Discussion:
For this discussion, select a game of chance, explain it briefly if it is likely to be unfamiliar to your classmates, then calculate probabilities of various outcomes like winning or losing in this game. For example, you might choose your state lottery, scratch card game, a card game like poker, or a dice game like Craps or Yahtzee, as your game of chance.
As illustration, read a lottery analysis in Powerball-Methodology.
Assignment:
Sex Ratio
The normal male to female live birth sex ratio ranges from about 1.03 to 1.07. The sex ratio is defined as the ratio of male births to female births. You might expect boy and girl births to be equally likely, but in fact, baby boys are somewhat more common than baby girls.
Higher sex ratios are thought to reflect prenatal sex selection, especially among cultures where sons are prized more heavily than daughters. We will review sex ratios in the United States as a whole, as well as in individual states, to determine whether sex ratios vary significantly among various ethnic and racial groups.
To do this analysis, we will utilize natality data for the United States, provided by the Centers for Disease Control.
In the first part of the assignment, we will look at sex ratios for your home state, over the time period 1995 to 2002, by race. To obtain this information:
- Go the CDC Wonder website,
- Click on Births under the WONDER Online Databases to bring you to the Natality Information screen
- On this screen, click Natality for 1995-2002.
- On the following screen, click I Agreein order to agree to abide by the government rules for data use (primarily, concerning confidentiality).
- This will bring us to the Natality, 1995-2002 Request screen.
- In the block 1. Organize table layout, group results by year, followed by race, and then gender.
- In the block 2. Select maternal residence, choose your state.
- You can leave blocks 3 through 6 at their default values (i.e., All).
- Click Send.
- A new screen will open, with data (births) tabulated by Year, Race, and Gender.
- Click Export, click Save, and a text file named Natality, _1995-2002 .txt or something similar will be downloaded onto your computer.
We can now process the downloaded data in Excel.
- Load the text file into Excel. This will probably open the Text Import Wizard.
- Accept the defaults, and you should have a spreadsheet with the natality data entered.
- We will need to edit the data slightly before calculating sex ratios and drawing graphs of the sex ratios. To do this:
- Scroll down to the end of the spreadsheet, and delete the rows with the extraneous information about the dataset. (This starts on or about row 203.)
- You may also delete the columns with headings Year CodeRace Code, and Gender Code since we will not be using them, however this is not necessary.
- Next, sort the data, in order to delete some extraneous rows. Select the remaining columns, choose Data > Sort, then sort by Race in ascending order.
- Scroll down to the end of the worksheet, and delete all rows with blanks for Race.
- We will now add a new column to the worksheet for ratios.
- Go to the first blank column in the worksheet: this column should be immediately to the right of a column labeled Births.
- In the first row of this column, type Ratios.
- Now, we will calculate different proportions of births, using formulas in excel. It is important to use excel to do the calculation, because it will allow you to quickly complete all of the ratios.
- First, calculate the ratio of female births to total births for the American Indian race (female births/total births).
- Next, calculate the ratio of male births to total births for the American Indian race (male births/total births).
- Finally, calculate the ratio of male births to female births (male births/total births)
- If you don’t know how to do this calculation easily in Excel, please check out the screencast, which reviews this.
- Once you have completed the first three cells in the ratio column, you can select them and copy them.
- Select the remaining cells in the column and paste.
- You have now completed calculating all of the ratios, however, you may wish to double check to ensure that the formulas have adjusted for each cell.
- Once you have the Ratio column filled out, select that column, then Copy.
- With the column still selected you want to select, click Paste Special and then Values. This will convert the formulas you entered to numbers, so they do not change when you do the next sort.
- Select all the columns, then Data>Sort>Notesin ascending order. We will be graphing the sex ratios for the years 1995 to 2002, by race.
- Feel free to drop the two to four races that have the fewest numbers of births in your state.
- Draw a line chart with markers with the year along the X-axis (we are looking at 1995 through 2002) and sex ratio along the Y-axis (with sex ratios typically between 1 and 1.1, though this may vary in your state).
