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.) **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.

Name: Number 20 **Testing for a Linear Correlation**In Exercises 13–28, cons
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Description: 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