projects for stat/Basic Statistics
MTH 1111A Spring 2017
Basic Statistics
Data Project # 3
Inference for Proportions
(100 points)
DUE: Monday April 24 at 8am. Late assignments may be accepted with a penalty of 4 points off/day.
No papers will be accepted after April 28 at 3pm. You may work with up to 2 other students in
the class and turn in only 1 report. Submissions by email will not be accepted.
Crohn’s Disease
Crohn’s disease is a chronic inflammatory bowel disorder that affects approximately 500,000 Americans,
typically beginning in their teens and early 20s. The gastrointestinal tract becomes inflamed and ulcerated
causing abdominal pain, diarrhea, vomiting, and weight loss.
Most Crohn’s disease patients are first treated with Corticosteriods, but long term users of steroid often
suffer side effects including osteoporosis, diabetes and mood swings. A biologic drug, infliximab
(Remicade), is often prescribed when a person with Crohn’s disease does not respond to the standard
treatments. Infliximab is an antibody that blocks the activity of a key inflammation-promoting protein
“tumour necrosis factor” (TNF) on the cell membrane and in the blood.
A study in The Lancet (2002; 359: 1541–49) suggests that sustained treatment with infliximab can
prolong remissions in patients with moderate to severe Crohn’s disease. “At last we have a therapy that
truly allows us to manage this disease over time, rather than just treating flare ups,” said lead investigator
Dr. Stephen Hanauer.
Design of the study:
The researchers enrolled 573 patients with moderate to severe Crohn’s disease at 55 centers in North
America, Europe, and Israel. Eligible patients had Crohn’s disease of at least 3 months’ duration. Patients
were excluded from the study if they had received previous treatment with infliximab or any other antiTNF
blocker. All patients received an initial dose of infliximab. Only those who respond positively to the
initial treatment were selected for the study. The 335 patients (58%) who responded to the initial dose
within 2 weeks were randomized to one of three treatment groups.
Group I received placebo (an infusion containing no medication) at weeks 2 and 6 of the study, then
every 8 weeks thereafter. On the same schedule, group II received 5mg/kg of infliximab, and group III
received 5 mg/kg of infliximab at weeks 2 and 6 followed by 10mg/kg beginning at week 14.
ASSIGNMENT: Use MINITAB to analyze the data in Table 1, and write a brief report that addresses the
questions given in this assignment. Your paper should be typed and should use complete sentences,
proper spelling, good grammar, and so on. Include an introduction that describes the context and a
conclusion that summarizes your results. Please staple a printout of your Minitab session window to your
report. See the Introduction to Minitab handout for more details.
Table 1. Results of the infliximab maintenance therapy
Treatment group
I II III
Patients in remission at week 30 23 44 50
Total number of patients 110 113 112
MTH 1111A Spring 2017
Basic Statistics
You need to check the necessary conditions for inference only in questions 4 and 5. In your report, you
should include the following:
1. Include an introduction that describes the purpose of the study and a conclusion that summarizes your
results. Note that the purpose of the study should refer to a population parameter, not a sample
statistics.
2. What kind of study is this? Experiment or observational study? Retrospective or prospective? Define
the sample, population, and parameter of interest.
3. Use the results of Group I to estimate the proportion of Crohn’s disease patients who remain in
remission at week 30 without the maintenance therapy. Based on this proportion, find a 95%
confidence interval for the proportion of patients who are in remission at week 30 without the
maintenance therapy. Interpret the confidence interval in context. Read the “What can go wrong?”
section in p. 484 of the text if you need help.
Minitab Instructions:
Select Stat > Basic Statistics > 1 Proportion…
Choose “Summarized data” from the drop down menu.
Click in the box for number of events and enter the appropriate responses. See “Patients in remission…” in
Group I.
Click in the box for number of trials and enter the appropriate sample size. See “Total number of patients”
in Group I.
Click on the Options… button to set the confidence level to 95.0. Leave the alternative as not equal.
Choose “Normal approximation” from the drop down menu for “Method”.
4. Compute a two-proportion z-interval using the data in Group I and Group II to estimate the difference
of proportions of Crohn’s disease patients who remains in remission between these two groups.
a. Check the necessary conditions for a two-proportion z-interval. Show all your work. See
notes and step-by-step examples in the textbook.
b. Compute a two sided two-proportion z-interval using Minitab.
Minitab Instructions:
Stat > Basic Statistics > 2 Proportions
Choose “Summarized data”
Put the results for Group I in the first sample, and results for Group II in the second sample.
