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Suppose that we wanted to estimate the true average number of eggs a queen bee lays with 95 percent confidence. The margin of error we are willing to accept is 0.5. Suppose we also know that s is about 10. At minimum, what sample size should we use ?

Respuesta :

dogacandu

Answer:

At least 1537 samples needed to estimate the true average number of eggs a queen bee lays with 95 percent confidence

Step-by-step explanation:

Minimum sample size required can be found using the formula

N≥[tex](\frac{z*s}{ME} )^2[/tex] where

  • N is the sample size
  • z is the corresponding z-score of 95% confidence level (1.96)
  • s is the standard deviation (10)
  • ME is the margin of error (0.5)

then N≥[tex](\frac{1.96*10}{0.5} )^2[/tex] =1536.64

Then, at least 1537 samples needed to estimate the true average number of eggs a queen bee lays with 95 percent confidence

raphealnwobi

The minimum sample size needed is 1537 for a margin of error of 0.5.

What is margin of error?

Margin of error is used to determine by what value there is deviation from the real value. Margin of error (E) is given by:

[tex]E=Z_\frac{\alpha}{2} *\frac{standard\ deviation}{\sqrt{sample\ size} }[/tex]

The 95% confidence level have a z score of 1.96. Hence for E = 0.5, standard deviation = 10. hence:

[tex]0.5=1.96*\frac{10}{\sqrt{sample\ size}}\\ \\sample\ size=1537[/tex]

The minimum sample size needed is 1537 for a margin of error of 0.5.

Find out more on margin of error at: https://brainly.com/question/10218601

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