Question

19. (18 pts) A randomized trial was performed to determine whether patients receiving drug therapy plus an electrical cardiac device (treatment group) versus drug therapy alone (control group) could reduce future hospitalizations. The data below represent the frequencies of individuals randomized to the treatment and control groups and the number of hospitalizations for each group.

                                                      Control                                           Treatment

                                                 (Drugs alone)               (Drugs plus electrical cardiac device)

             Hospitalized                         88                                                     82

             Not Hospitalized                132                                                   156

1. What is the estimated difference in the rates of hospitalization between the control and the treatment groups?
2. If the true rates of hospitalization were the same for each group, what is the probability of obtaining the sample estimated difference (part a) or something more extreme? (For calculating the SE use the sample estimated proportions).
3. Based on your answer to part (b), would you conclude that the rates of hospitalization in the treatment group is actually different? Why or why not?

Answer 1

Answer:

Question 19:

(a) 0.0555

(b) z = 1.23

The probability is 0.2196.

(c) Since the p-value (0.2196) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that the rates of hospitalization in the treatment group is actually different.

p1	p2	pc
0.4	0.3445	0.3712	p (as decimal)
88/220	82/238	170/458	p (as fraction)
88.	82.	170.	X
220	238	458	n
	0.0555	difference
	0.	hypothesized difference
	0.0452	std. error
	1.23	z
	.2196	p-value (two-tailed)

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