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.

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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
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.
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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