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# Chapter9NotesQBA.pdf

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Date Created: 09/03/14

QBA NOTES CHAPTER 9 October 20 2013 Hypothesis Testing The Steps Followed to do Hypothesis Testing 1 When the population and standard deviation sigma Greek letter is known a Determine whether the sample evidence is inconsistent with what is hypothesized under the null hypothesis to avoid biases b As a researcher interested in the opposite of the null hypothesis c First Principle i First assume that H0 is true ii then determine if the sample evidence contradicts this assumption to avoid biases iii If the sample evidence contradicts the assumption that the null hypothesis is true we can infer that the alternative hypothesis or our interest has been supported iv If the sample evidence does not contradict the assumption that the null hypothesis is true we have not found support for the alternative hypothesis d P Vaue Approach i The value of the test statistic for the hypothesis test of the population mean M when the population standard deviation 0 is known and computed as 1 where M0 is the hypothesized mean value ii Z test Sample mean population mean population square deviation square root of sample size iii P Vaue the likelihood of obtaining a sample mean that is at least as extreme as the one derived from the given sample under the assumption that the null hypothesis is true e Calculation of P Vaue Approach i Depends on the specification of the alternative hypothesis ii Left Tailed Test PZ lt z 1 probability that any value our sample Z being smaller than or equal to a specific 2 the cutoff point iii Right Tailed Test PZ g z 1 probability that any value our sample Z being greater than or equal to a specific 2 the cutoff point iv TwoTailed Test when 2 lt 0 then 2PZ lt z or z gt 0 then 2PZ gt z 1 If the two tailed test does not state a direction p vaue is computed in a certain way 2 To reject the Ho the p Vaue has to be smaller than alpha a 2 Four Steps of P Vaue Approach a Step 1 Specify the null and the alternative hypotheses b Step 2 Specify the test statistic and compute its value one sample z test 1Page QBA NOTES CHAPTER 9 October 20 2013 3 4 c Step 3 Calculate the Pvalue d Step 4 State the conclusion and review the results Example of the P Vaue approach a N25x 71o9 b Sample size n 25 25 data points c Sample mean English letter X 71 d Population standard deviation greek letter o 9 e Step 1 State the Hypothesis i Null Hypothesis m 5 67 population mean represented by this sample is less than or equal to 67 ii Alternative Hypothesis m gt 67 mean of this population is greater than 67 iii significantly different statistically different f Step 2 Compute the value of the test statistic i Use the z test formula to determine 2 score ii Unstandardized normal distribution 1 will show that the sample score of 71 turns into a z score of 222 2 will show that Mo of 67 has a z score of0 mean is always 0 iii the critical value the z score that is the cutoff need to find the z score for the cutoff point g Step 3 Now Compute the PValue i Note that since Ha m gt 67 this is a right tailed test ii Therefore PX 2 71 PZ 3 222 Pvalue 0132 iii Before implementing the test you need to choose an alpha level REJECT Ho when the p vaue lt a h Step 4 Determine Value of Pvalue compared to alpha level i Pvalue 0132 lt a 005 REJECT the Ho and conclude that the sample data support the alternative claim that m gt 67 Example 2 a Step 1 Ho m 60640 Ha 60640 b Step 2 Compute z score z 139 c Step 3 Based on Ha this is a two tail test the alpha has to be divided by two when computing a two tail test determine 2 score for 025 z 1196 d Step 4 In Class tRat Notes PS The alternative hypothesis Ha is used with the greater than or less than signs The null hypothesis H0 is used with the equal or inequality sign For one tail test look at the alternative hypothesis for a direction on the picture CVA Critical Value Approach a Zcrit 164 alpha level from the 2 table b Z obtained 150 comes from the formula c When the zcritical is greater than the z obtained you fail to reject the Ho d When the p vaue is greater than alpha you fail to reject the null hypothesis Significant systematic response not a 2Page

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