### Relationship Between Number of Children and Free Time for ParentsA survey was conducted with a sample of 11 parents to investigate the relationship between the number of children they have and the amount of free time they get in a week. Researchers hypothesized that parents with more children have less free time. Below is a scatterplot depicting the data, along with summaries and statistical analysis.#### Scatterplot ExplanationThe scatterplot has the number of children on the x-axis and free time in hours on the y-axis. Each point on the scatterplot represents one parent’s data. The overall trend indicates a negative association between the number of children and free time, suggesting that parents with more children tend to have less free time.![Scatterplot Image]#### Statistical Summaries- **Sample Mean:** - Number of children: 2.27 - Free time (hours): 12.45- **Sample Standard Deviation:** - Number of children: 1.42 - Free time (hours): 7.12- **Correlation between variables**: -0.83#### Statistical Questions and Calculations**(a) Identifying Variables:**- The number of children is the explanatory variable, while the free time (in hours) is the response variable according to the researchers.**(b) Units of Measurement:**- Will the correlation change if we measure free time in minutes instead of hours? - No, the correlation coefficient is unit-free.**(c) Regression Line Calculation:**- Compute the regression line for predicting the amount of free time (in hours) parents have in a given week. - $ \text{Free time} = \text{(To be calculated)} \times \text{Number of children} + \text{(To be calculated)} $**(d) Percentage of Variability:**- Compute the percentage of variability in the amount of free time that is explained by our regression model. - $ \text{Percentage} = (R^2 \text{ value to be calculated})\% $**(e) Standard Error and Hypothesis Testing:**- The standard error for the slope of the regression line in part (c) equals 0.921. We need to determine if the model provides strong evidence that the amount of free time is negatively associated with the number of children a parent has. - \( H_0: \beta

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Description: ### Relationship Between Number of Children and Free Time for ParentsA survey was conducted with a sample of 11 parents to investigate the relationship between the number of children they have and the amount of free time they get in a week. Research

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Sample mean Sample standard deviation | | Number of children | Free time (in hours) 12.45 7.12 2.27 1.42 The correlation between the variables is equal to -0.83. (a) --Select- (b) Will the correlation change if we measure the free time in minutes instead of hours? -Select-- (c) Compute the regression line for predicting the amount of free time (in hours) parents have in a given week. v is the explanatory variable and -Select--- is the response variable from the point of view of researchers. Free time - * Number of children +

Sample mean Sample standard deviation | | Number of children | Free time (in hours) 12.45 7.12 2.27 1.42 The correlation between the variables is equal to -0.83. (a) --Select- (b) Will the correlation change if we measure the free time in minutes instead of hours? -Select-- (c) Compute the regression line for predicting the amount of free time (in hours) parents have in a given week. v is the explanatory variable and -Select--- is the response variable from the point of view of researchers. Free time - * Number of children +

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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