Excel Programming Note:

If the sample proportions and sample sizes are known for two independent groups, you can use the 2sampleztest.xls Excel spreadsheet to find the sample and critical z values (click here).  Just edit the given values to reflect the sample data and hypotheses that you want to test.

Note:  If the MS-Excel spreadsheet won't generate the calculations for you, check to see whether Excel has its Analysis Tool Pack Add-Ins enabled.   To ascertain whether Excel has the Add-Ins enabled, start up Excel, click on the Office Button (top left) , then <Excel Options>  and <Add-Ins> and see if the two Analysis Tool Pak add-ins are check marked.  If they aren't, click on <Manage Excel Options><Go> and check mark the Analysis Tool Pak boxes and then click on OK.  

2.  Assume that a hospital can buy two brands of stents.  A random sample of 100 stents from FirmA finds that 14 fail resulting in new surgeries.  A random sample of 60 stents from FirmB finds that 6 fail. 
A.  Is the data above sufficient for conducting a z test for the difference in two population proportions?
B.  Test whether the population proportion of failure for FirmA stents is greater than that of Firm B.  Conduct the appropriate test showing the hypotheses, sample statistic, critical statistic and decision rule. 
C.  What does the estimated  p value (also called the sig. level) of the test show?

Doctor     Gender    Medicaid         Doctor   Gender     Medicaid

1              Male           No                   16              Female         No
2              Female       Yes                   17              Male            No
3              Female        No                   18              Male            Yes
4              Male           No                   19              Female         Yes
5             Female       Yes                   20              Male            No
6              Female       Yes                   21              Male            Yes
7              Female        No                   22              Female         Yes
8              Male           No                   23              Male             No
9              Male           Yes                  24              Male             No
10            Female       Yes                   25              Male            Yes
11            Male           No                   26              Female          No
12            Male           No                   27              Male             Yes
13            Male          Yes                   28              Male             No
14            Female       Yes                   29              Male             No
15            Male          Yes                   30              Male             Yes

A. Create a contingency table for the above 30 doctors showing the interactions between gender and Medicaid acceptance.  Place the dependent variable to the left of the table and the independent variable at the top of the table.  Does it appear that there’s a relationship between gender and Medicaid acceptance?  Calculate the appropriate percentages. 

Excel Programming Note:  Once you have created the contingency table, you can use the chi-squared.xls Excel spreadsheet to find the expected frequencies for each cell, and the sample and critical chi-squared values (click here).   Just edit the orange values on the table that conforms to the dimensions of your contingency table.

Note:  If the MS-Excel spreadsheet won't generate the calculations for you, check to see whether Excel has its Analysis Tool Pack Add-Ins enabled (i.e.,  click on <Tools> <Add-Ins> and see if the two Analysis Tool Pak add-ins are check marked.  If they aren't, check mark the boxes and click on OK).

B. Examine the expected frequencies for each cell for the contingency table.  What do they show?
C. Find the sample chi-square statistic for the above table.
D. What would it mean if a researcher found that there is a statistically significant relationship, at the 5% significance level, between gender and Medicaid acceptance?
E. Test whether there is a statistically significant relationship between gender and Medicaid acceptance.  Conduct the appropriate test showing the hypotheses, sample statistic, critical statistic and decision rule. Interpret the results.
F.  What are the data requirements for conducting the chi-square test?
G.  What does the estimated  p value (also called the sig. level) of the test show?

H.  Bonus SPSS Notes:
i.  To generate the sample chi squared using SPSS you must create a contingency table using the above information w/ SPSS.  To do so , you must first create a data file containing the two variables for the 30 doctors in the study.   The data file must contain two columns of 30 numbers, one for gender and one for Medicaid acceptance.  The first column will contain the gender of each doctor (1=male, 2=female), while the second column will contain the Medicaid acceptance information (1 =does accept, 2 = doesn't accept).  After typing in all of the data, click on the Variable View tab and give the gender variable a Name like gender, and also click on Labels so that you can give it an extended Variable Label like gender of neurologist.  Because the gender data is categorical, you’ll want to give Labels to each one of your numerical sex categories.  To do so, type in a 1 for the first Value, and then type in male as the Value Label, and then click on ADD. Then type in a 2 for the second Value, and then type in female as the Value Label, and thenclick on ADD.   Then click on OK.  Do the same for the Medicaid acceptance variable, giving it a Name like accept and a Label like Accepts Medicaid.  To type in the Labels, type in a 1 for the first Value, and then type in yes as the Value Label, and then click on ADD.  Then type in a 2 for the second Value, and then type in no as the Value Label, and then click on ADD.   Then click on OK.   To get SPSS to display the value labels, instead of the numbers, for gender and Medicaid acceptance in the data set, click on the Data View tab, then click on View and then click on Value Labels.

ii. Save the data on your desktop/U:drive/floppy disk, by clicking on File, then Save As, and then the down-triangle in the Save In box.
 Then click on the appropriate drive button, and then type in a name like medicaid in the File Name box and click on Save.   The next time you use SPSS you can reopen your data file by clicking on File, Open, down-triangle in the Look In box, and then on the appropriate drive button. 

iii. To create a contingency table for the gender and Medicaid acceptance variables using SPSS, click on Analyze, then Descriptive Statistics, and then Crosstabs.  Then click on the accept variable name and click on the right-triangle to move it to the Row(s)  box.  Then click on the gender variable name and click on the right-triangle to move it to the Column(s) box.   This will create a contingency table with the Medicaid categories on the left side of the table and the sex categories on top of the table.  To get SPSS to show the column percentages and the expected frequencies for each cell, click on Cells, and then click on Column percentages and Expected Counts.  Then click on Continue.  To get SPSS to compute the sample chi squared test statistic, click on Statistics, then Chi-square.  Then click on Continue. Then click on the OK button.  SPSS will then display the contingency table and test statistics on your screen and you can print them by pressing the printer icon button in the left-top corner of the screen.