AS/A2 Stats 1 Stats 3

S2 Topic 4: Hypothesis tests
Testing the parameter p of a Binomial distribution
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. The results of a Binomial experiment will provided, giving the number of successes in a number of trials. You must decide if the hypothesis test should have a non-significant or significant result based on the results of the Binomial experiement. Choose values for n, x and p, and use this form to obtain Binomial probabilities to help you complete the test below.

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= 0.5 H1: p ¹0.5 Level of test: 5% Binomial experiment: 18 successes out of 50
	Non-significant	Significant
2	H0: p= 0.5 H1: p <0.5 Level of test: 5% Binomial experiment: 18 successes out of 50
	Non-significant	Significant
3	H0: p= 0.5 H1: p ¹0.5 Level of test: 5% Binomial experiment: 25 successes out of 40
	Non-significant	Significant
4	H0: p= 0.5 H1: p >0.5 Level of test: 2.5% Binomial experiment: 27 successes out of 40
	Non-significant	Significant
5	H0: p= 0.4 H1: p <0.4 Level of test: 5% Binomial experiment: 7 successes out of 30
	Non-significant	Significant
6	H0: p= 0.4 H1: p ¹0.4 Level of test: 5% Binomial experiment: 10 successes out of 30
	Non-significant	Significant
7	H0: p= 0.4 H1: p<0.4 Level of test: 10% Binomial experiment: 15 successes out of 50
	Non-significant	Significant
8	H0: p= 0.4 H1: p<0.4 Level of test: 5% Binomial experiment: 15 successes out of 50
	Non-significant	Significant
9	H0: p= 0.4 H1: p<0.4 Level of test: 1% Binomial experiment: 11 successes out of 50
	Non-significant	Significant
10	H0: p= 0.4 H1: p>0.4 Level of test: 5% Binomial experiment: 17 successes out of 30
	Non-significant	Significant

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