What is the relationship between the number of minutes per day a woman spends talking on the phone and the woman's weight? The time on the phone and weight for 7 women are shown in the table below. Time 28 26 52 36 51 Pounds 138 123 157 139 175 66 172 42 138 Round to 2 decimal places. a. Find the correlation coefficient: r = b. The null and alternative hypotheses for correlation are: H₂: ?v=0 H₁:20 The p-value is: (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically significant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone. There is statistically insignificant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone. O There is statistically insignificant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the use of the regression line is not appropriate. O There is statistically significant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the regression line is useful.
What is the relationship between the number of minutes per day a woman spends talking on the phone and the woman's weight? The time on the phone and weight for 7 women are shown in the table below. Time 28 26 52 36 51 Pounds 138 123 157 139 175 66 172 42 138 Round to 2 decimal places. a. Find the correlation coefficient: r = b. The null and alternative hypotheses for correlation are: H₂: ?v=0 H₁:20 The p-value is: (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically significant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone. There is statistically insignificant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone. O There is statistically insignificant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the use of the regression line is not appropriate. O There is statistically significant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the regression line is useful.
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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![## Analyzing the Relationship Between Phone Time and Weight
This study examines the relationship between the number of minutes a woman spends talking on the phone per day and her weight. The data for 7 women is presented in the table below.
| Time (minutes) | 28 | 52 | 36 | 51 | 66 | 42 |
|----------------|----|----|----|----|----|----|
| Pounds | 138| 123| 157| 139| 175| 172| 138|
### Statistical Analysis
a. **Correlation Coefficient**
- Find the correlation coefficient \( r = \_\_\_\_ \) (Round to 2 decimal places).
b. **Hypotheses for Correlation**
- **Null Hypothesis (\( H_0 \)):** \( \rho = 0 \)
- **Alternative Hypothesis (\( H_1 \)):** \( \rho \neq 0 \)
- **P-value:** \_\_\_\_ (Round to four decimal places)
c. **Conclusion of the Hypothesis Test**
With a significance level of \( \alpha = 0.05 \), state the conclusion:
- There is statistically significant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone.
- There is statistically significant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the regression line is useful.
d. **Coefficient of Determination**
- Find \( r^2 = \_\_\_\_ \) (Round to two decimal places).
e. **Interpretation of \( r^2 \)**
- There is a large variation in women's weight, but if you only look at women with a fixed amount of time, their variation on average is reduced by 79%.
- 79% of variation in weight can be explained by time spent on the phone.
f. **Linear Regression Equation**
- The equation of the linear regression line is:
\[
\hat{y} = \_\_\_\_ + \_\_\_\_ x
\]
(Please show your answers to two decimal places)
g. **Prediction**
- Use the model to predict the weight of a woman who spends 56 minutes on the phone.
- Weight = \_\_\_\_ (Please round your answer to the nearest](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdfbe6a76-33fb-4739-b913-a49b2ab2e0d7%2F0f7b6a73-ffa6-48a7-87fe-1587c3bdecae%2Frywzlsg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Analyzing the Relationship Between Phone Time and Weight
This study examines the relationship between the number of minutes a woman spends talking on the phone per day and her weight. The data for 7 women is presented in the table below.
| Time (minutes) | 28 | 52 | 36 | 51 | 66 | 42 |
|----------------|----|----|----|----|----|----|
| Pounds | 138| 123| 157| 139| 175| 172| 138|
### Statistical Analysis
a. **Correlation Coefficient**
- Find the correlation coefficient \( r = \_\_\_\_ \) (Round to 2 decimal places).
b. **Hypotheses for Correlation**
- **Null Hypothesis (\( H_0 \)):** \( \rho = 0 \)
- **Alternative Hypothesis (\( H_1 \)):** \( \rho \neq 0 \)
- **P-value:** \_\_\_\_ (Round to four decimal places)
c. **Conclusion of the Hypothesis Test**
With a significance level of \( \alpha = 0.05 \), state the conclusion:
- There is statistically significant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone.
- There is statistically significant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the regression line is useful.
d. **Coefficient of Determination**
- Find \( r^2 = \_\_\_\_ \) (Round to two decimal places).
e. **Interpretation of \( r^2 \)**
- There is a large variation in women's weight, but if you only look at women with a fixed amount of time, their variation on average is reduced by 79%.
- 79% of variation in weight can be explained by time spent on the phone.
f. **Linear Regression Equation**
- The equation of the linear regression line is:
\[
\hat{y} = \_\_\_\_ + \_\_\_\_ x
\]
(Please show your answers to two decimal places)
g. **Prediction**
- Use the model to predict the weight of a woman who spends 56 minutes on the phone.
- Weight = \_\_\_\_ (Please round your answer to the nearest
![**Interpreting the Regression Line in Context**
**h. Interpret the slope of the regression line in the context of the question:**
- For every additional minute women spend on the phone, they tend to weigh on average 1.21 additional pounds.
- As x goes up, y goes up.
- The slope has no practical meaning since you cannot predict a woman's weight.
**i. Interpret the y-intercept in the context of the question:**
- The average woman's weight is predicted to be 97.
- The y-intercept has no practical meaning for this study.
- If a woman does not spend any time talking on the phone, then that woman will weigh 97 pounds.
- The best prediction for the weight of a woman who does not spend any time talking on the phone is 97 pounds.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdfbe6a76-33fb-4739-b913-a49b2ab2e0d7%2F0f7b6a73-ffa6-48a7-87fe-1587c3bdecae%2Fs7cr07h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Interpreting the Regression Line in Context**
**h. Interpret the slope of the regression line in the context of the question:**
- For every additional minute women spend on the phone, they tend to weigh on average 1.21 additional pounds.
- As x goes up, y goes up.
- The slope has no practical meaning since you cannot predict a woman's weight.
**i. Interpret the y-intercept in the context of the question:**
- The average woman's weight is predicted to be 97.
- The y-intercept has no practical meaning for this study.
- If a woman does not spend any time talking on the phone, then that woman will weigh 97 pounds.
- The best prediction for the weight of a woman who does not spend any time talking on the phone is 97 pounds.
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