AS/A2 Stats 1 Stats 3

S2 Topic 4: Hypothesis tests
Critical regions of Poisson distributions
You will be given a number of hypothesis tests. In each case a null and alternative hypothesis will be suggested, where l refers to the mean of the population Poisson distribution P(l), and a level of test. You must decide what the critical region for the hypothesis test should be. Choose values for l and x, and use this form to obtain Poisson probabilities to help you choose the correct critical region.

l: 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 x: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 P(X £ x) = P(X ³ x) =

Correct:

Attempts:

% Correct:

1	H0: l= 4 H1: l >4 Level of test: 5%
	X ³5	X ³6	X ³7	X ³8	X ³9
2	H0: l= 9 H1: l <9 Level of test: 1%
	X £1	X £2	X £3	X £4	X £5
3	H0: l= 3.5 H1: l <3.5 Level of test: 5%
	X =0	X £1	X £2	X £3	X £4
4	H0: l= 5.5 H1: l >5.5 Level of test: 20%
	X ³6	X ³7	X ³8	X ³9	X ³10
5	H0: l= 6.5 H1: l >6.5 Level of test: 5%
	X ³8	X ³9	X ³10	X ³11	X ³12
6	H0: l= 10 H1: l <10 Level of test: 5%
	X £1	X £2	X £3	X £4	X £5
7	H0: l= 3 H1: l >3 Level of test: 1%
	X ³6	X ³7	X ³8	X ³9	X ³10
8	H0: l= 8 H1: l >8 Level of test: 5%
	X ³13	X ³14	X ³15	X ³16	X ³17
9	H0: l= 8 H1: l >8 Level of test: 1%
	X ³13	X ³14	X ³15	X ³16	X ³17
10	H0: l= 9 H1: l >9 Level of test: 1%
	X ³17	X ³18	X ³19	X ³20	X ³21

Summary In any hypothesis test we are testing the evidence to see if it is sufficient to reject the null hypothesis. A significant result implies: the null hypothesis is rejected the alternative hypothesis is accepted as true there is a chance that this conclusion is wrong and that the null hypothsis is in fact true. This is called a Type I error the probability of a Type I error is given by the level of the test A non-significant result implies: the null hypothesis is not rejected there is a chance that this conclusion is wrong and that the null hypothsis is in fact false. This is called a Type II error © MathsNet 2001