Are olympians getting faster? to determine if there is a significant difference

Question

Are olympians getting faster? to determine if there is a significant difference in the mean times of athletes from various Olympics, the time (in seconds) for the gold medal winners of four 100m swimming events from the last four summer olympic games are evaluated.

a) Identify the following for this experiment.

Response: _______________________________

Experimental Unit: _________________________

x14: ______   T2: _______ B3: ________

b) Complete the ANOVA table for this experiment.

Note: for full credit, show your work for the SS column at minimum.

c) Does the data provide sufficient evidence to indicate a significant differnece in the mean gold medal swimming times from the various Olympics? Use the critical value approach at the 1% level of significance. (Show all work)

d) If appropriate, determine all of the pairwise differnces in the mean gold medal swimming times at the various Olympics. (Show all work) If not appropriate, explain why or why not?

e) Was blocking appropriate for this experiment? Perform an appropriate test at the 10% level of significance using the p-value approach. (Show all work)

f) Construct a 95% confidence interval for the mean gold medal swimming time for men's 100m backstroke. (Show all work)

100m Swimming Rio (2016) London (2012) Beijing (2008) Athens (2004) Total Women's Butterfly 55.48 55.98 56.73 57.72 225.91 Men's Breaststroke 57.13 58.46 58.91 60.08 234.58 Women's Backstroke 58.45 58.33 58.96 60.37 236.11 Men's Backstroke 51.97 52.16 52.54 54.06 210.73 Total 223.03 224.93 227.14 232.23 907.33

Explanation / Answer

Anova: Two-Factor Without Replication SUMMARY Count Sum Average Variance Women's Butterfly 4 225.91 56.4775 0.950025 Men's Breaststroke 4 234.58 58.645 1.4863 Women's Backstroke 4 236.11 59.0275 0.875625 Men's Backstroke 4 210.73 52.6825 0.899491667 Rio (2016) 4 223.03 55.7575 7.851825 London (2012) 4 224.93 56.2325 8.670091667 Beijing (2008) 4 227.14 56.785 9.089766667 Athens (2004) 4 232.23 58.0575 8.510691667 ANOVA Source of Variation SS df MS F P-value F crit Rows 101.5593188 3 33.85310625 377.1671193 8.88246E-10 3.862548358 Columns 11.82651875 3 3.942172917 43.92087366 1.06415E-05 3.862548358 Error 0.80780625 9 0.08975625 Total 114.1936438 15

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