Question

Use the given information to find the minimum sample size required to estimate an unknown population mean `\mu`?

"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 3.4 lb of the population mean, and the population standard deviation is known to be 25 lb."

Answer 1

`147` people

Explanation:

E = 3.4, `\sigma=25` lb;
since confidence level is 90%, `\alpha/2=(1=0.90)/2=0.10/2=0.05`
`\thereforez_{\alpha//2}=z_0.05\approx1.645`

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minimum sample size `n` formula:
`n=[(z_{\alpha//2}\cdot\sigma)/E]^2`

`\thereforen=[(1.645\cdot\25)/3.4]^2`
`\approx146.3033` (or, in whole numbers, 147 people)