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 diameters were tested in shower heads. The data from the experiment are shown In the following table. (a) Does the size of the affect the mean percentage of radon released? Use alpha = 0.05. Round all intermediate calculations to four decimal places (e.g. 12.3456). Since F_0 = 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).

Explanation / Answer

(a) Critical value of F - test at alpha level = 0.05 and dF1(Numerator) =5 and dF2 (denominator)= 18

F0.05, 5, 18 = 2.773

F 0 =30.235 is in rejection region, there is sufficient evidence to conclude that the mean percantage varies according to orifice diameter.

(b) FInd Bound on P - value for the F - statistic.

As F - statistic = 30.235

so Lower bound will be 0

Upper bound is 0.0001

Anova: Single Factor SUMMARY Groups Count Sum Average Variance 0.37 4 330 82.5 4.333333 0.51 4 308 77 5.333333 0.71 4 300 75 3.333333 1.02 4 287 71.75 10.91667 1.4 4 260 65 12.66667 1.99 4 251 62.75 7.583333 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 1112.833 5 222.5667 30.23547 3.71E-08 2.772853 Within Groups 132.5 18 7.361111 Total 1245.333 23

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