Module 3: Critical Thinking Assignment

Part I

1. Review the overall population of data using the attached data set. Write a paragraph about your initial thoughts looking at the data from the states.

2. Copy/Paste the column of data (Percentage of Adults Classified as Obese) into StatDisk. Remember to not include the column title. You can edit the column title in StatDisk.

3. Using StatDisk, create a histogram of the data, using the “Auto-fit” option. Download the graph and paste it into your document.

4. Using StatDisk, compute the summary statistics, including the mean, median, and standard deviation, for all the data points, including the District of Columbia and Puerto Rico. Either copy/paste the results into your document or simply type the requested values.

5. Explain the shape of the distribution and justify your reasoning.

Part 2

1. In the attached data set, click on the tab for “Sample of size 10.” DO NOT adjust the Excel formulas for the mean and standard deviation.

2. Use this random number generator (https://www.calculatorsoup.com/calculators/statistics/random-number-generator.php) to take 20 samples of size 10. Here are the step-by-step instructions to generate your samples. The first section is the range. Since the states are numbered from 1 to 52, the minimum is 1 and the maximum is 52. You want to generate 20 samples of size 10, so input 20 as the number of sets, and 10 as the numbers per set. Click Calculate. You should see your 20 sets of 10 numbers. These 10 numbers represent the state
number, not the obesity rates, so you will need to convert the numbers for the spreadsheet. For example, if your sample 10 numbers are 42, 9, 27, 50, 19, 29, 48, 12, 32, and 34, the numbers you enter in the spreadsheet will be 22.7, 36.2, 30.1, 25.6, 29.8, 33.9, 34.2, 28.6, 31.3, and 26.7. Enter all 20 samples into the data sheet. Remember the mean and standard deviation should automatically calculate once you start inputting the values.

3. Using StatDisk, input the 20 sample means into a column of the sample editor.

4. Create a histogram of the sample means from problem 3. Explain the overall shape of the histogram.

5. Generate an additional 20 samples of size 10 and add these new sets of numbers to the set of 20, making a total of 40 sample means.

6. What do you expect the histogram to look like when you add the additional 20 sample means?

7. Add the additional 20 sample means to the data and create another histogram for the entire set of 40. Explain the shape of the histogram. Did it turn out like you expected?

8. What if you added another set of 20 sample means to the data? How would that change the data? Explain, using the concepts learned in this module.

9. Using the summary statistics found in part 1, what will be the mean of the sampling distribution for all possible samples of size 10 from this population?

10. Using the summary statistics found in part 1, what will be the standard deviation of the sampling distribution for all possible samples of size 10 from this population?

11. Explain one reason why medical professionals may want to be aware of how sampling distributions work or how its application could be important.