### Correlation Between Bills and Tips#### Problem StatementListed below are amounts of bills for dinner and the amounts of the tips that were left. Construct a scatter plot, find the value of the linear correlation coefficient $ r $, and find the P-value of $ r $. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of $ \alpha = 0.01 $. If everyone were to tip with the same percentage, what should be the value of $ r $?#### Data| Bill (dollars) | 30.46 | 48.91 | 90.03 | 93.68 | 64.35 | 104.74 ||----------------|-------|-------|-------|-------|-------|--------|| Tip (dollars) | 3.59 | 8.21 | 8.36 | 14.33 | 12.70 | 17.38 |#### Instructions1. **Construct a Scatter Plot:** - Plot the given bill amounts on the X-axis. - Plot the corresponding tip amounts on the Y-axis.2. **Calculate the Linear Correlation Coefficient ($ r $):** - Use statistical software or a calculator formula for determining $ r $.3. **Find the P-value of $ r $:** - Again, utilize statistical software or standard statistical tables to determine the P-value for the given $ r $.4. **Interpret the Results:** - Compare the P-value with the significance level $ \alpha = 0.01 $. - Determine if there is sufficient evidence to support a claim of linear correlation between the bill amounts and the tip amounts.#### Hypothetical Scenario- If everyone were to tip with the same percentage, the data points on the scatter plot would lie on a straight line passing through the origin. This would result in a perfect positive linear relationship, and the value of $ r $ should be 1.### Explanation of Graphs or Diagrams- **Scatter Plot:** A graphical representation where each pair of bill and tip amounts is a point plotted on the graph. The X-axis represents the bill amounts, and the Y-axis represents the tip amounts. The patterns and distribution of these points help visualize the relationship between the bill and tip amounts.By following these steps and assessing the values, you can determine

The correlation coefficient is used to measure the linear relation between two variables. There will…

Listed below are amounts of bills for dinner and the amounts of the tips that were left. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a = 0.01. If everyone were to tip with the same percentage, what should be the value of r? Bill (dollars) Tip (dollars) 30.46 48.91 3.59 8.21 90.03 93.68 64.35 104.74 O 8.36 14.33 12.70 17,38

Listed below are amounts of bills for dinner and the amounts of the tips that were left. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a = 0.01. If everyone were to tip with the same percentage, what should be the value of r? Bill (dollars) Tip (dollars) 30.46 48.91 3.59 8.21 90.03 93.68 64.35 104.74 O 8.36 14.33 12.70 17,38

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Listed below are the amounts of bills for dinner and the amounts of the tips that were left. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of α=0.01. If everyone were to tip with the same percentage, what should be the value of r? Bill (dollars) 31.65 53.83 87.10 103.64 60.34 109.80 Tip (dollars) 3.74 5.76 14.73 16.86 7.44 20.73 1. The linear correlation coefficient is r= 2. What are the null and alternative hypotheses? 3. The test statistic is t= 4. The P-Value is P=
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