Question

The paper "Lessons from Pacemaker Implantations" gave the results of a study that followed 89 heart patients who had received electronic pacemakers. The time (in months) to the first electrical malfunction of the pacemaker was summarized in the table below.

20	14	8	25	22	26	29	8	17	28	22	25
6	22	15	20	17	8	20	22	15	24	14	13
11	6	30	22	27	14	24	7	15	6	14	27
15	29	25	18	17	7	19	24	9	13	27	20
8	18	28	17	16	26	22	19	6	7	9	22
17	27	29	26	4	28	3	12	16	9	32	29
32	24	26	20	20	18	13	13	15	23	35	35
12	35	28	22	33

(a) Fill in the following table. (Round your answer to four decimal places if needed.)

Classes	Frequency	Relative Frequency	Cumulative Relative Frequency
0 - <6
6 - <12
12 - <18
18 - <24
24 - <30
30 - <36

(b) Use the cumulative relative frequencies to give approximate answers to the following questions. (Round your answer to four decimal places if needed.)

i. What proportion of those who participated in the study had pacemakers that did not malfunction within the first year?
p =

ii. If the pacemaker must be replaced as soon as the first electrical malfunction occurs, approximately what proportion required replacement between 1 and 2 years after implantation?
p =

(c) Construct a cumulative relative frequency plot. Prepare an Excel document. The file should be named with a .xls extension.
Use it to answer the following questions. (Round your answers to the nearest whole number if needed.)

i. What is the approximate time at which about 50% of the pacemakers had failed?
t =  months

ii. What is the approximate time at which only about 10% of the pacemakers initially implanted were still functioning?
t =  months

Answer 1

(a)

Class interval	Frequency	Relative frequency	Cumulative Relative Frequency
0 - <6	2	2 / 89 = 0.0225	0.0225
6 - <12	15	15 / 89 = 0.1685	0.1910
12 - <18	22	22 / 89 = 0.2472	0.4382
18 - <24	20	20 / 89 = 0.2247	0.6629
24 - <30	23	23 / 89 = 0.2584	0.9213
30 - <36	7	7 / 89 = 0.0787	1.0000

(b) i. proportion of pacemakers that did not malfunction within the first year = 1 - 0.1910 = 0.8090

ii. proportion required replacement between 1 and 2 years after implantation = 0.6629 - 0.1910

= 0.4719

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(c) I. approximate time at which about 50% of the pacemakers had failed.

t = 20 months

ii. approximate time at which only about 10% of the pacemakers initially implanted were still functioning?
t = 28 months