What Is the Relationship Between Diamond Price and Carat Size

question 40

Multiple Choice

What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats) . The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the carat size of the diamond was 1 carat. The results are shown here: 95% confidence interval for E(Y) : ($9091.60, $9509.40) 95% prediction interval for Y: ($7091.50, $11,510.00) Which of the following interpretations is correct if you want to use the model to determine the price of a single 1-carat diamond?

• A) We are 95% confident that the price of a 1-carat diamond will fall between $7091.50 and $11,510.00.
• B) We are 95% confident that the average price of all 1-carat diamonds will fall between $7091.50 and $11,510.00.
• C) We are 95% confident that the price of a 1-carat diamond will fall between $9091.60 and $9509.40.
• D) We are 95% confident that the average price of all 1-carat diamonds will fall between $9091.60 and $9509.40.

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