Std. deviation
WR	44	4.5161	0.09884
CB	29	4.4962	0.08621
SAF	20	4.5580	0.10660

Answer 1

Result:

Compare the mean 40-yard dash times for the three positions: wide receiver (WR); cornerback (CB); and safety (SAF). Do the three positions have the same population mean time? Present a graph to compare the 40-yard dash times for the three positions, and state your visual conclusions based on the graph. Also conduct a formal test to compare the population mean times across the three positions, giving the test statistic and P-value of your test. General Manager Jones of the Cowboys wants a 0.10 significance level for this inference, while General Manager Dimitroff of the Falcons wants a 0.05 significance level. As their statistical consultant, what conclusions should you report to each of Jones and Dimitroff? [Summary statistics for the three groups are given below.]

	Sample Size	Sample Mean	Sample Std. deviation
WR	44	4.5161	0.09884
CB	29	4.4962	0.08621
SAF	20	4.5580	0.10660

Group	Mean	SD	n	Total		SSGroups	SSError
1	4.5161	0.09884	44	198.7084		0.000346	0.420082
2	4.4962	0.08621	29	130.3898		0.01495	0.208101
3	4.558	0.1066	20	91.16		0.030568	0.215908

ANOVA
Source	df	SS	MS	F	P-value
Groups	2	0.045865	0.022932	2.445125	0.092457
Error	90	0.84409	0.009379
Total	92	0.889955

test statistic F= 2.445 and P-value = 0.0925.

Report to Jones:

There is sufficient evidence to conclude that population mean times across the three positions are significantly different, F(2,90) = 2.445, P < 0.10.

Report to Dimitroff:

There is not sufficient evidence to conclude that population mean times across the three positions are significantly different, F(2,90) = 2.445, P > 0.05.