Question

1. Arsenic concentration in public drinking water is a potential health risk. An article in Arizona Republic (May 27, 2001) reported drinking water Arsenic concentrations in ppb (parts per billion) for 10 Metro Phoenix communities and 10 communities in Rural Arizona. The summary statistics for Metro Phoenix are; sample mean equals 12.5, and sample standard deviation equals 7.63. The summary statistics for Rural Arizona are; sample mean equals 27.5, and sample standard deviation equals 15.3. Test if there is any significant difference of the Arsenic concentrations between Metro Phoenix and Rural Arizona. Assume that the data are independent.

2. What is the type of statistical test procedure that should be used to test the hypotheses? Explain.

3. Construct a 95% confidence interval for the true mean difference. Test the hypotheses using the confidence interval. Interpret the test result clearly.

4. Test the hypotheses using the Test Statistic / Critical Value method (you must clearly indicate the test statistic, and the critical value(s) use Take α=5%). Do you get the same answer as part (c)? If your answer is the same as (c), you do not have to interpret again. Otherwise, interpret the test findings.

5. What is the P value of the test? Test the hypotheses using the P value. Take α=5%. Do you get the same answer as parts (c) and (d)? If your answer is the same as (c) and (d), you do not have to interpret again. Otherwise, interpret the test findings.

Answer 1

Given:

The summary statistics for Metro Phoenix are:

sample mean = 1 = 12.5,

sample standard deviation = s1 = 7.63

Sample size = n1 = 10,

The summary statistics for Rural Arizona are :

sample mean = 2 = 27.5

sample standard deviation = s2 = 15.3

Sample size = n2 = 10

a) Two sample independent t-test procedure that should be used to test the hypotheses.

b) A 95% confidence interval for the true mean difference :

Since confidence interval does not contain hypothesized population mean, we reject the null hypothesis.

Conclusion :

There is any significant difference of the Arsenic concentrations between Metro Phoenix and Rural Arizona.

b) Hypothesis test :

The null and alternative hypothesis is

H_0:

H_0:

Since P-value is less than significance level 0.05, we reject the null hypothesis.

We got the same answer as part c and d.