# Chi-square tests and Logistic Regression

The data in tab 19 (Delivery data) in DS7 show the distribution of women recently delivered of a newborn infant at two hospitals. The data show the numbers of women delivered by caesarean section (and non-caesarean delivery) for each hospital. Using these data, do the following:

1. Assuming an alpha of 0.05, test the hypothesis of independence between the prevalence of caesarean section deliveries and hospital (use both the CHISQ.TEST and the CHISQ.DIST.RT functions in Excel). Report the results of your statistical test and provide an interpretation of these results. (6 points)
2. Create a table displaying the conditional probabilities and describe any relationships suggested by these probabilities. Be sure to report the prevalence of C-section delivery for each hospital. (2 points)
3. Repeat the test of independence from part 19.a but assuming that an alpha of 0.1 indicates statistical significance and report the results. (1 point)
4. Interpret your results from part 19.a but assuming now an alpha of 0.01. (I.e., report whether you accept or reject the null hypothesis under these conditions.) Report your interpretation in the Word document for this problem set. (1 point)

20. Assume the data in tab 20. (Clinic wait time) of DS7 represent random samples of 90 records from each of four health centers. These data display the distribution of patients by health center and whether the time each spent waiting to be seen was excessive. Perform the following:

1. Compute the prevalence of excessive waiting time (i.e., compute the conditional probabilities), describe the conditional probabilities and any relationship suggested by these probabilities. Include the conditional probability table and the prevalence figures in your report. (2 points).
2. Assume that alpha is 0.05, test the hypothesis that waiting time does not differ by health center (use both the CHISQ.TEST and CHISQ.DIST.RT functions in Excel). Report the results of the statistical tests and your interpretation of these. (6 points)
3. Calculate the critical value of the chi-square statistic for alpha = 0.05 and the appropriate degrees of freedom for these data; repeat for alpha = 0.001. Report the results of your calculations in your Word document for this problem. (1 point)
4. Interpret your results from part 20.b assuming alpha for statistical significance is 0.001. Report your interpretation in the Word document for this problem set. (1 point)

21. Assume the data in tab 21. (Prenatal care) of DS7 represent a properly collected representative sample of women delivering infants at your hospital. The data show the number of women in each of three categories of socio-economic status (SES) according to the category of healthcare professional attending her delivery.

1. Consider the proposition that any apparent differences in source of prenatal care according to the socio-economic status of the mother are due to chance alone. What are the null and alternate hypotheses implied by this statement? (2 points)
2. Combine the data from the Generalist column and the Specialist column into a single column (any physician). This will produce a new data table with three rows for SES (High, Middle, Low) and two columns for source of care (Midwife, Physician). Using this new data table, test the hypothesis that source of care (Midwife v. Physician) is independent of SES and report your results and interpretation. (6 points)

3. Compute the conditional probabilities for this new data set and describe the results in a single sentence. (2 points)