AS/A2 Stats 1 Stats 3

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

n: 5 10 12 15 20 25 30 40 50 x: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 p: 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 P(X £ x) = P(X ³ x) =

Correct:

Attempts:

% Correct:

1	H0: p= 0.2 H1: p >0.2; n = 10; Level of test: 5%
	X ³5	X ³6	X ³7	X ³8	X ³9
2	H0: p= 0.15 H1: p <0.15; n = 20; Level of test: 5%
	X =0	X £1	X £2	X £3	X £4
3	H0: p= 0.35 H1: p >0.35; n = 10; Level of test: 1%
	X ³5	X ³6	X ³7	X ³8	X ³9
4	H0: p= 0.1 H1: p >0.1; n = 20; Level of test: 1%
	X ³6	X ³7	X ³8	X ³9	X ³10
5	H0: p= 0.1 H1: p >0.1; n = 20; Level of test: 10%
	X ³3	X ³4	X ³5	X ³6	X ³7
6	H0: p= 0.4 H1: p <0.4; n = 30; Level of test: 5%
	X £6	X £7	X £8	X £9	X £10
7	H0: p= 0.4 H1: p <0.4; n = 40; Level of test: 5%
	X £6	X £7	X £8	X £9	X £10
8	H0: p= 0.4 H1: p >0.4; n = 40; Level of test: 5%
	X ³21	X ³22	X ³23	X ³24	X ³25
9	H0: p= 0.4 H1: p >0.4; n = 40; Level of test: 1%
	X ³21	X ³22	X ³23	X ³24	X ³25
10	H0: p= 0.05 H1: p >0.05; n = 30; Level of test: 1%
	X ³4	X ³5	X ³6	X ³7	X ³8

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