Question

do the following problem from the text book. please use R software and oost the code along woth answes and any graphs that you are required to make, olease read both pictures

13-10. An article in Environment International [1992, Vol. 18(4)] described 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 0.37 0.51 0.71 1.02 1.40 1.99 Radon Released (%) 83 79 76 74 67 64 80 75 74 67 62 60 83 75 73 72 62 61 85 79 74 69 (a) Does the size of the orifice affect the mean percentage of radon released? Use α-0.05. (b) Find the P-value for the F-statistic in part (a). (c) Analyze the residuals from this experiment. (d) Find a 95% confidence interval on the mean percent of radon released when the orifice diameter is 1.40. 13-10556 For part d) instead of finding the 95% confidence interval for the 1.4 treatment. Find the 95% confidence interval for the difference between the 1.4 and 1.99 treatments. Does this confidence interval suggest that they have significantlv different treatment meanc?

Answer 1

a)

H₀: The size of the orifice do no affect the radon released.

H₁: The size of the orifice affect the radon released.

>model<-aov (diameter-radon, data-data) mmary (model) Df Sum Sq Mean Sq F value Pr (>F) 1 6.149 6.149 104.3 8.22e-10* radon Residuals 22 1.2970.059 Signif. codes

Since the p value < 0.05,we reject H₀. Therefore we can conclude that the size of the orifice affect the radon released.

b)

P value = 8.22e-10

F statistics = 104.3

c)

Residuals,

> data.frame (data,resid (model)) diameter radon resid.model. 80 -0.098501728 83 0.110612346 83 0.110612346 85 0.250021728 75 -0.307025185 75 -0.307025185 79-0.028206420 79-0.028206420 74 -0.176729877 73 -0.246434568 76 -0.037320494 77 0.032384198 67 -0.354662716 72 -0.006139259 74 0.133270123 74 0.133270123 62 -0.323186173 62 -0.323186173 67 0.025337284 69 0.164746667 60 0.127404444 61 0.197109136 64 0.406223210 66 0.545632593 0.37 0.37 0.37 0.37 0.51 0.51 0.51 0.51 0.71 0.71 0.71 0.71 1.02 1.02 1.02 1.02 1.40 1.40 1.40 1.40 1.99 1.99 1.99 1.99 2 7 10 12 13 14 15 16 17 18 19 20 21 23

d)

95% Confidence Interval for orifice 1.4 = 55 ± 17.1 = (37.9 , 72.1)

e)

95% Confidence Interval for the Difference of mean of orifice 1.4 and 1.99 = ( -3.2555 , 7.7555 )