Question

13.2.1 GO Tutorial 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 (%) 0.37 80 83 83 85 0.51 75 75 79 79 0.71 74 73 76 77 1.02 67 72 74 74 1.40 62 62 68 69 1.99 60 61 6466 (a) Does the size of the orifice affect the mean percentage of radon released? Use a = 0.05. Round all intermediate calculations to four decimal places (e.g. 12.3456). Since Fo = IS in the rejection region, there is 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. P-value 0

Answer 1

Answer: U let T = The su sung all observation of 0.37 diameter -331 Similarly T2=308;T3-300, To=287, T5=261,7=251 for other diameters Grand total (G) = TtTy +T3 +TQ + TS+T6 -1738 x² = 127116 n=24 Sstot = {x² - G (1738) 127116 - 1255.8333 24 Ssa 'Between 24 4 Sn=n, = n2 = 24 225 Share ang 4 - 126979-125860.1666 1118.8333 ss within = 1255.8333 1118.8333 =137

SS Retween For 12 Ss within 1118.8333 S 137 18 24-6 F There is Fo=/29.4 Critical value = f(5718,0.05] =2.77=7 Fo in the rejection region, sufficient evidence to conclude that the mean percentage varies according to orifice diameters b) p-value =P(>29.4) - 0.0000 p-value 2005