Q. 6.136 - Elementary Statistics

Question

Philosophical and health issues are prompting an increasing number of Taiwanese to switch to a vegetarian lifestyle. In the paper "LDL of Taiwanese Vegetarians Are Less Oxidizable than Those of Omnivores" (Journal of Nutrition, Vol. 130, Pp. 1591-1596), S. Lu et al. compared the daily intake of nutrients by vegetarians and omnivores living in Taiwan. Among the nutrients considered was protein. Too little protein stunts growth and interferes with all bodily functions; too much protein puts a strain on the kidneys, can cause diarrhea and dehydration, and can leach calcium from bones and teeth. The daily protein intakes, in grams, for 51 female vegetarians and 53 female omnivores are provided on the Weiss Stats site. Use the technology of your choice to do the following for each of the two sets of sample data.

a. Obtain a histogram of the data and use it to assess the (approximate) normality of the variable under consideration.

b. Obtain a normal probability plot of the data and use it to assess the (approximate) normality of the variable under consideration.

c. Compare your results in parts (a) and (b).

Step-by-Step Solution

Answer

a. Because of the huge number of observations, the histogram graph is similar to that of a normal plot in both circumstances.

b. The data of daily intake of nutrients by vegetarians and omnivores is approximately normally distributed.

c. Both have the same outcome. The variable under discussion is nearly regularly distributed in both circumstances.

Part (a) Step 1: Given Information

The histogram of the data and to assess the normality of the variable under Consideration.

Part (a) Step 2: Explanation

Consider the daily nutrient consumption of vegetarians and omnivores.

The following is a histogram of vegetarians and omnivores.

Because of the huge number of observations, the histogram graph is similar to that of a normal plot in both circumstances.

Part (b) Step 1: Given Information

The normal probability plot of given data.

Part (b) Step 4: Explanation

Consider the daily nutrient consumption of vegetarians and omnivores.

The following is a normal probability map of vegetarians and omnivores.

We may see from the graph above that

In the plot, there are no outliers.

The variable in question has a linear shape.

Hence, the data of daily intake of nutrients by vegetarians and omnivores is approximately normally distributed.

Part (c) Step 1: Given Information

The compare your results of part $a$ and $b$.

Part (c) Step 2: Explanation

Consider the daily nutrient consumption of vegetarians and omnivores.

Consider component a and b's histogram graph and normal probability plot.

Both have the same outcome. The variable under discussion is nearly regularly distributed in both circumstances.