What Is the Relationship Between Diamond Price and Carat Size $\text { Predictor }$

question 16

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
$\text { Predictor }$



The model was then used to create $95 \%$ confidence and prediction intervals for $\mathrm { y }$ and for E(Y) when the carat size of the diamond was 1 carat. The results are shown here:
$95 \%$ confidence interval for $\mathrm { E } ( \mathrm { Y } ) : ( \$ 9091.60 , \$ 9509.40 )$
$95 \%$ prediction interval for $Y : ( \$ 7091.50 , \$ 11,510.00 )$
Which of the following interpretations is correct if you want to use the model to estimate $E ( Y )$ for all 1 -carat diamonds?

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

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