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You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately
σ=39.7. You would like to be 95% confident that your estimate is within 3 of the true population mean. How large of a sample size is required?

Respuesta :

xxamari

Answer:

673 people

Step-by-step explanation:

Statistics<3

Use the margin of error formula.

ME = t*[tex]\frac{s}{\sqrt{n} }[/tex]

  • Margin of error or ME = 3
  • Critical t or t* with a confidence level of 95% on the calculator is invNorm(.975) = 1.96. You would use invt, except you don't have the degrees of freedom, so you can approximate with invNorm. It's close enough.
  • Standard deviation or s = 39.7
  • Solve for n!

3 = 1.96*[tex]\frac{39.7}{\sqrt{n} }[/tex]

3/1.96 = [tex]\frac{39.7}{\sqrt{n} }[/tex]

1.531 = [tex]\frac{39.7}{\sqrt{n} }[/tex]

39.7/1.531 = [tex]\sqrt{n}[/tex]

25.937 = [tex]\sqrt{n}[/tex]

25.937^2 = [tex]\sqrt{n}[/tex]^2

672.7 = n

You need at least 673 people to be confident!

fichoh

Using the sample size relation with the standard normal distribution, the required sample size is 673 samples.

  • n = [(Z* × σ) / ME]²

  • ME = margin of error

  • Z* = Zcritical at 95% = 1.96

Substituting the values into the equation :

n = [(Z* × σ) / ME]²

n = [(1.96 × 39.7) / 3]²

n = (77.812 / 3)²

n = 25.937²

n = 672.7

Therefore, the Number of samples required is 673 samples.

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