Question

The average zinc concentration recovered from a sample of measurements taken in 37 different locations in a river is found to be 2.6 grams per milliliter. Assume that the population standard deviation is 1.1 gram per milliliter.

(a) Find the lower limit of the 95% confidence intervals for the mean zinc concentration in the river. Answer for part 1

(b) Find the upper limit of the 95% confidence intervals for the mean zinc concentration in the river. Answer for part 2

(c) Find the lower limit of the 98.8% confidence intervals for the mean zinc concentration in the river. Answer for part 3

(d) Find the upper limit of the 98.8% confidence intervals for the mean zinc concentration in the river

Answer 1

a) For 95% confidence interval, the critical value is z_0.025 = 1.96

The lower limit of the 95% confidence interval is

= 2.6 - 0.35

= 2.25

b) The upper limit of the 95% confidence interval is

= 2.6 + 0.35

= 2.95

c) For 98.8% confidence interval, the critical value is z_0.006 = 2.51

The lower limit of the 98.8% confidence interval is

= 2.6 - 0.45

= 2.15

d) The upper limit of the 98.8% confidence interval is

= 2.6 + 0.45

= 3.05