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The paper "Lessons from Pacemaker Implantations" (Journal of the American Medical Association [1965]: $231-232$ ) gave the results of a study that followe...

Question

The paper "Lessons from Pacemaker Implantations" (Journal of the American Medical Association [1965]: $231-232$ ) 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 recorded: $egin{array}{rrrrrrrrrrrr}24 & 20 & 16 & 32 & 14 & 22 & 2 & 12 & 24 & 6 & 10 & 20 \ 8 & 16 & 12 & 24 & 14 & 20 & 18 &am

The paper "Lessons from Pacemaker Implantations" (Journal of the American Medical Association [1965]: $231-232$ ) 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 recorded: $egin{array}{rrrrrrrrrrrr}24 & 20 & 16 & 32 & 14 & 22 & 2 & 12 & 24 & 6 & 10 & 20 \ 8 & 16 & 12 & 24 & 14 & 20 & 18 & 14 & 16 & 18 & 20 & 22 \ 24 & 26 & 28 & 18 & 14 & 10 & 12 & 24 & 6 & 12 & 18 & 16 \ 34 & 18 & 20 & 22 & 24 & 26 & 18 & 2 & 18 & 12 & 12 & 8 \ 24 & 10 & 14 & 16 & 22 & 24 & 22 & 20 & 24 & 28 & 20 & 22 \ 26 & 20 & 6 & 14 & 16 & 18 & 24 & 18 & 16 & 6 & 16 & 10 \ 14 & 18 & 24 & 22 & 28 & 24 & 30 & 34 & 26 & 24 & 22 & 28 \ 30 & 22 & 24 & 22 & 32 & & & & & & & end{array}$ a. Summarize these data in the form of a frequency distribution, using class intervals of 0 to $<6,6$ to $<12$, and so on. b. Compute the relative frequencies and cumulative relative frequencies for each class interval of the frequency distribution of Part (a). c. Show how the relative frequency for the class interval 12 to $<18$ could be obtained from the cumulative relative frequencies. d. Use the cumulative relative frequencies to give approximate answers to the following: i. What proportion of those who participated in the study had pacemakers that did not malfunction within the first year? 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? e. Construct a cumulative relative frequency plot, and use it to answer the following questions. i. What is the approximate time at which about $50 %$ of the pacemakers had failed? ii. What is the approximate time at which only about $10 %$ of the pacemakers initially implanted were still functioning?



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One year, there were about $3,000$ institutions of higher learning in the U.S. (including junior colleges and community colleges). As part of a continuing study of higher education, the Carnegit Commission took a simple random sample of 400 of these institutions.? The average enrollment in the 400 sample schools was $3,700,$ and the SD was $6,500 .$ The Commission estimates the average enrollment at all $3,000$ institutions to be around $3,700 ;$ they put a give-or-take number of 325 on this estimate. Say whether each of the following statements is true or false, and explain. If you need more information to decide, say what you need and why.
(a) An approximate 68$\%$ -confidence interval for the average enrollment of all 3, 000 institutions from $3,375$ to $4,025 .$
(b) If a statistician takes a simple random sample of 400 institutions out of $3,000,$ and goes one SE either way from the average enrollment of the 400 sample schools, there is about a 68$\%$ chance that his interval will cover the average enrollment of all $3,000$ schools.
(c) About 68$\%$ of the schools in the sample had enrollments in the range $3,700 \pm 6,500 .$
(d) It is estimated that 68$\%$ of the $3,000$ institutions of higher learning in the U.S. enrolled between $3,700-325=3,375$ and $3,700+325=$ $4,025$ students.
(e) The normal curve can't be used to figure confidence levels here at all, because the data don't follow the normal curve.


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