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 81 83 85 0.51 75 79 0.71 74 73 76 77 1.02 67 72 74 1.40 62 62 56 69 1.99 60 61 64 66 (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 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. Statistical Tables and Charts the absolute tolerance is +/-0.05

Answer 1

From the given scenario, the null and alternate hypotheses can be stated as follows: Null hypothesis: The mean percentage is equal according to all office diameters. H,:4 = Hz = Hz = HA = His = Ho Alternate hypothesis: The mean percentage is not equal according to all office diameters. H:At least one , is differ from other. . Calculate ANOVA-one way for the given data by using Excel as follows: Instructions: Import the data into Excel work sheet. Go to Addins → Megastat → Analysis of variance → One factor ANOVA Choose the data from work sheet and click ok. The resultant output is as shown below: One factor ANOVA n 4 4 Mean 82.3 77.0 75.0 71.8 64.8 62.8 72.3 Std. Dev 2.22 2.31 1.83 3.30 3.40 2.75 7.34 4 0.37-I 0.51-II 0.71-III 1.02-IV 1.40-V 1.99-VI Total 4 4 24 ANOVA table Source SS df MS Treatment 1,107.5000 5.0000 221.5000 30.4351 Error 131.0000 18.0000 7.2778 Total 1,238.5000 23.0000 p-value 0.0000 From the above output, the test statistic value is F. = 30.4351 Distribution Plot F, df1=5, df2=18 0.8 0.7 0.6 0.5 Density 0.4 0.3 0.025 0.2 0.1 0.025 0.0 00572 3.382 х Th test statistic is in rejection region, there is enough evidence to conclude that the mean percentage varies according to office diameter. b) The P-value for the F-test is P=0.0000 The P-value is less than the level of significance 0.05. Thus, the researcher can reject the null hypothesis. The mean percentage is not equal according to all office diameters.