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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 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? support Bill (dollars) Tip (dollars) 34.96 53.84 92.72 101.01 60.33 114.42 D 4.40 10.49 11.30 19.53 6.64 13.84 C Construct a scatterplot. Choose the correct graph below. OA. OB. Oc. OD. 25 25 25 30 B Amount () 120 30 a Amount (S: 120 30 120 BRAmunt ) 120 B Amount (S) The linear correlation coefficient is r (Round to three decimal places as needed.) Determine the null and alternative hypotheses. Họ: p O H p (Type integers or decimals. Do not round.) The test statistic is t (Round to two decimal places as needed.)

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 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? support Bill (dollars) Tip (dollars) 34.96 53.84 92.72 101.01 60.33 114.42 D 4.40 10.49 11.30 19.53 6.64 13.84 C Construct a scatterplot. Choose the correct graph below. OA. OB. Oc. OD. 25 25 25 30 B Amount () 120 30 a Amount (S: 120 30 120 BRAmunt ) 120 B Amount (S) The linear correlation coefficient is r (Round to three decimal places as needed.) Determine the null and alternative hypotheses. Họ: p O H p (Type integers or decimals. Do not round.) The test statistic is t (Round to two decimal places as needed.)

MATLAB: An Introduction with Applications
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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**Correlation Analysis of Restaurant Bills and Tips** 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 \(\alpha = 0.01\). If everyone were to tip with the same percentage, what should be the value of \( r \)? | Bill (dollars) | 34.96 | 53.84 | 92.72 | 101.60 | 80.33 | 114.42 | |----------------|-------|-------|-------|--------|-------|--------| | Tip (dollars) | 4.40 | 10.49 | 11.30 | 19.53 | 6.64 | 13.84 | **Construct a scatterplot. Choose the correct graph below:** - **Option A** - **Option B** - **Option C** - **Option D** **Analysis Steps:** 1. **Linear Correlation Coefficient Calculation:** The linear correlation coefficient is \( r = \). *(Round to three decimal places as needed.)* 2. **Determine the Null and Alternative Hypotheses:** - \( H_0: \) - \( H_1: \) *(Type integers or decimals. Do not round.)* 3. **Test Statistic Calculation:** The test statistic is \( t = \). *(Round to two decimal places as needed.)* **Graphs Explanation:** - Each of the scatterplot options displays the relationship between two variables: the bill amount (in dollars) on the x-axis and the tip amount (in dollars) on the y-axis. - The graphs help visualize the data points to determine if there is a linear correlation between the bill amounts and the tips left. By comparing the scatterplots, you can identify which best represents a linear relationship, if any, by observing how closely the points fit a line. **Conclusion:** The chosen scatterplot and calculated statistical values will determine whether or not there is a significant linear correlation between the amounts of the bills and the tips given at this restaurant setting.
Transcribed Image Text:**Correlation Analysis of Restaurant Bills and Tips** 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 \(\alpha = 0.01\). If everyone were to tip with the same percentage, what should be the value of \( r \)? | Bill (dollars) | 34.96 | 53.84 | 92.72 | 101.60 | 80.33 | 114.42 | |----------------|-------|-------|-------|--------|-------|--------| | Tip (dollars) | 4.40 | 10.49 | 11.30 | 19.53 | 6.64 | 13.84 | **Construct a scatterplot. Choose the correct graph below:** - **Option A** - **Option B** - **Option C** - **Option D** **Analysis Steps:** 1. **Linear Correlation Coefficient Calculation:** The linear correlation coefficient is \( r = \). *(Round to three decimal places as needed.)* 2. **Determine the Null and Alternative Hypotheses:** - \( H_0: \) - \( H_1: \) *(Type integers or decimals. Do not round.)* 3. **Test Statistic Calculation:** The test statistic is \( t = \). *(Round to two decimal places as needed.)* **Graphs Explanation:** - Each of the scatterplot options displays the relationship between two variables: the bill amount (in dollars) on the x-axis and the tip amount (in dollars) on the y-axis. - The graphs help visualize the data points to determine if there is a linear correlation between the bill amounts and the tips left. By comparing the scatterplots, you can identify which best represents a linear relationship, if any, by observing how closely the points fit a line. **Conclusion:** The chosen scatterplot and calculated statistical values will determine whether or not there is a significant linear correlation between the amounts of the bills and the tips given at this restaurant setting.
