An article in Environment International (Vol. 18, No. 4, 1992) describes an expe

Question

An article in Environment International (Vol. 18, No. 4, 1992) describes an experiment in which the amount of radon released in showers was investigated. Radon-enriched water was used in the experiment, and six different orifice diameters were tested in shower heads. The data from the experiment are shown in the following table Orifice Diameter Radon Released (%) 80 83 8385 75 75 79 79 74 73 7677 67 72 7474 62 62 68 69 60 61 6466 0.37 0.51 0.71 1.02 1.40 1.99 = 0.05 (a) Does the size of the orifice affect the mean percentage of radon released? Use Round all intermediate calculations to four decimal places (e.g. 12.3456) Since Fo = 1 in the rejection region, there sufficient evidence to conclude that the mean percentage varies according to orifice diameter (b) Find bounds on the P-value for the F-statistic in part (a) Use only Table VI of Appendix A.

Explanation / Answer

Here ANOVA analysis

(A) since F0 = 29.4

is in the rejection region , there is sufficient evidence to conclude that the mean percantage variaes according to orifice diameter.

B) Here p - value for the staisitic is in between 0 to 0.001

p - value = 4.62 x 10-8

Anova: Single Factor SUMMARY Groups Count Sum Average Variance 0.37 4 331 82.75 4.25 0.51 4 308 77 5.333333 0.71 4 300 75 3.333333 1.02 4 287 71.75 10.91667 1.4 4 261 65.25 14.25 1.99 4 251 62.75 7.583333 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 1118.833 5 223.7667 29.4 4.62E-08 2.772853 Within Groups 137 18 7.611111 Total 1255.833 23

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