## Related questions with answers

Diamonds sold on the open market. Refer to the sample of 308 diamond stones that were listed for sale on the open market in Singapore's Business Times. Recall that the color of each diamond is classified as D, E, F, G, H, or I, while the clarity of each is classified as VVS1, VVS2, VS1, or VS2. Find a $99 \%$ confidence interval for the proportion of all diamonds for sale on the open market that are classified as "D" color. Interpret the result.

Solution

Verified16 of the 308 colors in the data set are D.

$\begin{aligned} n&=\text{Sample size}=308 \\ x&=\text{Number of successes}=16 \\ c&=\text{Confidence coefficient}=99\%=0.99 \end{aligned}$

We need to determine a confidence interval about the population proportion $p$.

The confidence interval about the population proportion is $\hat{p}\pm E$ with $E=z_{\alpha/2}\cdot \sqrt{\dfrac{\hat{p}\hat{q}}{n}}$.

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