Question

Question 3: (6 marks) A French study was conducted in the 1990s to compare the effectiveness of using an Instrument called a cardiopump with the effectiveness of using traditional cardiopulmonary resuscitation (CPR) in saving lives of heart attack victims. Heart attack patients in participating cities were treated with either a cardiopump or CPR, depending on whether the individual's heart attack occurred on an even-numbered or an odd-numbered day of the month. Before the start of the study, a coin was tossed to determine which treatment, a cardiopump or CPR, was given on the even-numbered days. The other treatment was given on the odd-numbered days. In total, 754 patients were treated with a cardiopump, and 37 survived at least one year, while 746 patients were treated with CPR, and 15 survived at least one year. a. The conditions for inference are satisfied in the study. State the conditions and indicate how they are satisfied. b. Perform a statistical test to determine whether the survival rate for patients treated with a cardiopump is significantly higher than the survival rate for patients treated with CPR.

Answer 1

(a)

Two Independent Samples Proportions Z test to determine whether the difference between two Independent Samples proportion is significant isemployed and the following conditions are met:

(i) The sampling method for each population is Simple Random Sampling.

(ii) The samples are independent

(iii) Each sample includes at least 10 successes and 10 failures

(iv) Each population is at last 20 times as big as its sample.

(b)

H0: Null Hypothesis: p1 $\leq$ p2 (The survival rate for patients treated with a cardiopump is not significantly higher than the patients treated with CPR.)

HA: Alternative Hypothesis: p1 > p2 (The survival rate for patients treated with a cardiopump is significantly higher than the patients treated with CPR.) (Claim)

n1 = 754

$\hat{p}$1 = 37/754 = 0.0491

n2 = 746

$\hat{p}$2 = 15/746 = 0.0201

Pooled Proportion iis given by:

$\bar{p}=\frac{37+15}{754+746}=0.0347$

Take $\alpha$ = 0.05

From Table, critical value of Z = 1.64

Test Statistic is given by:

$Z=\frac{0.0491-0.0201}{\sqrt{0.0347\times (1-0.0347)\times (1/754+1/746)}}=3.066$

Since calculated value of Z = 3.066 is greater than critical value of Z = 1.64, the differnce is significant. Reject null hypothesis.

Conclusion:
The data support the claim that the survival rate for patients treated with a cardiopump is significantly higher than the patients treated with CPR.