### Understanding Linear Correlation in Billing and Tipping In this exercise, we examine the relationship between the amounts of bills for dinner and the tips left by constructing scatterplots to find the linear correlation coefficient, \( r \), and the P-value of \( r \). We use a significance level of \( \alpha = 0.01 \) to determine if a linear correlation exists between these variables. ### Bill and Tip Data - **Bills (in dollars)**: 34.96, 63.84, 92.72, 101.60, 60.33, 114.42 - **Tips (in dollars)**: 4.40, 10.49, 11.30, 19.53, 6.64, 13.84 ### Goals: 1. **Calculate the Linear Correlation Coefficient \( r \):** - The coefficient measures the strength and direction of the linear relationship between bill amounts and tip amounts. - Values range from -1 to 1, where 1 indicates a strong positive correlation, -1 indicates a strong negative correlation, and 0 indicates no correlation. 2. **Determine Hypotheses:** - Null Hypothesis (\( H_0 \)): There is no linear correlation (\( \rho = 0 \)). - Alternative Hypothesis (\( H_1 \)): There is a linear correlation (\( \rho \neq 0 \)). 3. **Calculate the Test Statistic \( t \):** - This statistic helps determine the likelihood that the observed correlation is due to chance. 4. **Compute the P-value:** - A critical component to conclude the statistical significance of the correlation. ### Analysis and Conclusion - **Interpretation of the P-value:** - If the P-value is less than the significance level (\( \alpha = 0.01 \)), we reject the null hypothesis, indicating sufficient evidence of a linear correlation. - **Assumption of Consistent Tipping:** - If tipping percentages were constant, \( r \) would likely be 1, indicating a perfect positive correlation. ### Scatterplots The graphs visualize the data points of bill amounts against tip amounts, allowing for visual assessment of any potential linear patterns. Each scatterplot includes labeled axes representing the bill amounts (x-axis) and tip amounts (y-axis). In conclusion, by computing \( r \), the test statistic, and
Transcribed Image Text:### Understanding Linear Correlation in Billing and Tipping In this exercise, we examine the relationship between the amounts of bills for dinner and the tips left by constructing scatterplots to find the linear correlation coefficient, \( r \), and the P-value of \( r \). We use a significance level of \( \alpha = 0.01 \) to determine if a linear correlation exists between these variables. ### Bill and Tip Data - **Bills (in dollars)**: 34.96, 63.84, 92.72, 101.60, 60.33, 114.42 - **Tips (in dollars)**: 4.40, 10.49, 11.30, 19.53, 6.64, 13.84 ### Goals: 1. **Calculate the Linear Correlation Coefficient \( r \):** - The coefficient measures the strength and direction of the linear relationship between bill amounts and tip amounts. - Values range from -1 to 1, where 1 indicates a strong positive correlation, -1 indicates a strong negative correlation, and 0 indicates no correlation. 2. **Determine Hypotheses:** - Null Hypothesis (\( H_0 \)): There is no linear correlation (\( \rho = 0 \)). - Alternative Hypothesis (\( H_1 \)): There is a linear correlation (\( \rho \neq 0 \)). 3. **Calculate the Test Statistic \( t \):** - This statistic helps determine the likelihood that the observed correlation is due to chance. 4. **Compute the P-value:** - A critical component to conclude the statistical significance of the correlation. ### Analysis and Conclusion - **Interpretation of the P-value:** - If the P-value is less than the significance level (\( \alpha = 0.01 \)), we reject the null hypothesis, indicating sufficient evidence of a linear correlation. - **Assumption of Consistent Tipping:** - If tipping percentages were constant, \( r \) would likely be 1, indicating a perfect positive correlation. ### Scatterplots The graphs visualize the data points of bill amounts against tip amounts, allowing for visual assessment of any potential linear patterns. Each scatterplot includes labeled axes representing the bill amounts (x-axis) and tip amounts (y-axis). In conclusion, by computing \( r \), the test statistic, and
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