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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. 14 21 8 Time Money 30 5 99 23 28 18 94 77 70 97 29 a. Find the correlation coefficient: r = 0.93 ✓ Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: p H₁: p 00 of The p-value is: 0.0020 (Round to four decimal places) 0.05 to state the conclusion of the hypothesis test in the context c. Use a level of significance of a of the study. O 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. 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

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. 14 21 8 Time Money 30 5 99 23 28 18 94 77 70 97 29 a. Find the correlation coefficient: r = 0.93 ✓ Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: p H₁: p 00 of The p-value is: 0.0020 (Round to four decimal places) 0.05 to state the conclusion of the hypothesis test in the context c. Use a level of significance of a of the study. O 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. 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

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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Need help with, d,f, and g and the answer is not 0.86 or 0.92^2
### Relationship Between Time Spent in Store and Money Spent: A Study A grocery store manager conducted a study to investigate 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: #### Data Table | **Time (minutes)** | 30 | 5 | 28 | 18 | 14 | 21 | 8 | |--------------------|----|----|----|----|----|----|----| | **Money (dollars)**| 99 | 23 | 94 | 77 | 70 | 97 | 29 | #### Analysis: a. **Finding the Correlation Coefficient:** The correlation coefficient \( r \) is calculated to be **0.93** (rounded to 2 decimal places). b. **Hypothesis Testing for Correlation:** - **Null Hypothesis (\( H_0 \)):** \( \rho = 0 \) - **Alternative Hypothesis (\( H_1 \)):** \( \rho \neq 0 \) The p-value is: **0.0020** (rounded to four decimal places). c. **Conclusion Using a Significance Level of \( \alpha = 0.05 \):** Based on the study: - \[ \boxed{ \text{There is statistically significant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store.} } \]
Transcribed Image Text:### Relationship Between Time Spent in Store and Money Spent: A Study A grocery store manager conducted a study to investigate 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: #### Data Table | **Time (minutes)** | 30 | 5 | 28 | 18 | 14 | 21 | 8 | |--------------------|----|----|----|----|----|----|----| | **Money (dollars)**| 99 | 23 | 94 | 77 | 70 | 97 | 29 | #### Analysis: a. **Finding the Correlation Coefficient:** The correlation coefficient \( r \) is calculated to be **0.93** (rounded to 2 decimal places). b. **Hypothesis Testing for Correlation:** - **Null Hypothesis (\( H_0 \)):** \( \rho = 0 \) - **Alternative Hypothesis (\( H_1 \)):** \( \rho \neq 0 \) The p-value is: **0.0020** (rounded to four decimal places). c. **Conclusion Using a Significance Level of \( \alpha = 0.05 \):** Based on the study: - \[ \boxed{ \text{There is statistically significant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store.} } \]
--- ### Linear Regression Analysis Exercise This exercise is designed to help understand how to use linear regression to predict customer behavior in a store. #### Questions **d.** \( r^2 \) \_\_\_\_\_\_\_ (Round to two decimal places) **e.** Interpret \( r^2 \): - ( ) 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%. - ( ) 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. - ( ) 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. - (X) 87% of all customers will spend the average amount of money at the store. **f.** The equation of the linear regression line is:\[ \hat{y} = \_\_\_\_\_\_\_ + \_\_\_\_\_\_\_ x \] (Please show your answers to two decimal places) **g.** Use the model to predict the amount of money spent by a customer who spends 16 minutes at the store. Dollars spent = \_\_\_\_\_\_\_ (Please round your answer to the nearest whole number.) **h.** Interpret the slope of the regression line in the context of the question: --- #### Explanation of Graphs/Diagrams References In the context of linear regression, the graph typically used is a scatter plot with a best-fit line. Here is a brief overview of the common terms and components: 1. **Scatter Plot**: - **X-Axis**: Represents the independent variable (in this case, presumably the time spent in the store). - **Y-Axis**: Represents the dependent variable (in this case, the amount of money spent by customers). 2. **Best-Fit Line / Regression Line**: - It's the line that best represents the data points on the scatter plot. - The equation of the regression line comes in the format \( \hat{y} = b_0 + b_1 x \), where \( \hat{y} \) (predicted value) is
Transcribed Image Text:--- ### Linear Regression Analysis Exercise This exercise is designed to help understand how to use linear regression to predict customer behavior in a store. #### Questions **d.** \( r^2 \) \_\_\_\_\_\_\_ (Round to two decimal places) **e.** Interpret \( r^2 \): - ( ) 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%. - ( ) 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. - ( ) 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. - (X) 87% of all customers will spend the average amount of money at the store. **f.** The equation of the linear regression line is:\[ \hat{y} = \_\_\_\_\_\_\_ + \_\_\_\_\_\_\_ x \] (Please show your answers to two decimal places) **g.** Use the model to predict the amount of money spent by a customer who spends 16 minutes at the store. Dollars spent = \_\_\_\_\_\_\_ (Please round your answer to the nearest whole number.) **h.** Interpret the slope of the regression line in the context of the question: --- #### Explanation of Graphs/Diagrams References In the context of linear regression, the graph typically used is a scatter plot with a best-fit line. Here is a brief overview of the common terms and components: 1. **Scatter Plot**: - **X-Axis**: Represents the independent variable (in this case, presumably the time spent in the store). - **Y-Axis**: Represents the dependent variable (in this case, the amount of money spent by customers). 2. **Best-Fit Line / Regression Line**: - It's the line that best represents the data points on the scatter plot. - The equation of the regression line comes in the format \( \hat{y} = b_0 + b_1 x \), where \( \hat{y} \) (predicted value) is
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