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 \(\$ 9509.40\).

---

Definitions:

Developmental Outcomes

The results or changes in an individual’s capabilities or behaviors over time due to growth and experience.

Positive Youth Development

A general approach to adolescence that emphasizes the strengths and positive qualities of youth that contribute to their psychological health as well as to the welfare of their communities.

Psychological Health

A state of well-being where an individual realizes their abilities, can cope with normal stresses of life, and can work productively.

Adolescent Development

The physical, psychological, emotional, and social growth and changes that occur during the period of transition from childhood to adulthood.