AS/A2 Stats 1 Stats 2

S3 Topic 3: Estimation, confidence intervals and tests
Testing a sample value
You will be given a number of hypothesis tests. In each case a null and alternative hypothesis will be suggested, where m refers to the population mean, and a level of test. You will then be given the standard deviation of the population (assumed to be normally distributed), s, and a single sample value from that population. You must decide if the hypothesis test should have a non-significant or significant result based on that sample value. A table of critical values is provided but you will have to work out the test statistic yourself, using:

Critical values	One-tailed	One-tailed	Two-tailed
10%	1.282	-1.282	±1.645
5%	1.645	-1.645	±1.96
2.5%	1.96	-1.96	±2.241
1%	2.326	-2.326	±2.575

Correct:

Attempts:

% Correct:

1	H0: m= 200 H1: m ¹200 Level of test: 5% s=10, sample value= 212
	Non-significant	Significant
2	H0: m= 100 H1: m ¹100 Level of test: 5% s=15, sample value= 130
	Non-significant	Significant
3	H0: m= 100 H1: m >100 Level of test: 5% s=15, sample value= 125
	Non-significant	Significant
4	H0: m= 100 H1: m >100 Level of test: 2.5% s=15, sample value= 125
	Non-significant	Significant
5	H0: m= 100 H1: m <100 Level of test: 2.5% s=15, sample value= 78
	Non-significant	Significant
6	H0: m= 50 H1: m <50 Level of test: 5% s=10, sample value= 41
	Non-significant	Significant
7	H0: m= 50 H1: m <50 Level of test: 1% s=10, sample value= 25
	Non-significant	Significant
8	H0: m= 50 H1: m ¹50 Level of test: 1% s=10, sample value= 25
	Non-significant	Significant
9	H0: m= 50 H1: m ¹50 Level of test: 1% s=10, sample value= 23
	Non-significant	Significant
10	H0: m= 50 H1: m ¹50 Level of test: 1% s=2, sample value= 44
	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