Question

You want to estimate the amount of arsenic in a well to within 2 miligrams per liter. From previous work,, you know that the level varies with ?= 5 miligrams per liter. If you want to be 99$=% certain, how many samples do you need to take?

A) 36

B) 38

C) 40

D) 42

E) 44

F) 46

G)48

Answer 1

Solution :

Given that,

standard deviation = = 5

margin of error = E = 2

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Sample size = n = ((Z_/2 * ) / E)²

= ((2.576 * 5 ) / 2 )²

= 41.5

= 42

Sample size = 42

Option D ) is correct.

Answer 2

Solution :

Given that,

standard deviation = = 5

margin of error = E = 2

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Sample size = n = ((Z_/2 * ) / E)²

= ((2.576 * 5 ) / 2 )²

= 41.5

= 42

Sample size = 42

Option D ) is correct.