## Related questions with answers

The U.S. Department of Agriculture (USDA) Center for Nutrition Policy and Promotion (CNPP) uses the Healthy Eating Index to monitor the diet quality of the U.S. population, particularly how well it conforms to dietary guidance. The HEI–2005 measures how well the population follows the recommendations of the 2005 Dietary Guidelines for Americans (Guenther et al. 2007). Data collected on a random sample of individuals who participated in two extended interviews and medical examinations are contained in the data file HEI Cost Data Variable Subset, where the first interview is identified by daycode = 1 and data for the second interview are identified by daycode = 2. One variable in the HEI–2005 study is a participant’s activity level, coded as 1 = sedentary, 2 = active, and 3 = very active. Previously, we constructed bar charts of participants’ activity level by gender for data collected on the first interview. Determine if there is an association between activity level and gender.

$\begin{array}{lcc} \hline \text { Activity Level } & \text { Male } & \text { Female } \\ \hline \text { Sedentary } & 957 & 1226 \\ \text { Active } & 340 & 417 \\ \text { Very active } & 842 & 678 \\ \hline \end{array}$

Solution

VerifiedWe are tasked to find the association between two categories, those with different levels that needs to be paired with each other. Therefore, we can use the **Chi-Square Random Variable for Contingency Tables** since it has a good approximation when no more than 20% of the estimated expected numbers is less than 5.

To determine if there is an association between the activity level and gender, we shall first find the cross-classification of observations between two characteristics, namely: type of lifestyle and gender. To find this, we shall use the following:

$\begin{equation} E_{ij}=\dfrac{R_iC_j}{n}, \end{equation}$

where $R_i$ and $C_j$ are corresponding row and column totals, while $n$ is the sample size.

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