Question

An environmental activist research group collects 16 samples from a wastewater effluent stream of a chemical plant in Bhopal (India) and measures the concentration of a potent cyanide-based toxin. Their results yield a mean concentration of ?. ? ?pm with a sample variance of ?. ?5 ???^?. It may be assumed that the data are the realization of a normally distributed random variable.

(a) What is the two-sided 98% confidence interval for the measured toxin concentration in the effluent stream?

(b) Construct a right-tailed ??% concentration interval of the form [?. ?0,?_?] such that the chemical plant can claim with 98% confidence that the toxin concentration could not possibly exceed ?_? ppm.

(c) Construct a left-tailed ?8% concentration interval of the form [?_?, ?.?0] such that the activists could claim with 98% confidence that the toxin concentration definitely exceeds ?_? ppm.

Answer 1

Given,

Number of sample points, n = 16

mean concentration ,
Standard Deviation concentration,

Part (a)

The required two-sided 98% confidence interval for the measured toxin concentration, on light of the given data is obtained as follows,

where is the upper /2 point of a standard normal distribution and = 0.02

Thus, the required two sided Confidence interval is obtained as,

Part (b)

The required left-sided 98% confidence interval for the measured toxin concentration, on light of the given data is obtained as follows,

where is the upper point of a standard normal distribution and = 0.02

Thus, the required two sided Confidence interval is obtained as,

Part (c)

The required right-sided 98% confidence interval for the measured toxin concentration, on light of the given data is obtained as follows,

where is the upper point of a standard normal distribution and = 0.02

Thus, the required two sided Confidence interval is obtained as,