- If your version of excel has the Chart Wizard:
- In step two of the Chart Wizard, choose the Series tab; in this window you’ll be adding all the information for the various plots.
- Under category (X) axis labels, drag your mouse over the cells 1995, 1996… 2002.
- For values, draw your mouse over the seven successive sex ratios for the particular racial group you chose; in the name box, enter the racial group; do this for each of the groups you want to display.
- Select Next when you have finished with all the racial groups, and you will be brought to the Chart Options screen.
- Here, you can customize your graph, with a title and X and Y axis labels (i.e., your state births, year, and sex ratio respectively).
- Continue with Next, and finish the graph.
- If your version of excel does not have the Chart Wizard, you will need to do some reformatting of your data before you can create a line chart. It is good practice to create a new worksheet in order to preserve your original data.
- Your data should mimic the way you want your line chart to look. In this case, you want to create horizontal labels for each of the years (1995 through 2002) and vertical labels for each of the races. It should follow this format:
- If your version of excel has the Chart Wizard:
Year 1 |
Year 2 |
Year 3 | |
Race A | Ratio for Race A in Year 1 | Ratio for Race A in Year 2 | Ratio for Race A in Year 3 |
Race B | Ratio for Race B in Year 1 | Ratio for Race B in Year 2 | Ratio for Race B in Year 3 |
- After you have reformatted your data, select all of the data, then select Insert, then Line, then Line with Markers.
- You should now have a line chart with each race having its own line, the ratios on the Y-axis, and the years on the X-axis.
- You may wish to modify the Y-axis by right-clicking on it. Your upper and lower values on the axis should be just above and below your highest and lowest ratio values.
- In a Word document, paste the graph you created (or, alternatively, submit your Excel workbook along with the Word document) and describe your findings, making sure to:
- Summarize the sex ratios for each of the racial groups.
- Explain whether the sex ratios are relatively constant through the 1995 to 2002 period for all of the racial groups or if there are trends?
- Explain any racial groups that have noticeably higher or lower sex ratios than other groups.
- Explain the conclusions you are drawing from your graph.
In the second part of this assignment, you will undertake some formal statistical procedures with the natality data. We will repeat the previous steps, with some slight modifications.
- Return to the CDC Wonder website.
- Click on Births under the WONDER Online Databases to get to the Natality Information screen.
- Select Natality for 2007 – 2012.
- On the next screen, click I Agree in order to agree to abide by the government rules for data use (primarily, concerning confidentiality).
- This will bring us to the Natality, 2007-2012 Request screen.
- In block 1. Organize table layout, group results by race and then gender (not year).
- In block 2. Select maternal residence, choose your state.
- You can leave block 3 at its default values (typically, All).
- In block 4. Select birth characteristics; select All Years under Year, and 1st child born alive to mother under Live Birth Order.
- Blocks 5 and 6 can be left at their default values.
- Click Send. A new screen will open, with data (births) tabulated by race and gender.
- Click Export, click Save, and a text file named Natality 2007-2012.txt (or something similar) will be downloaded onto your computer.
We have only four racial groups in this dataset: American Indians or Alaska Natives, Asian or Pacific Islanders, Black or African Americans, and Whites.
Using the normal approximation to the binomial distribution (without continuity correction), calculate z statistics for assessing whether the proportion of boys is .51 in each of the 4 racial groups, where n is the total number of births in a particular cohort, p = .51, q = 1 – p = .49, and x is the number of boy births; z = ((x – np) / sqrt(npq) ).
Under the null hypothesis that the proportion of boys should be 0.51, and under the normal approximation to the binomial distribution, the z statistics should have (approximately) standard normal distributions, (mean 0, standard deviation 1). Do any of the z statistics suggest that the proportion of boy births in any particular racial group differs significantly from .51?
Comment on your findings in your written report. Describe whether you think your results would change if we hadn’t limited consideration to the first-born. Assignment should be at least 250-500 words in APA format supported by scholarly sources.