Answer to Question #209198 in Statistics and Probability for Jayz

Question #209198

A particular brand of coffee contains an average of 112 mg of caffeine per cup with a standard deviation of 20 mg. A barista wants to investigate the same to estimate the true population mean caffeine content correct to within 5 mg adopting 95% confidence. How many cups of the same brand of coffee does he need for a sample?


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Expert's answer
2021-06-22T05:57:33-0400

The critical value for α=0.05\alpha=0.05 is zc=z1α/2=1.96z_c=z_{1-\alpha/2}=1.96

The corresponding confidence interval is computed as shown below:


CI=(xzc×σn,x+zc×σn)CI=(x-z_c\times \dfrac{\sigma}{\sqrt{n}}, x+z_c\times \dfrac{\sigma}{\sqrt{n}})

SE=zc×σn=>n=(zcσSE)2SE=z_c\times \dfrac{\sigma}{\sqrt{n}}=>n=( \dfrac{z_c\sigma}{SE})^2

Substitute


n=(1.96(20)5)2=61n=( \dfrac{1.96(20)}{5})^2=61

He needs 61 cups of the same brand of coffee for a sample.



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