20. Diamond Prices The table below lists weights (carats) and prices (dollars) of randomly selected diamonds. All of the diamonds are round with ratings of "very good" cut, they all have a color rating of F ("slight color"), and a clarity rating of VSI ("very slightly included"). The values are based on data from the retailer Blue Nile. For diamonds of the type described, is there sufficient evidence to conclude that there is a linear correlation between weights and prices? Do the results also apply to other types of diamonds, such as those with different color and clarity ratings? суре Weight 0.3 0.4 0.5 0.5 1.0 0.7 Price 510 1151 1343 1410 5669 2277

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Concept explainers
Topic Video
Question
Number 20
**Testing for a Linear Correlation**

In Exercises 13–28, construct a scatterplot, and find the value of the linear correlation coefficient \( r \). Also find the P-value or the critical values of \( r \) from Table A-6 using \( \alpha = 0.05 \). Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-3 exercises.)
Transcribed Image Text:**Testing for a Linear Correlation** In Exercises 13–28, construct a scatterplot, and find the value of the linear correlation coefficient \( r \). Also find the P-value or the critical values of \( r \) from Table A-6 using \( \alpha = 0.05 \). Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-3 exercises.)
**Diamond Prices**

The table below lists weights (carats) and prices (dollars) of randomly selected diamonds. All of the diamonds are round with ratings of "very good" cut, they all have a color rating of F ("slight color"), and a clarity rating of VS1 ("very slightly included"). The values are based on data from the retailer Blue Nile. For diamonds of the type described, is there sufficient evidence to conclude that there is a linear correlation between weights and prices? Do the results also apply to other types of diamonds, such as those with different color and clarity ratings?

| Weight (carats) | 0.3 | 0.4 | 0.5 | 0.6 | 1.0 | 0.7 |
|-----------------|-----|-----|-----|-----|-----|-----|
| Price (dollars) | 510 | 1151 | 1343 | 1410 | 5669 | 2277 |

**Table Explanation:**

This table presents two rows of data:
- The top row indicates the weight of diamonds in carats, with values ranging from 0.3 to 1.0 carats.
- The second row shows the corresponding prices in dollars for each weight category.

The data shows an increase in price with an increase in carat weight, suggesting a positive correlation between the size of the diamond and its price. However, the extent and linearity of this correlation would require further statistical analysis to determine if it holds across different diamonds.
Transcribed Image Text:**Diamond Prices** The table below lists weights (carats) and prices (dollars) of randomly selected diamonds. All of the diamonds are round with ratings of "very good" cut, they all have a color rating of F ("slight color"), and a clarity rating of VS1 ("very slightly included"). The values are based on data from the retailer Blue Nile. For diamonds of the type described, is there sufficient evidence to conclude that there is a linear correlation between weights and prices? Do the results also apply to other types of diamonds, such as those with different color and clarity ratings? | Weight (carats) | 0.3 | 0.4 | 0.5 | 0.6 | 1.0 | 0.7 | |-----------------|-----|-----|-----|-----|-----|-----| | Price (dollars) | 510 | 1151 | 1343 | 1410 | 5669 | 2277 | **Table Explanation:** This table presents two rows of data: - The top row indicates the weight of diamonds in carats, with values ranging from 0.3 to 1.0 carats. - The second row shows the corresponding prices in dollars for each weight category. The data shows an increase in price with an increase in carat weight, suggesting a positive correlation between the size of the diamond and its price. However, the extent and linearity of this correlation would require further statistical analysis to determine if it holds across different diamonds.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 4 images

Blurred answer
Knowledge Booster
Application of Algebra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman