Problem: In a study published in November 2006, Skyberg et al. (Infect Immun. 74(11):6287-6292) examined different pathogenic strains of E. coli. The authors tested each strain's ability to kill chicken embryos. The data is in a table below:
|
strain
|
# of embryos
|
# of deaths
|
|
NC
|
66
|
10
|
|
APEC 02
|
64
|
48
|
a. What is p-hat, the weighted average of the proportion?
b. Construct a 95% confidence interval for the true proportion of chicken embryo deaths by the NC strain.
c. Construct a 95% confidence interval for the true proportion of chicken embryo deaths by the APEC 02 strain.
d. Do the intervals overlap?
e. Perform a two-sided hypothesis test to compare the proportion of NC deaths to the proportion of APEC 02 deaths. What is the p-value?
f. What is the conclusion of this test?