Question

13.2.1 GO Tutorial X Note that we reject the null hypothesis of equal treatment means when the test statistic is large enough. 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 8385 0.51 75 757979 0.71 74 73 76 77 1.02 67 72 74 74 1.40 62 62 66 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). X (0.6661 Since Fo = x is not in the rejection region, there is not 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. T0.05 P-value 0.10 V Activate Windows Go to Settings to activate Windows.

Answer 1

using excel>data>data analysis>ANOVA without replication

we have

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
0.37	4	329	82.25	4.916667
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	259	64.75	11.58333
1.99	4	251	62.75	7.583333
RR 1	6	418	69.66667	62.66667
RR 2	6	424	70.66667	60.26667
RR 3	6	442	73.66667	54.66667
RR 4	6	450	75	47.6
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Office diameter	1107.5	5	221.5	179.5946	7.88E-13	2.901295
Radon Released	112.5	3	37.5	30.40541	1.28E-06	3.287382
Error	18.5	15	1.233333
Total	1238.5	23

a ) Since F0 = 179.5946

is in the rejection regionthere is sufficient evidence to conclude that mean percetage varies according to office diameter

b ) p valuje <0.01