52) High concentration of the toxic element arsenic is all toocommon in groundwa

Question

52) High concentration of the toxic element arsenic is all toocommon in groundwater. It reported that for sample of n=5 waterspecimens selected for treatment by coagulation, the sample meanarsenic concentration was 24.3mg/L and the sample standarddeviation was 4.1.

a) Calculate and interpret a 95% CI for true average arsenicconcentration in all such water specimens.

b) Calculate a 90% confidence bound for the standard deviationof the arsenic concentrations distribution

c) Predict the arsenic concentration for a single water specimenin a way that conveys information about precision andreliability

Explanation / Answer

Given n=5, xbar=24.3, s=4.1 (a) =0.05, t(0.025, df=n-1=4)=2.78 (check student ttable) The 95% CI is xbar ± t*s/n --> 24.3 ± 2.78*4.1/sqrt(5) --> (19.203, 29.397)

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