Arsenic concentration in public drinking water supplies is a potential health ri

Question

Arsenic concentration in public drinking water supplies is a potential health risk. An article in the Arizona Republic (Sunday, May 27, 2001) reported drinking water arsenic concentrations in parts per billion (pb) for 10 metropolitan Phoenix communities and 10 communities in rural Arizona. The data follow: Metro Phoenix Phoenix, 3; Chandler 7; Gilbert, 25; Glendale, 10; Mesa, 15; Paradise Valley, 6; Peoria, 12 Scottsdale, 25; Tempe, 15; Sun City, 7; Rural Arizona Rimrock, 48; Goodyear, 44; New River, 40; Apachie Junction, 38; Buckeye, 33; Nogales, 21 Black Canyon City, 20; Sedona, 12; Payson, 1; Casa Grande, 18; We would like to perform a test on if there is any difference between metro Phoenix and rural Arizona areas in terms of arsenic concentrations (use = 0.01) (a) What is the p-value? (0.75 points) (b) What is the acceptance region? (0.75 points)

Explanation / Answer

we can quickly perform the analysis in the open source statisitcal package R , the complete R snippet is as shoen below

Pheonix <- c(3,7,25,10,15,6,12,25,15,7)
Arizona <- c(48,44,40,38,33,21,20,12,1,18)

# t test
t.test(Pheonix,Arizona,alternative = "two.sided",conf.level=0.99)

The results are

t.test(Pheonix,Arizona,alternative = "two.sided",conf.level=0.99)

   Welch Two Sample t-test

data: Pheonix and Arizona
t = -2.7669, df = 13.196, p-value = 0.01583 ## as the p value is less than 0.05 , hence we reject the null hypothesis in favor of alternate hypothesis to conclude that the mean values of Pheonix and Arizona are significantly different
alternative hypothesis: true difference in means is not equal to 0
99 percent confidence interval:
-31.289827 1.289827
sample estimates:
mean of x mean of y
12.5 27.5

The t critical values as seen from the t table for df = 13 is

t-value (two-tailed): +/- 3.01

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