13. The percentage of people not covered by health care insurance in 2003 was 15

Question

13. The percentage of people not covered by health care insurance in 2003 was 15.6%. A congressional rged with conducting a sample survey to obtain more current information. What sample size would you recommend if the committee's goal is to estimate the current proportion of individuals without health care insurance with a width of 5% (.05). Use a 90% confidence level. a. b. Repeat part (a) assuming you have no knowledge of the proportion. What impact does the confidence level have on the sample size?

Explanation / Answer

a.

Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)

Z a/2 at 0.1 is = 1.645

Sample Proportion = 0.156

ME = 0.05

n = ( 1.645 / 0.05 )^2 * 0.156*0.844

= 142.5144 ~ 143

b.

Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)

Z a/2 at 0.1 is = 1.645

Sample Proportion = 0.5

ME = 0.05

n = ( 1.645 / 0.05 )^2 * 0.5*0.5

= 270.6025 ~ 271

c.

the size of the sample size increases when confidence increases

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