Click on the Options… button to set the confidence level to 95.0. Choose “Estimate the proportions
separately” from the drop down menu for “Test method”. Leave the null hypothesis as zero and the
alternative as not equal.
c. Interpret the confidence interval in proper context. Is 0 contained in the confidence interval?
Is 0 above or below the confidence interval? What does this tell you? (Hint: Read the answer
to question 2 of the “Just Checking” section in p. 592 of the text.). Read the two examples in
P. 590 and 591 of the text if you need help.
MTH 1111A Spring 2017
Basic Statistics
For Question 5 you should ignore the output statement about Fisher’s exact test.
5. Perform a two-proportion z-test using the data in Group I and Group III to see if the patients on the
maintenance therapy are more likely to be in remission at week 30.
a. State the hypotheses. Read the “What can go wrong?” section in p. 508 of the text on how to
set up the null hypothesis and the alternative hypothesis.
b. Check the necessary conditions for a two-proportion z-Test. Show all your work. See step-bystep
examples in the notes and textbook.
c. Compute the appropriate test statistic and p-value using Minitab.
Minitab Instructions:
Stat > Basic Statistics > 2 Proportions
Choose “Summarized data”
Put the results for Group I in Sample 1, and results for Group III in Sample 2.
Click on the Options… button to set the confidence level to 95.0. “Hypothesized difference” is the
value specified by your null hypothesis for p1 – p2. (for H0: p1 = p2 , this value is 0)
Select an appropriate alternative hypothesis. (Is p1 – p2 ≠ 0? > 0? or < 0?
For test method, choose “Use the pooled estimate of proportion”.
d. State your conclusion in context.
Don’t forget to staple a printout of your Minitab session window to your report.
The MINITAB assignment will be graded out of 100 points as follows:
15 points for the writing (no typos, correct grammar and spelling, intro/conclusion, …)
5 points for the Session Window
27 points for correct Minitab use (all steps completed in session window and statistics are included in
the report)
49 points for correct statistical reasoning
4 points for meeting project milestones
– 4 points/day late fee
Please note: It is okay to discuss how to use Minitab or the computer portion of the work with
other people—but each group needs to go through all the steps of using the program. You can’t
just watch someone else—you need to do it yourselves! When it comes time for the write-up,
ALL WORK IS TO BE STRICTLY YOUR OWN. Inappropriate collaboration will result in a
grade of 0 on the assignment. If you have any questions about what is allowed, ask me for
clarification.
MTH 1111A Spring 2017
Basic Statistics
Data Project # 3
Inference for Proportions
(100 points)
DUE: Monday April 24 at 8am. Late assignments may be accepted with a penalty of 4 points off/day.
No papers will be accepted after April 28 at 3pm. You may work with up to 2 other students in
the class and turn in only 1 report. Submissions by email will not be accepted.
Crohn’s Disease
Crohn’s disease is a chronic inflammatory bowel disorder that affects approximately 500,000 Americans,
typically beginning in their teens and early 20s. The gastrointestinal tract becomes inflamed and ulcerated
causing abdominal pain, diarrhea, vomiting, and weight loss.
Most Crohn’s disease patients are first treated with Corticosteriods, but long term users of steroid often
suffer side effects including osteoporosis, diabetes and mood swings. A biologic drug, infliximab
(Remicade), is often prescribed when a person with Crohn’s disease does not respond to the standard
treatments. Infliximab is an antibody that blocks the activity of a key inflammation-promoting protein
“tumour necrosis factor” (TNF) on the cell membrane and in the blood.
A study in The Lancet (2002; 359: 1541–49) suggests that sustained treatment with infliximab can
prolong remissions in patients with moderate to severe Crohn’s disease. “At last we have a therapy that
truly allows us to manage this disease over time, rather than just treating flare ups,” said lead investigator
Dr. Stephen Hanauer.
Design of the study:
The researchers enrolled 573 patients with moderate to severe Crohn’s disease at 55 centers in North
America, Europe, and Israel. Eligible patients had Crohn’s disease of at least 3 months’ duration. Patients
were excluded from the study if they had received previous treatment with infliximab or any other antiTNF
blocker. All patients received an initial dose of infliximab. Only those who respond positively to the
initial treatment were selected for the study. The 335 patients (58%) who responded to the initial dose
within 2 weeks were randomized to one of three treatment groups.
Group I received placebo (an infusion containing no medication) at weeks 2 and 6 of the study, then
every 8 weeks thereafter. On the same schedule, group II received 5mg/kg of infliximab, and group III
received 5 mg/kg of infliximab at weeks 2 and 6 followed by 10mg/kg beginning at week 14.
