Lecture 20 Chapter 15 Tests Of Significance Continued Tests of Significance Hypothesis Testing Step 1 Write the null and alternate hypotheses Null Hypothesis Ho 0 Alt Hypothesis Ha 0 OR Ha 0 OR Ha 0 Step 2 Get data calculate Xbar and calculate a test statistic Z xbar mu zero sigma sqrt n Step 3 Determine the P Value PValue is the probability of this result occurring if the null hypothesis is true The PValue is the area in the tail of the Xbar distribution It is the right tail for a right side test and the left tail for a left side test It is both tails for a two side test Step 4 Decide whether the evidence is strong enough to reject the null hypothesis or not The rule always is If the P Value is equal to or less than the Examples For a two side test the P Value 2 Area in the tail Chapter 18 Inference about when is not known t procedures When is not known we have to use the standard deviation calculated from the sample s The sample standard deviation is a statistic it varies around the true but unknown value of Furthermore it is a biased estimator of so using s causes additional uncertainty in the development of confidence intervals and in the hypothesis test procedures The t procedures are very similar to the z procedures as shown a comparison of the formulas The value of t in the confidence interval formula comes from the T Table Table C in the appendix It depends on the confidence desired like the z did but it also depends on the degrees of freedom which is sample size 1 Examples Confidence Desired 90 z 1 645 df t 5 10 20 30 40 100 1000 2 015 1 812 1 725 1 697 1 684 1 660 1 646
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