Question

According to an article the bottled water you are drinking may contain more bacteria and other potentially carcinogenic chemicals than are allowed by state and federal regulations. Of the more than 1100 bottles​ studied, nearly​ one-third exceeded government levels. Suppose that a department wants an updated estimate of the population proportion of bottled water that violates at least one government standard. Determine the sample size​ (number of​ bottles) needed to estimate this proportion to within plus or minus0.03 with​ 99% confidence.

The sample size needed to estimate this proportion to within plus or minus 0.03 with​ 99% confidence is ( ) nothing. ​(Round up to the nearest whole​ number.)

Answer 1

Solution :

Given that,

= 0.5

1 - = 0.5

margin of error = E = 0.03

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 * * (1 - )

= (2.576 / 0.03)² * 0.5 * 0.5

= 1843.27

sample size = 1844