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

question 112

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 $\mathrm { E } ( \mathrm { Y } )$ 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 determine the price of a single 1 -carat diamond?

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

Recognize the relationship between the production of goods and environmental damage.

Differentiate between negative and positive externalities.

Assess the effects of human activity on the environment.

Understand the role of market economies in regulating pollution levels.

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