Homework 5 (24 points)
STAT 301
Name(s) ____SOLUTION__________
Due: Thursday, March 7th @ 11:59pm
1. A study was conducted over 10 years to investigate the long-term complication rates in patients
treated with two different therapies. The data are given in the table below.
Therapy 1
Therapy 2
Total
Complications
89
127
216
No Complications
911
873
1784
Total
1000
1000
2000
Research Question – Is there a difference in the complication rates in patients for the
two therapies?
a. Determine the appropriate null and alternative hypotheses to test the research question
of interest. (3 points)
H0: pTherapy 1 = pTherapy 2
Ha: pTherapy 1 ≠ pTherapy 2
b. Should Fisher’s Exact Test or the Chi-square Test be used? Fully explain your reasoning.
(3 points)
Expected Counts:
216
Overall % Complications =
= 0.11
2000
1784
Overall % No Complications =
= 0.89
2000
Therapy 1
Therapy 2
Total
Complications
1000(0.11) = 110
1000(0.11) = 110
216
No Complications
1000(0.89) = 890
1000(0.89) = 890
1784
Total
1000
1000
2000
Since all expected counts ≥ 5, we should use Chi-square test.
c. Using JMP, find the appropriate test statistic and p-value. If no test statistic is needed,
simply write “No Test Statistic.” Include a detailed sketch of or paste your JMP output
below. (3 points)
Test Statistic = 7.495
p-value = 0.0062
1
d. What conclusion can be made regarding the research question of interest? Make sure
to fully explain your answer. (3 points)
There is statistically significant evidence (since 0.0062 < 0.05) that there is a
difference in the complication rates in patients for the two therapies.
2. Under standard care, 10% of all patients suffering their first MI are readmitted to the hospital
within 6 weeks. A study was conducted to directly compare standard care to a new protocol
using a randomized trial. The number of patients readmitted within six weeks was recorded and
the data collected are given in the table below.
Standard Care
New Protocol
Total
Readmitted
16
11
27
Not Readmitted
109
114
223
Total
125
125
250
Research Question – Is there evidence that the new protocol resulted in a
reduction in the readmission rate when compared to standard care?
a. Determine the appropriate null and alternative hypotheses to test the research question
of interest. (3 points)
H0: pstandard ≤ pnew
Ha: pstandard > pnew
b. Should Fisher’s Exact Test or the Chi-square Test be used? Fully explain your reasoning.
(3 points)
We should use Fisher’s Exact Test because we are just testing that one group is
larger than the other.
c. Using JMP, find the appropriate test statistic and p-value. If no test statistic is needed,
simply write “No Test Statistic.” Include a detailed sketch of or paste your JMP output
below. (3 points)
No Test Statistic
p-value = 0.2077
2
d. What conclusion can be made regarding the research question of interest? Make sure
to fully explain your answer. (3 points)
There is not statistically significant evidence (since 0.2077 > 0.05) that the new
protocol resulted in a reduction in the readmission rate when compared to
standard care.
3