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Question 6
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately $σ = 32.3$ . You would like to be $99 %$ confident that your esimate is within 0.2 of the true population mean. How large of a sample size is required?
$n =$

Do not round mid-calculation. However, use a critical value accurate to three decimal places - this is important for the system to be able to give hints for incorrect answers.

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Final Answer: The required sample size is $173076$ .

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Step 1 ：The formula for the sample size in this case is given by: $n = {(\frac{Z_{α / 2} \cdot σ}{E})}^{2}$ where: $Z_{α / 2}$ is the z-score corresponding to the desired confidence level (in this case, 99% confidence corresponds to a z-score of 2.576), $σ$ is the population standard deviation (32.3 in this case), $E$ is the desired margin of error (0.2 in this case).

Step 2 ：We can substitute the given values into the formula to find the required sample size.

Step 3 ：The `math.ceil` function is used to round up to the nearest whole number, since we can't have a fraction of a sample.

Step 4 ：Final Answer: The required sample size is $173076$ .

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