Question

Six measurements were made of the magnesium ion concentration (in parts per million, or ppm) in a city's municipal water supply, with the following results. It is reasonable to assume that the population is approximately normal.

188 135 160 173 183 168

Construct a 95% confidence interval for the mean magnesium ion concentration.

A) 165.0 < µ < 170.7

B)164.7 < µ < 171.0

C)147.9 < µ < 187.8

D) 146.0 < µ < 189.7

Answer 1

From the given information,

By using confidence interval for mean calculator,

Solution: We need to construct the 95% confidence interval for the population mean u. The following information is provided: Sample Mean à = 167.8333 Sample Standard Deviation (s) 18.9886 = Sample Size (n) = 6 The critical value for a = 0.05 and is tc = df = n − 1 = 5 degrees of freedom 21-a/2;n-1 = 2.571 . The corresponding confidence interval is computed as shown below: s S CI = X-tc X X + te X n 'n 18.989 2.571 = 167.833 - 167.833 + . V6 = (147.906, 187.761)

Hence,

Required 95% confidence interval is,

147.9 < µ < 187.8

i.e., Option C. is correct.

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