Chapter 9 Hypothesis testing 1 Hypothesis Ho mu 20 Null H mu not equal 20 Alternative Put conditions to prove here ex less than mu 2 Graph 1 tail if greater than equal to less than equal to 2 tail both sides find Zcrit or Tcrit with tables 3 Decision rule 4 Calculate test stat If test stat z is 1 96 or 1 96 reject Ho Otherwise do not reject 5 Conclusion Reject Ho Do not reject Ho 6 Evidence supports the claim that Evidence does not support the claim Pop std deviation known Sample std deviation known Pop Proportion t x s n z p p p 1 p n z x n Point estimate p x n 2 population means Pop std deviation known Sample std deviation known Pop Proportion z x 1 x 2 1 1 2 2 n1 n2 Point estimator of P when p1 p2 p3 p n1p1 n2p2 n1 n2 t x 1 x 2 s1 1 s2 2 n1 n2 DF n1 n2 2 Point estimate p1 x n Standard Error p 1 p 1 n1 1 n2 Z values 05 01 1 tail 1 65 2 33 Point estimate p2 x n 2 tail 1 96 2 58 Test Stat p 2 z p 1 p 1 p 1 n1 1 n2 SUMMARY OF HYPOTHESIS TESTS ABOUTA POPULATION MEAN KNOWN CASE SUMMARY OF HYPOTHESIS TESTS ABOUTA POPULATION MEAN UNKNOWN CASE SUMMARY OF HYPOTHESIS TESTS ABOUTA POPULATION PROPORTION Null hypothesisThe hypothesis tentatively assumed true in the hypothesis testing procedure Alternative hypothesisThe hypothesis concluded to be true if the null hypothesis is rejected Type I error The error of rejecting H0 when it is true Type II error The error of accepting H0 when it is false Level of significance The probability of making a Type I error when the null hypothesis is true as an equality One tailed test A hypothesis test in which rejection of the null hypothesis occurs for values of the test statistic in one tail of its sampling distribution Test statistic A statistic whose value helps determine whether a null hypothesis should be rejected p value A probability that provides a measure of the evidence against the null hypothesis given by the sample Smaller p values indicate more evidence against H0 For a lower tail test the p value is the probability of obtaining a value for the test statistic as small as or smaller than that provided by the sample For an upper tail test the p value is the probability of obtaining a value for the test statistic as large as or larger than that provided by the sample For a two tailed test the p value is the probability of obtaining a value for the test statistic at least as unlikely as or more unlikely than that provided by the sample Critical value A value that is compared with the test statistic to determine whether H0 should be rejected Two tailed test A hypothesis test in which rejection of the null hypothesis occurs for values of the test statistic in either tail of its sampling distribution Power The probability of correctly rejecting H0 when it is false Power Curve A graph of the probability of rejecting H0 for all possible values of the population parameter not satisfying the null hypothesis The power curve provides the probability of correctly rejecting the null hypothesis Chapter 10 Inference About Means and Proportions with Two Populations ESTIMATING THE DIFFERENCE BETWEEN TWO POPULATION MEANS Independent simple random samples Samples selected from two populations in such a way that the elements making up one sample are chosen independently of the elements making up the other sample Matched samples Samples in which each data value of one sample is matched with a corresponding data value of the other sample Pooled estimator of p An estimator of a population proportion obtained by computing a weighted average of the point estimators obtained from two independent samples Chapter 11 Inferences About Population Variances SUMMARY OF HYPOTHESIS TESTS ABOUTA POPULATION VARIANCE SUMMARYOF HYPOTHESIS TESTS ABOUT TWO POPULATION VARIANCES Chapter 13 Experimental Design and Analysis of Variance F value chart DFTR across lower DFE down level of significance k number of groups treatments n sample size Ho mu1 mu2 m3 H At least one is different Treatments Sum of squares SS Given SSTR Error Given SSE Degrees of freedom DF Mean Square MSTR SSTR k 1 DFTR DFTR MSE SSE DFE n k DFE SST Sum of squares SS n 1 Degrees of freedom DF Mean Square Total K 3 N 47 Treatments Error Total 1200 600 1800 3 1 2 47 3 44 n 1 MSTR 1200 600 2 MSE 600 13 64 44 F value MSTR MSE F value 600 43 99 13 64 Factor Another word for the independent variable of interest Treatments Different levels of a factor Single factor experiment An experiment involving only one factor with k populations or treatments Response variable Another word for the dependent variable of interest Experimental units The objects of interest in the experiment ANOVA table A table used to summarize the analysis of variance computations and results It contains columns showing the source of variation the sum of squares the degrees of freedom the mean square and the F value s Partitioning The process of allocating the total sum of squares and degrees of freedom to the various components Multiple comparison procedures Statistical procedures that can be used to conduct statistical comparisons between pairs of population means Comparisonwise Type I error rate The probability of a Type I error associated with a single pairwise comparison Experimentwise Type I error rate The probability of making a Type I error on at least one of several pairwise comparisons Completely randomized design An experimental design in which the treatments are randomly assigned to the experimental units Blocking The process of using the same or similar experimental units for all treatments The purpose of blocking is to remove a source of variation from the error term and hence provide a more powerful test for a difference in population or treatment means Randomized block design An experimental design employing blocking Factorial experiment An experimental design that allows simultaneous conclusions about two or more factors Replications The number of times each experimental condition is repeated in an experiment Interaction The effect produced when the levels of one