試題詳解

28. (5%) From the general knowledge, the population occurrence rate of asthma is 0.1 for children who visit hospitals. A pediatrician moved his clinic to a new place and he found 9 children with asthma among 50 appointments in his first day at the new place. If the 50 appointments are considered as Bernoulli random variables with O and 1 outcomes, the total number of asthma children, indicated as X, should follow a Binomial distribution with probability 0.1 under the general condition. He then makes the following guesses. Which one is a correct inference for the occurrence rate at the new place?
(A) If the occurrence rate holds the same as other places, the standard deviation of each Bernoulli random variable in this problem is . The standard deviation of X should be 50 x 0.3=15
(B) Since 9/50=0.18 is greater than 0.1, there must be an increase of the occurrence rate
(C) If the occurrence rate is greater than 0.1, we should also see the proportion of asthma children to be greater than 0.1 in the next day
(D) Since P(X=9)=0.033 is smaller than 0.05, we will decide this as an unusual situation, and the evidence supports an increased occurrence rate. The threshold 0.05 can be applied when the number of appointments is 70 in a day
(E) Since P(X≧9)=0.058 is greater than 0.05, we do not have to worry too much about the situation, and it might be a random fluctuation from day to day. The threshold 0.05 can be applied when the number of appointments is 70 in a day