- #1
Mogarrr
- 120
- 6
Homework Statement
Latency Time(years): Number of patients
0: 2
1: 6
2: 9
3: 33
4: 49
5: 66
6: 52
7: 37
8: 18
9: 11
10: 4
(I don't know how to make a proper table with latex... tried \being{tabular}{l r} but this doesn't work)
Homework Equations
When the variance is unknown, the t-distribution may be used
\mu = \bar{x} \pm t_{n,1- \frac {\alpha}2} \cdot \frac {s}{\sqrt {n}}
and estimating the variance, we have...
(n-1) \cdot \frac {s^2}{ \chi^2_{n-1,1- \frac {\alpha}2}} \leq \sigma^2 \leq (n-1) \cdot \frac {s^2}{ \chi^2_{n-1,\frac {\alpha}2}}
lastly, for the poisson distribution the confidence interval is given by \mu_1, \mu_2, that satisfies
\frac {\alpha}2 = P(X \geq \mu | \mu = \mu_1) = \sum_{k=x}^{\infty} \frac {e^{-\mu_1} \mu_1^{k}}{k!}
\frac {\alpha}2 = P(X \leq \mu | \mu = \mu_2) = \sum_{k=0}^{x} \frac {e^{-\mu_2} \mu_2^{k}}{k!}
The Attempt at a Solution
I'm not really sure how to handle this. I'm used to just once column where I can compute the mean and sample variance. Here I'm asked to compute the mean and variance of the latency time. Since this is a time interval, I think I should be using the Poisson distribution, however it's given that the distribution is normal.
I don't know how to proceed. Any help would be appreciated.