Help with these two Find the sample size required for a margin of error of 3.6 p

Question

Help with these two

Find the sample size required for a margin of error of 3.6 percentage points, and then find one for a margin of error of 1.8 percentage points; for both, use 95% confidence. Find the ratio of the larger sample size to the smaller sample size. To reduce the error by half, what do you need to multiply the sample size by? Use the shortcut formula n where n represents the population size and m represents the margin of error in decimal form, to find the necessary sample size required for a margin of error of 3.6 percentage points. n(Round up to the nearest integer.)

Explanation / Answer

PART A.

For a margin error of 3.6%

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

Z a/2 at 0.05 is = 1.96

Sample Proportion = 0.5

ME = 0.036

n = ( 1.96 / 0.036 )^2 * 0.5*0.5

= 741.0494 ~ 742

For a margin error of 1.8%

Z a/2 at 0.05 is = 1.96

Sample Proportion = 0.5

ME = 0.018

n = ( 1.96 / 0.018 )^2 * 0.5*0.5

= 2964.1975 ~ 2965

PART B.

OPTOIN B: With 95% confidence, the population proportion of people who think marriage is becoming obsolete is between 0.37030 and0.441309

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