Data Analysis & Statistical Methods Flashcards

A dealer wants to estimate the clarity mix of a large melee parcel that is already sorted by sieve size. Which sampling method best ensures every size group is represented?

Answer: Stratified random sampling

Stratified sampling draws randomly from each subgroup, so every sieve size is represented in proportion.

What happens to the standard error of a sample mean when the sample size increases?

Answer: It decreases

Standard error equals SD divided by the square root of n, so it shrinks as n grows.

A study reports a 95% confidence interval of $3,800-$4,200 for the mean price per carat of a sapphire grade. What is the best interpretation?

Answer: The method used captures the true mean in about 95% of repeated samples

A confidence level describes how reliable the interval-building method is over repeated sampling.

The correlation coefficient between carat weight and total price in a diamond dataset is r = 0.92. What does this indicate?

Answer: A strong positive linear relationship

An r close to +1 means a strong positive linear association.

Fluorescent diamonds in a dataset sell for less on average. Why can't a consultant conclude that fluorescence alone causes the lower price?

Answer: Correlation does not prove causation, so other variables may be involved

Confounding factors such as color grade or market perception can explain an association.

A gem weighs 4.00 ct in air and 3.00 ct in water. What is its specific gravity?

Answer: 4.00

SG = weight in air / (weight in air - weight in water) = 4.00 / 1.00 = 4.00, which is consistent with corundum.

When testing whether heated and unheated sapphires of the same grade sell at different average prices, what is the null hypothesis?

Answer: There is no difference in mean price

The null hypothesis assumes no effect or no difference until the data shows otherwise.