18. Find the sample s ze required or a margin o error o 2.6 percentage ports, an

Question

18. Find the sample s ze required or a margin o error o 2.6 percentage ports, and then nd one for a margin o error o 1.3 percentage ponts. for both use 95% confidence. Find the ratio o 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 nwhere 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 2.6 percentage points Round up to the nearest integer.) Find the necessary sample size required for a margin of error of 1.3 percentage points. Round up to the nearest integer.) Use the populations obtained above to find the ratio of the larger sample size to the smaller sample size Type an integer or decimal rounded to the nearest hundredth as needed.) To reduce the error by half, what do you need to multiply the sample size by? Type an integer or decimal rounded to the nearest hundredth as needed.)

Explanation / Answer

m = 2.6% = 0.026

n = 1/m2

n = 1/0.0262

n = 1479.3 = 1479 for margin of error 2.6%

m = 1.3% = 0.013

n = 1/0.0132

n = 5917.2 = 5917 for margin of error 1.3%

ratio of larger to smaller sample size = 5917/1479 = 4.00067 = 4

Hence to reduce the error by half i.e 2.6% to 1.3% we need to multiply the sample size by 4. I.e we need four times as large a sample size to reduce the error by half.

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