In this comprehensive statistical analysis, we delve into the intricate interplay between dietary habits and overall health. Our study begins by categorizing participants into three groups based on their dark green vegetable consumption, shedding light on their dietary preferences. We then explore the potential connections between these dietary choices and two key health indicators: Body Mass Index (BMI) and dining-out habits. Through rigorous statistical tests, we investigate whether these variables are correlated, providing valuable insights into the intricate balance between nutrition and health.

## Problem Description

The objective of this statistical analysis assignment is to analyze the association between a participant's dietary habits, specifically the consumption of dark green vegetables, and two different variables: BMI and dining out frequency. The primary task involves creating a new categorical variable called 'GreenVegies' to categorize participants into three groups based on their dark green vegetable consumption: less than 3 weeks, 3-4 weeks, and more than 4 weeks. The subsequent steps analyze the association between this variable and participants' BMI, as well as their dining-out habits.

## Solution:

**Categorizing Green Vegetable Consumption:****Descriptive Statistics:****Association between BMI and Green Vegetable Consumption:**

To categorize participants based on their dark green vegetable consumption, we created a new variable called 'GreenVegies' with three categories: 3 weeks, 3-4 weeks, and 4 weeks.

We conducted a frequency analysis to describe the 'GreenVegies' variable. The following table summarizes the distribution of participants in each category:

Category of Green Veggies | Frequency | Percent | Valid Percent | Cumulative Percent |

3 weeks | 0 | 25.4% | 25.6% | 25.6% |

3-4 weeks | 133 | 27.2% | 27.5% | 53.1% |

4 weeks | 227 | 46.4% | 46.9% | 100.0% |

Total | 484 | 99.0% | 100% |

With the majority of participants (46.9%) consuming dark green vegetables more than 4 times a week, we can conclude that most participants have a high consumption frequency.

We aimed to determine if there's an association between a participant's BMI and their dark green vegetable consumption. To do this, we used a one-way ANOVA test, considering that we were comparing a categorical variable ('GreenVegies') with a continuous variable (BMI). The hypotheses were as follows:

**Null hypothesis**: There's no difference in mean BMI for the three 'GreenVegies' categories.**Alternative hypothesis**: There's a difference in mean BMI for the three categories.

Descriptive statistics for BMI were as follows:

GreenVegies Category | N | Mean | Std. Deviation | Std. Error | 95% Confidence Interval for Mean | Minimum | Maximum |

3 weeks | 123 | 27.16 | 5.74 | 0.52 | 26.14 to 28.19 | 16.61 | 43.37 |

3-4 weeks | 133 | 27.86 | 5.60 | 0.49 | 26.90 to 28.82 | 16.43 | 44.71 |

4 weeks | 226 | 27.27 | 5.80 | 0.39 | 26.51 to 28.03 | 15.73 | 44.33 |

The ANOVA test resulted in a p-value of 0.553, indicating that there is no significant difference in the mean BMI across the three 'GreenVegies' categories. Therefore, there is no significant association between BMI and dark green vegetable consumption.

**Association between Dining Out Frequency and Green Vegetable Consumption:**

To assess the association between a participant's decision to eat out at a restaurant and their dark green vegetable consumption, we conducted a chi-square test of independence, as both variables are categorical. The hypotheses were as follows:

**Null hypothesis**: There's no association between a participant's decision to eat out at a restaurant and their dark green vegetable consumption.**Alternative hypothesis**: There's an association between the two.

We created a crosstabulation to represent the relationship and performed the chi-square test. The crosstabulation is shown in the output.

The chi-square test yielded a p-value of 0.739, indicating that there is not sufficient evidence to support the claim that there is an association between a participant's decision to eat out at a restaurant and their dark green vegetable consumption.

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