1. A, B, and C are three countries that have Ebola epidemics. In average, three out of 100000 people is infected in A, one out of 100000 is infected in B, and one out of 200000 is infected in C. Some blood samples are sent to a lab for testing. In order to avoid bias, the tester is told that these blood samples come from one of the above countries but is not told which one.

a. The tester tests the first two samples, they are negative. What is the probability that the third sample will be tested positive?

b. The tester tests the first two samples, they are positive. What is the probability that the third sample will be tested negative?

2. Let X~B(n,p), for the test problem H_o: p=0.2↔H_a:p=0.5, let the rejection region be X≥6.

A. if you have a sample of 12 (n=12), find the α and β;

B. in order to reduce β to be less than 5%, how large n you have to have?

3. College students are doing a research on smoking. If the non-smoking proportion in Texas is 80%. In an experiment, in order to collect data, they need to talk to certain number of people in Texas, how many people they have to talk to so that they are 90% sure that no less than 75 of them are non-smokers?

Subject | Mathematics |

Due By (Pacific Time) | 11/01/2014 10:00 pm |

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