Question

Trace metals in drinking water affect the flavor and an unusually high concentration can pose a health hazard. We obtain the following data for 9 glasses of water. Each glass contained the same amount of water. We look at the zinc concentration (mg/L) in bottom water and the zinc concentration in surface water for each glass. It is fine to round any standard deviations to 2 decimals.

Glass 1 2 3 4 5 6 7 8 9

Bottom Water .48 .32 .62 .58 .76 .77 .70 .64 .52

Surface Water .42 .24 .39 .41 .61 .61 .63 .52 .41

Use a 96% confidence interval. Assume that the differences follow a normal distribution.

Answer 1

necessary calculation table:-

bottom water ()	surface water ()
0.48	0.42	0.06	0.004597
0.32	0.24	0.08	0.002285
0.62	0.39	0.23	0.010445
0.58	0.41	0.17	0.001781
0.76	0.61	0.15	0.000493
0.77	0.61	0.16	0.001037
0.7	0.63	0.07	0.003341
0.64	0.52	0.12	0.000061
0.52	0.41	0.11	0.000317
		sum=1.15	sum=0.024356

sample size (n) = 9

t critical value at 96% confidence level,both tailed test:-

[ using excel for df = (9-1) = 8,alpha=0.04, both tailed test]

hypothesis:-

the 96% confidence interval is:-

decision:-

as 0 in outside the confidence interval, we fail to reject the null hypothesis.

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