Hypotheses: asthma attack; heart failure patients; ICU days

See the attached file for clarity in the tables.

1. It is suspected that high pollution levels (measured by number of particulates found in the air) increase the levels of asthma attacks. A researcher collects data on50 people who experienced an asthma attack during the course of one year. For each person the number of particulates was recorded for the day of the attack (day of attack) and for a day exactly one month before the day of the attack (control). The results are as follows:

Number of attacks.
Pollution day of attack > pollution on control day 30
Pollution day of attack < pollution on control day 15
Pollution day of attack = pollution on control day 5
Total 50

Assume a null hypothesis that pollution has nothing to do with having an asthma attack. How many attacks would you expect when the pollution level on the day of the attack is higher than the control day, ignoring the days when pollution level days are equal?

Given the data in the table, assess whether pollution is affecting asthma attacks. (Hint: use the normal approximation to the binomial distribution).

c. Now assume a seasonal variation on the pollution levels. Say in the winter instead of 30 we have 10, instead of 15 we have 4 and 2 cases when they are equal. Given this data does pollution affect asthma attacks?

6. Recently a clinical trial was conducted to test the ability of heart failure patients to improve the amount of time they could walk on a treadmill post a surgical intervention. 107 patients were randomly assigned to regular medical therapy and 105 to the surgical intervention. The patients were tested at baseline and again at 6 months post surgery. The results are shown below:

Mean Change in 6month-baseline (minutes) Standard deviation N
Regular medical therapy 0.5 2.2 100
Surgical procedure 2.1 3.1 99

What test would we do to test for a change in mean total change for a specific group?

b. Report the value of this test for the medical group and report a p-value.

7. It is very hard to predict how long post-surgical trauma patients typically spend in the ICU (those who survive to make it to the ICU). Below is typical data on the number of days spent in ICU for these types of patients from 2 different hospitals

Days in ICU..
Hospital ICU A 10, 21, 60, 32, 5, 29, 44, 8, 33, 26, 13
Hospital ICU B 76, 68, 87, 10, 86, 27, 125, 238, 96, 44, 73, 35, 60

Why is a t-test not a good test for this type of data?

b. Pick a non-parametric test that is most appropriate for determining if the number of days spent in the ICU for these two hospitals is comparable. What is the result of this test?