Determining Required Sample Size

00:00 4 marks

A researcher wants to estimate the average weight of apples in an orchard with a 95% confidence interval. The population standard deviation is known to be \(\sigma = 15\) grams. Determine the minimum sample size required to achieve a margin of error of no more than 5 grams. Use the critical value \(z^* \approx 1.96\).

Hint Hint

Hint

Recall that the margin of error for a confidence interval for the mean is given by \(ME = z^* \times \frac{\sigma}{\sqrt{n}}\). Rearrange this formula to solve for \(n\).

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Complete Answer

The required sample size is \(n = \left( \frac{1.96 \times 15}{5} \right)^2 = 34.5744\), so rounding up to the nearest whole number gives \(n = 35\).

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