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you need to compute the 99% confidence interval for the population mean. how large a sample should you draw to ensure that the sample mean does not deviate from the population mean by more than 1.2? (use 6.0 as an estimate of the population standard deviation from prior studies).

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contexto1019

The sample size of the population to 99% confidence interval for the population mean is 166.

The formula to the sample size is  n = (zⁿ ×∝÷ E)

where  = Z critical z value ( confidence level) ,

E = Margin of error,

= population standard deviation.

Here E= 1.3

Critical z-value for 99% confidence level = 2.576

A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance. Although less robust in practice, it is algebraically easier than the average absolute deviation.

Then, required sample size :

n= (6.9 × 2.576÷2.3)² = 7.728²

59.72≈ 60

n = (6.0 × 2.765÷ 1.2)²

  = 12.88²

 169.89 ≈ 166

   

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