Confidence 61774

What is the smallest number of men we would have to choose to estimate the mean height of men with an accuracy of +, - 0.5cm, and 95% confidence, assuming a standard deviation of 8cm?

Correct answer:

n =  984

Step-by-step explanation:

$$\begin{gathered} \alpha =0.05 \\ \beta =1-\alpha /2=1-0.05/2=\frac{39}{40}=0.975 \\ z(\beta ) \\ z=1.96 \\ \sigma =8\text{cm} \\ \Delta =0.5\text{cm} \\ n\ge (\frac{\sigma }{\Delta }\cdot z{)}^2 \\ {n}_0=(\frac{\sigma }{\Delta }\cdot z{)}^2=(\frac{8}{0.5}\cdot 1.96{)}^2=983.4496 \\ n=\lceil n_0\rceil =\lceil 983.4496\rceil =984 \end{gathered}$$

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