A cohort of hemophiliacs is followed to elicit information on the distribution of time to onset of AIDS following seroconversion (referred to as latency time). All patients who seroconvert become symptomatic within 10 years, according to the distribution available in the table below. Latency time to AIDS among hemophiliacs who become HIV positive Latency time (years) Number of patients 0 1 2 3 4 5 6 7 8 9 10 LAUSE SALT 2 6 8 36 50 68 55 36 19 10 4 (a) Consider the following questions. (Enter your answers using interval notation. Round your numerical values to three decimal places.) Assuming an underlying normal distribution, compute a 95% CI for the mean of the latency times. Assuming an underlying normal distribution, compute a 95% CI for the variance of the latency times. (b) Still assuming normality, estimate the probability p that a patient's latency time will be at least 8 years. (Round your answer to four decimal places.) (c) Now suppose we are unwilling to assume a normal distribution for latency time. Re-estimate the probability p that a patient's latency time will be at least 8 years, and provide a 95% CI for p. (Enter your answer using interval notation. Round your numerical values to four decimal places
A cohort of hemophiliacs is followed to elicit information on the distribution of time to onset of AIDS following seroconversion (referred to as latency time). All patients who seroconvert become symptomatic within 10 years, according to the distribution available in the table below. Latency time to AIDS among hemophiliacs who become HIV positive Latency time (years) Number of patients 0 1 2 3 4 5 6 7 8 9 10 LAUSE SALT 2 6 8 36 50 68 55 36 19 10 4 (a) Consider the following questions. (Enter your answers using interval notation. Round your numerical values to three decimal places.) Assuming an underlying normal distribution, compute a 95% CI for the mean of the latency times. Assuming an underlying normal distribution, compute a 95% CI for the variance of the latency times. (b) Still assuming normality, estimate the probability p that a patient's latency time will be at least 8 years. (Round your answer to four decimal places.) (c) Now suppose we are unwilling to assume a normal distribution for latency time. Re-estimate the probability p that a patient's latency time will be at least 8 years, and provide a 95% CI for p. (Enter your answer using interval notation. Round your numerical values to four decimal places
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Infectious Disease
A cohort of hemophiliacs is followed to elicit information on the distribution of time to onset of AIDS following seroconversion (referred to as latency time). All patients who seroconvert become symptomatic within 10 years, according to the distribution available in the table below.
Latency time to AIDS among hemophiliacs
who become HIV positive
Latency time (years) Number of patients
0
1
2
3
4
5
6
7
8
9
10
USE SALT
2
6
8
36
50
68
55
36
19
10
4
(a) Consider the following questions. (Enter your answers using interval notation. Round your numerical values to three decimal places.)
Assuming an underlying normal distribution, compute a 95% CI for the mean of the latency times.
Assuming an underlying normal distribution, compute a 95% CI for the variance of the latency times.
(b) Still assuming normality, estimate the probability p that a patient's latency time will be at least 8 years. (Round your answer to four decimal places.)
(c) Now suppose we are unwilling to assume a normal distribution for latency time. Re-estimate the probability p that a patient's latency time will be at least 8 years, and provide a 95% CI for p. (Enter your answer using interval notation. Round your numerical values to four decimal places.)
Expert Solution
Step 1
Given information:
| Latency time(years) |
Number of patients
|
| 0 | 2 |
| 1 | 6 |
| 2 | 8 |
| 3 | 36 |
| 4 | 50 |
| 5 | 68 |
| 6 | 55 |
| 7 | 36 |
| 8 | 19 |
| 9 | 10 |
| 10 | 4 |
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