Question

p	Margin of Error	n
0.32	0.01
0.32	0.02
0.32	0.03
0.32	0.04

Write a formula in cell C2 to calculate the sample size needed to be 95% confident that the actual population proportion is within the 1% margin of error of the 32% sample proportion.

Then use the fill-down feature to complete column C. Note that the value in C4 gives the sample size needed to be 95% confident that the actual population proportion is within the 3% margin of error of the 32% sample proportion.

Suppose a new poll was conducted and it was reported that 25% of the sample responded in favor of a particular question and that this poll had a 3.5% margin of error with a 95% confidence level.

Complete cell A6 to indicate this sample proportion.

Complete cell B6 to indicate the margin of error.

Use the auto-fill feature to determine the needed sample size in cell C6 for this new poll.

Answer 1

Confidence Level, CL =    0.95

Significance level, α = 1 - CL =    0.05

Critical value, z = NORM.S.INV(0.05/2) = 1.96

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For cell C2:

Sample size, n = (z² * p * (1-p)) / E² = (1.96² * 0.32 * 0.68)/ 0.01²  

= 8359.014 = 8360

For cell C3:

Sample size, n = (z² * p * (1-p)) / E² = (1.96² * 0.32 * 0.68)/ 0.02²  

= 2089.7536 = 2090

For cell C4:

Sample size, n = (z² * p * (1-p)) / E² = (1.96² * 0.32 * 0.68)/ 0.03²  

= 928.7794 = 929

For cell C5:

Sample size, n = (z² * p * (1-p)) / E² = (1.96² * 0.32 * 0.68)/ 0.04²  

= 522.4384 = 523

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Cell A6: p = 0.25

Cell B6: E = 0.035

Cell C6:

Sample size, n = (z² * p * (1-p)) / E² = (1.96² * 0.25 * 0.75)/ 0.035²  

= 587.9784 = 588