ASSIGNMENT: Use MINITAB to analyze the data in Table 1, and write a brief report that addresses the
questions given in this assignment. Your paper should be typed and should use complete sentences,
proper spelling, good grammar, and so on. Include an introduction that describes the context and a
conclusion that summarizes your results. Please staple a printout of your Minitab session window to your
report. See the Introduction to Minitab handout for more details.
Table 1. Results of the infliximab maintenance therapy
Treatment group
I II III
Patients in remission at week 30 23 44 50
Total number of patients 110 113 112
MTH 1111A Spring 2017
Basic Statistics
You need to check the necessary conditions for inference only in questions 4 and 5. In your report, you
should include the following:
1. Include an introduction that describes the purpose of the study and a conclusion that summarizes your
results. Note that the purpose of the study should refer to a population parameter, not a sample
statistics.
2. What kind of study is this? Experiment or observational study? Retrospective or prospective? Define
the sample, population, and parameter of interest.
3. Use the results of Group I to estimate the proportion of Crohn’s disease patients who remain in
remission at week 30 without the maintenance therapy. Based on this proportion, find a 95%
confidence interval for the proportion of patients who are in remission at week 30 without the
maintenance therapy. Interpret the confidence interval in context. Read the “What can go wrong?”
section in p. 484 of the text if you need help.
Minitab Instructions:
Select Stat > Basic Statistics > 1 Proportion…
Choose “Summarized data” from the drop down menu.
Click in the box for number of events and enter the appropriate responses. See “Patients in remission…” in
Group I.
Click in the box for number of trials and enter the appropriate sample size. See “Total number of patients”
in Group I.
Click on the Options… button to set the confidence level to 95.0. Leave the alternative as not equal.
Choose “Normal approximation” from the drop down menu for “Method”.
4. Compute a two-proportion z-interval using the data in Group I and Group II to estimate the difference
of proportions of Crohn’s disease patients who remains in remission between these two groups.
a. Check the necessary conditions for a two-proportion z-interval. Show all your work. See
notes and step-by-step examples in the textbook.
b. Compute a two sided two-proportion z-interval using Minitab.
Minitab Instructions:
Stat > Basic Statistics > 2 Proportions
Choose “Summarized data”
Put the results for Group I in the first sample, and results for Group II in the second sample.
Click on the Options… button to set the confidence level to 95.0. Choose “Estimate the proportions
separately” from the drop down menu for “Test method”. Leave the null hypothesis as zero and the
alternative as not equal.
c. Interpret the confidence interval in proper context. Is 0 contained in the confidence interval?
Is 0 above or below the confidence interval? What does this tell you? (Hint: Read the answer
to question 2 of the “Just Checking” section in p. 592 of the text.). Read the two examples in
P. 590 and 591 of the text if you need help.
MTH 1111A Spring 2017
Basic Statistics
For Question 5 you should ignore the output statement about Fisher’s exact test.
5. Perform a two-proportion z-test using the data in Group I and Group III to see if the patients on the
maintenance therapy are more likely to be in remission at week 30.
a. State the hypotheses. Read the “What can go wrong?” section in p. 508 of the text on how to
set up the null hypothesis and the alternative hypothesis.
b. Check the necessary conditions for a two-proportion z-Test. Show all your work. See step-bystep
examples in the notes and textbook.
c. Compute the appropriate test statistic and p-value using Minitab.
Minitab Instructions:
Stat > Basic Statistics > 2 Proportions
Choose “Summarized data”
Put the results for Group I in Sample 1, and results for Group III in Sample 2.
Click on the Options… button to set the confidence level to 95.0. “Hypothesized difference” is the
value specified by your null hypothesis for p1 – p2. (for H0: p1 = p2 , this value is 0)
Select an appropriate alternative hypothesis. (Is p1 – p2 ≠ 0? > 0? or < 0?
For test method, choose “Use the pooled estimate of proportion”.
d. State your conclusion in context.
Don’t forget to staple a printout of your Minitab session window to your report.
The MINITAB assignment will be graded out of 100 points as follows:
15 points for the writing (no typos, correct grammar and spelling, intro/conclusion, …)
5 points for the Session Window
27 points for correct Minitab use (all steps completed in session window and statistics are included in
the report)
49 points for correct statistical reasoning
4 points for meeting project milestones
– 4 points/day late fee
Please note: It is okay to discuss how to use Minitab or the computer portion of the work with
other people—but each group needs to go through all the steps of using the program. You can’t
just watch someone else—you need to do it yourselves! When it comes time for the write-up,
ALL WORK IS TO BE STRICTLY YOUR OWN. Inappropriate collaboration will result in a
grade of 0 on the assignment. If you have any questions about what is allowed, ask me for
clarification.
