4. An article in Environmental International vol 181 described an experiment in

Question

4. An article in Environmental International vol 181 described an experiment in which the amount of Radon released in shower was investigated. Radon-enriched water was used in the experiment, and six different orifice diameters were tested in shower heads The data follows: Orifice Diameter Radon Released 0.37 0.51 75 75 79 79 1.02 One-way ANOVA: Radon versus orifice Diameter All means are equal Alternative hypothesis At least one mean is different Equal variances were assumed for the analysis orifice Diameter 6 0.37, 0.51, 0.7, 102, 140, 199 Analysis of Variance F Value P Value 11834 226 675 3085 1323 7347 2.71058 0.37 1990, 8560 231 15, 7985) 0.51 75 000 1825 Fisher Pairwise Comparisons Grouping Information Using the Fisher LSD Method and95 Confdence Mean Grouping 0.37 7700 0.71 71.75 Means that do not share a letter are significantly different

Explanation / Answer

Part-a

Parameter of interest is radon released and the factor affecting it is diameter of orifice.

Part-b

Null Hypotheses H0: radon released is same for all diameter of orifice.

Alternative Hypotheses Ha: radon released is not the same for all diameter of orifice.

Part-c

Test statistic F(5,18)=30.85

Part-d

p-value=0.0000<0.05, so reject null hypothesis

Part-e

The radon released is not the same for all diameter of orifice

Part-f

Following pairs have similar diameter

(0.51,0.71)

(0.71,1.02)

(1.40,1.99)

Part-g

Normal plot shows points along the line, so normality assumption is satisfied.

Residual versus fit plot showed random pattern, so homoscedasticity assumption satisfied.

Residual versus order shows no pattern indicating independence assumption satisfied

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