BSTT 400 Fall (Online) Homework 7 100% Satisfaction

BSTT 400 Fall (Online)
Homework 7 (Due: Monday, 11/2/2015)

To receive full credit, you must:


Show all the relevant steps used to arrive at your solution and report the appropriate unit of
measurement.



Clearly state any necessary assumptions and/or conclusions made.



Write in a clear, concise manner and do not include raw statistical output or code unless it is
absolutely necessary. The results of your analysis should be edited for relevance.



Figures and tables must be labeled and captioned or described in the text of the associated
answer.



While it is acceptable to discuss concepts and seek clarification from colleagues, you should

1. Sickle-cell and malaria: Sickle-cell anemia is hereditary condition that is common
among African-Americans and can cause medical problems. Some biologists suggest that
the sickle-cell trait protects against malaria. That would explain why it is found in people
whose ancestors originally came from Africa, where malaria is common. A study in
Africa tested 523 children for the sickle-cell trait and also for malaria. Here are the
results.
Severe malaria infection
Sickle-cell trait
No sickle-cell trait

Yes
31
147

No
95
250

a. Estimate the proportion of severe malaria infection in those with the sickle-cell
trait and those without it. In each case, provide the 95% confidence interval (CI)
and interpret its value. (6 points).
b. Based on the estimates and their confidence intervals, what does this tell you
about the possible relationship between malaria infection and sickle-cell? (2
points).
c. Now we wish to verify whether there is an association between malaria and sickle
cell using a chi-square test.
a. What are the null and alternative hypotheses for this test? (2 pts)
b. Find the expected cell counts under the null hypothesis. Verify that the
expected counts meet the guideline for use of the chi-square test. (3 pts)
c. Compute the chi-square statistic and find p-value for this test. (3 pts)
d. What is your conclusion? Is there a good evidence of a relationship
between the sickle-cell trait and severe malaria infection? Why or why
not? (1 pt)

d. An alternative approach to evaluating the association between the outcome
(severe malarial infection) and exposure (sickle-cell trait) is to test the difference
of the risks (proportions) using a z-score.
a. What are the null and alternative hypotheses of this test if it was a twotailed test? (2 points)
b. What is the point estimate and its standard error? (5 points)
c. Compute the test statistic and determine whether there is a significant
difference in proportions using an alpha of 5%. State your conclusions and
discuss how they compare to the conclusions in both (b) and (c). (4 points)