17. Which of the following is FALSE? (a) The 95% confidence in \"95% confidence

Question

17. Which of the following is FALSE? (a) The 95% confidence in "95% confidence interval for " means that if we took many samples and made a 95% confidence interval for each sample, about 95% of the intervals would contain the population mean . (b) Increasing the confidence percentage of a confidence interval will increase its (c) The small sample confidence interval formula X ±to/2n-lsNn could be used for (d) The large sample confidence interval formula X ±za/28Wn could be used for width. X1,, Xn~ Poisson(A) independent with n smaller than 30. Xi,...,Xn ~Poisson(A) independent with n larger than 30

Explanation / Answer

Confidence Intervals for Poisson data For an observation from a Poisson distribution, we have ^2 = . If we observe r events, then our estimate ˆ= n : N(, ) If n is bigger than 20, we can use this to find an approximate confidence interval.

Hence we see that here n>20 and so we can use z distribution hence C is False.

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