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How many women must be randomly selected to estimate the mean weight of women in one age group. We want 90% confidence that the sample mean is within 3.7 lb of the population mean, and the population standard deviation is known to be 28 lb.

Sagot :

JeanaShupp

Answer: the required sample size = 155

Step-by-step explanation:

If the standard deviation of the prior study is known, then the formula to compute required sample size:

[tex]n=(\frac{z^*\times\sigma}{E})^2[/tex], where E = Margin of error, z* = Critical value, [tex]\sigma[/tex] =  populion standard deviation.

Given: E = 3.7 , [tex]\sigma=28[/tex]

Critical value for 90% confidence = 1.645

Required sample size: [tex]n=(\frac{1.645\times28}{3.7})^2[/tex]

[tex]n=(12.4486486486)^2\approx155[/tex]

Hence, the required sample size = 155

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