A cohort of hemophifcacs is followed to elicit information on the distribution o

Question

A cohort of hemophifcacs is followed to elicit information on the distribution of time to onset of AIDS following seroconversion (referred to as latency time). All patients who sero-convert become symptomatic within 10 years, accordng to the distnbution in Table 6.11. Assuming an underlying normal distnbution. compute 95% CIs for the mean and variance of the latency tmea. 6.69 Still assuming normality, estmate the probability p that a patient's latency time will be at least 8 years. 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% Cl for rho.

Explanation / Answer

Here we have to find 95% confidence interval for mean number of patients.

This we can find by using TI-83 calculator.

Here we use t-interval for data because sample size is small and population standard deviation is unkonwn.

TI-83 steps :

STAT --> ENTER --> Enter the data in L1 --> STAT --> TESTS --> 8:TInterval --> ENTER --> Highlight on Data --> ENTER --> List : select L1 --> Freq : 1 --> C-level : 0.95 --> Calculate --> ENTER

95% confidence interval for population mean is (11.049, 41.132).

Here we have to find P(a patient latency time will be at least 8 years) = P(X >=8).

P(X>=8) = P(X=8 or 9 or 10) / total no of patients

= (18+11+4) / 287

= 33 / 287

= 0.1150

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