You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 23%. You would like to be 98% confident that your estimate is within 1% of the true population proportion. How large of a sample size is required?

Question
Asked Nov 22, 2019
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You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 23%. You would like to be 98% confident that your estimate is within 1% of the true population proportion. How large of a sample size is required?

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Expert Answer

Step 1

Step-by-step procedure to obtain the value of z using MINITAB:

  • Choose Graph > Probability Distribution Plot choose View Probability > OK.
  • From Distribution, choose ‘Normal’ distribution.
  • Click the Shaded Area
  • Choose Probability and Both Tail for the region of the curve to shade.
  • Enter the Probability value as 2.
  • Click OK.

Output using the MINITAB software is given below:

Distribution Plot
Normal, Mean=0, StDev=1
0.4
0.3
0.2
0.1
0.1
0.1
0.0
-1.282
0
1.282
X
Density
help_outline

Image Transcriptionclose

Distribution Plot Normal, Mean=0, StDev=1 0.4 0.3 0.2 0.1 0.1 0.1 0.0 -1.282 0 1.282 X Density

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Step 2

From the output, the value of z is 1.282 for 98% confidence...

(1-)
n =i
E
1.282
0.23(1-0.23)
0.01
2,910.6
2,911
help_outline

Image Transcriptionclose

(1-) n =i E 1.282 0.23(1-0.23) 0.01 2,910.6 2,911

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Math

Statistics

Hypothesis Testing

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