Question

You decide to monitor deaths caused by drugs in your community. For the next 250 individuals whose deaths are drug-related, 123 were caused by legally prescribed drugs and the rest were the result of illicit drug use. Find the 90% confidence interval for the proportion of drug related deaths that are caused by legally prescribed drugs.

Use the information to determine the sample size that you would need if you wanted to replicate the study with 99% confidence and a maximum error of estimate equal to .01 or 1%.

Answer 1

Solution :

Given that,

n = 250

x = 123

Point estimate = sample proportion = = x / n = 0.492

1 - = 0.508

a)

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z _0.05 = 1.645

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645 * (((0.492*0.508) / 250)

= 0.052

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.492 - 0.052 < p < 0.492 - 0.052

0.440 < p < 0.544

The 90% confidence interval is ( 0.440 , 0.544 )

b)

margin of error = E = 0.01

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 / 0.01)² * 0.492*0.508

= 16585.19

sample size = 16586