Question

72. Hard water by region Recall from Chapter 7, Exercise 75, that data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns in England and Wales. In addition, the water hardness was recorded as the calcium concen- tration (parts per million, ppm) in the drinking water. The dataset also notes, for each town, whether it was south or north of Derby. Is there a significant difference in mortality rates in the two re- gions? Here are the summary statistics. (Data in Hard water) Summary of: mortality For categories in: Region Group Count Mean Median StdDev North 34 1631.59 1631 138.470 South 27 1388.85 1369 151.114 2000 - 0 Mortality North South Region a) Test appropriate hypotheses and state your conclusion. b) The boxplots of the two distributions show an outlier among the data in the North region. What effect might that have had on your test?

Answer 1

(a) The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ ≠ µ₂

The output is:

North	Spoth
1631.59	1388.85	mean
138.47	151.114	std. dev.
34	27	n
	59	df
	242.74000	difference (North - Spoth)
	20,787.48332	pooled variance
	144.17865	pooled std. dev.
	37.16589	standard error of difference
	0	hypothesized difference
	6.531	t
	1.67E-08	p-value (two-tailed)

Since the p-value (0.000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we have sufficient evidence to conclude that there is a significant difference in the two regions.

(b) The normality condition is violated with the presence of an outlier.

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