There is concern that increased industrialization may be inc

There is concern that increased industrialization may be increasing the mineral content of river water. Ten years ago, the silicon content of the water in a certain river was 5 mg/L. Eighty-five water samples taken recently from the river have mean silicon content 5.4 mg/L and standard deviation 1.2 mg/L.

a) Carry out the appropriate hypothesis test by hand.

b) Verify your work in part (a) by using an appropriate confidence interval. (Don’t forget to state the appropriate level of confidence)

Solution

a)

mu = 5

Sample mean = 5.4

n=85

Sample SD = 1.2

This is z test.

z = (Sample Mean - mu)/(SD/sqrt(n))

= (5.4 - 5)/(1.2/sqrt(85))

= 3.07

b)

Confidence Level =0.05

Margin of error = (z*SD)/sqrt(n)

= (1.96 * 1.2 )/sqrt(85)

= 0.2551

Confidence Interval :

( 5 - 0.2551 , 5+0.2551)

= (4.74 , 5.26) Answer