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What is the smallest sample size that guarantees that the margin of error is less than 1% when constructing a 97% confidence interval for a population proportion

Sagot :

tushargupta0691

In order to get 97% confidence level, with confidence interval of

+/- 1%, and standard deviation of 0.5 our sample size should be 11,772 samples

A confidence interval for a population mean, when the population standard deviation is known based on the conclusion of the Central Limit Theorem that the sampling distribution of the sample means follow an approximately normal distribution.

Accordingly, the Necessary Sample Size is calculated as follows:

Necessary Sample Size = [tex](Z-score)^{2} . StdDev*(1-StdDev) / (Margin Of Error)^{2}[/tex]

Given:-

  • At  97% confidence level Z-score = 2.17
  • Assuming standard deviation = 0.5,
  • margin of error (confidence interval) of +/- 1%.

Substituting in the given formula we get

Necessary Sample Size =

= ((2.17)² x 0.5(0.5)) / (0.01)²

= (4.7089x 0.25) / .0001

= 1.177225 / 0.0001

= 11,772.25

Hence in order to get 97% confidence level, with confidence interval of

+/- 1%,  and standard deviation of 0.5 our sample size should be 11,772

Learn more about sample size here :

https://brainly.com/question/10068670

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