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A grocery store manager did a study to look at the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The results of the survey are shown below. 30 5 28 18 14 21 8 Time Money 99 23 94 77 70 97 29

A grocery store manager did a study to look at the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The results of the survey are shown below. 30 5 28 18 14 21 8 Time Money 99 23 94 77 70 97 29

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
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### Correlation Study on Time Spent and Money Spent in a Grocery Store A grocery store manager conducted a study to understand the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The survey results are displayed below: | **Time (minutes)** | 30 | 5 | 28 | 18 | 14 | 21 | 8 | |---------------------|----|---|----|----|----|----|---| | **Money (dollars)** | 99 | 23 | 94 | 77 | 70 | 97 | 29 | ### Tasks and Questions: **a. Find the correlation coefficient:** \[ r = \_\_\_\_ \] (Round to 2 decimal places) **b. The null and alternative hypotheses for correlation are:** \[ H_0 : \rho = 0 \] \[ H_1 : \rho \ne 0 \] **The p-value is:** \[ \_\_\_\_\] (Round to four decimal places) **c. Use a significance level of \( \alpha = 0.05 \) to state the conclusion of the hypothesis test in the context of the study.** - \( \circ \) There is statistically insignificant evidence to conclude that a customer who spends more time at the store will spend more money than a customer who spends less time at the store. - \( \circ \) There is statistically significant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store. Thus, the regression line is useful. - \( \circ \) There is statistically significant evidence to conclude that a customer who spends more time at the store will spend more money than a customer who spends less time at the store. **Explanation of Graphs or Diagrams:** In the data table, the first row indicates the various times, in minutes, that customers spent in the store. The second row shows the corresponding amounts of money, in dollars, that those customers spent. To analyze this data, we will calculate the correlation coefficient \(r\) to determine the strength and direction of the linear relationship between time spent and money spent. A hypothesis test for correlation will also be performed using the given hypotheses \(H_0\) and \(H_1\) to decide if there's
Transcribed Image Text:### Correlation Study on Time Spent and Money Spent in a Grocery Store A grocery store manager conducted a study to understand the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The survey results are displayed below: | **Time (minutes)** | 30 | 5 | 28 | 18 | 14 | 21 | 8 | |---------------------|----|---|----|----|----|----|---| | **Money (dollars)** | 99 | 23 | 94 | 77 | 70 | 97 | 29 | ### Tasks and Questions: **a. Find the correlation coefficient:** \[ r = \_\_\_\_ \] (Round to 2 decimal places) **b. The null and alternative hypotheses for correlation are:** \[ H_0 : \rho = 0 \] \[ H_1 : \rho \ne 0 \] **The p-value is:** \[ \_\_\_\_\] (Round to four decimal places) **c. Use a significance level of \( \alpha = 0.05 \) to state the conclusion of the hypothesis test in the context of the study.** - \( \circ \) There is statistically insignificant evidence to conclude that a customer who spends more time at the store will spend more money than a customer who spends less time at the store. - \( \circ \) There is statistically significant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store. Thus, the regression line is useful. - \( \circ \) There is statistically significant evidence to conclude that a customer who spends more time at the store will spend more money than a customer who spends less time at the store. **Explanation of Graphs or Diagrams:** In the data table, the first row indicates the various times, in minutes, that customers spent in the store. The second row shows the corresponding amounts of money, in dollars, that those customers spent. To analyze this data, we will calculate the correlation coefficient \(r\) to determine the strength and direction of the linear relationship between time spent and money spent. A hypothesis test for correlation will also be performed using the given hypotheses \(H_0\) and \(H_1\) to decide if there's
### Linear Regression Analysis for Store Spending In this section, we will explore how linear regression can be used to model and predict the amount of money customers spend at a store based on the time they spend there. #### Key Concepts and Tasks **d. Coefficient of Determination (R²)** - \( R² = \_\_\_\_\_\_\_ \) (Round to two decimal places) **e. Interpret \( R² \):** - Select the correct interpretation of \( R² \): - \( \bigcirc \) There is a large variation in the amount of money that customers spend at the store, but if you only look at customers who spend a fixed amount of time at the store, this variation on average is reduced by 87%. - \( \bigcirc \) Given any group that spends a fixed amount of time at the store, 87% of all of those customers will spend the predicted amount of money at the store. - \( \bigcirc \) There is an 87% chance that the regression line will be a good predictor for the amount of money spent at the store based on the time spent at the store. - \( \bigcirc \) 87% of all customers will spend the average amount of money at the store. **f. Equation of the Linear Regression Line:** - Determine the linear regression equation: \( \hat{y} = \_\_\_\_\_ + \_\_\_\_\_ x \) (Please show your answers to two decimal places) **g. Prediction Using the Model:** - Use the model to predict the amount of money spent by a customer who spends 16 minutes at the store. Round your answer to the nearest whole number. - Dollars spent = \( \_\_\_\_\_ \) **h. Interpret the Slope of the Regression Line:** - Select the correct interpretation of the slope in the context of the question: - \( \bigcirc \) As \( x \) goes up, \( y \) goes up. - \( \bigcirc \) The slope has no practical meaning since you cannot predict what any individual customer will spend. - \( \bigcirc \) For every additional minute customers spend at the store, they tend to spend on average $3.14 more. ### Detailed Explanation of Key Terms 1. **R² (Coefficient of Determination):** -
Transcribed Image Text:### Linear Regression Analysis for Store Spending In this section, we will explore how linear regression can be used to model and predict the amount of money customers spend at a store based on the time they spend there. #### Key Concepts and Tasks **d. Coefficient of Determination (R²)** - \( R² = \_\_\_\_\_\_\_ \) (Round to two decimal places) **e. Interpret \( R² \):** - Select the correct interpretation of \( R² \): - \( \bigcirc \) There is a large variation in the amount of money that customers spend at the store, but if you only look at customers who spend a fixed amount of time at the store, this variation on average is reduced by 87%. - \( \bigcirc \) Given any group that spends a fixed amount of time at the store, 87% of all of those customers will spend the predicted amount of money at the store. - \( \bigcirc \) There is an 87% chance that the regression line will be a good predictor for the amount of money spent at the store based on the time spent at the store. - \( \bigcirc \) 87% of all customers will spend the average amount of money at the store. **f. Equation of the Linear Regression Line:** - Determine the linear regression equation: \( \hat{y} = \_\_\_\_\_ + \_\_\_\_\_ x \) (Please show your answers to two decimal places) **g. Prediction Using the Model:** - Use the model to predict the amount of money spent by a customer who spends 16 minutes at the store. Round your answer to the nearest whole number. - Dollars spent = \( \_\_\_\_\_ \) **h. Interpret the Slope of the Regression Line:** - Select the correct interpretation of the slope in the context of the question: - \( \bigcirc \) As \( x \) goes up, \( y \) goes up. - \( \bigcirc \) The slope has no practical meaning since you cannot predict what any individual customer will spend. - \( \bigcirc \) For every additional minute customers spend at the store, they tend to spend on average $3.14 more. ### Detailed Explanation of Key Terms 1. **R² (Coefficient of Determination):** -
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