RVUC- Statistics Short Note (2).doc

14 15 p a g e test statistics a test statistic is a

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15 | P a g e Test Statistics A test statistic is a quantity calculated from the sample information. It is a value, determined from sample information, used to determine whether to reject the null hypothesis. It is used to determine whether we reject the null hypothesis or not. Select the test statistic that will be used to decide whether or not to reject the null hypothesis. For example; Z – distribution, t - distribution, F- distribution,x 2 distribution 15
16 | P a g e Testing for a Population Mean with a Known Population Standard Deviation Formula for z is given below 16

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17 | P a g e Degree of Freedom: it is the number of items in a sample that are free to vary. Parameter : a measure used to describe characteristics of a population. Statistic/ estimator : a measure used to describe characteristics of a sample. P -Value ( probability value) Probability of observing a test statistic. - If the p -Value is less than the significance level , we reject the null hypothesis. If the probability value is less than or equal to the significance level, then the null hypothesis is rejected. - If the probability value is greater than the significance level, the null hypothesis is not rejected. Procedures of hypothesis testing The Steps in the test of a hypothesis should be memorized and followed correctly. Major Steps in hypothesis testing 1. Stating the null and alterative hypothesis. Accept the alternative hypothesis if you reject the null hypothesis. Eg. : Suppose we randomly sampled 100 new graduates of Addis Ababa university and determined their salary of their first job. The sample mean salary was birr 950 with a standard deviation of birr 200. Is the mean salary of a newly graduated student equal to Br 1000? null & alternative hypothesis are Ho: = Birr 1000 Ha: Birr 1000 Ho: o Population mean= 17
18 | P a g e Estimated mean= o mean = 950 - hypothesizes parametric value = 1000 Sd= 200 n= 100 2. Determining the significant level Choose significance levels equal to 0.01,0.05, or 0.10. - Assume level of significance of 0.05 - Test statistic to be used is Z - score test - Critical value corresponding to this level of significance is 1.96 you can read from normal distribution table. i.e. Z(0.05)=1.96 Compare Z cal & Table value Reject Ho If /Z cal / >1.96. (Z cal) - value of z score calculated from the sample data. 3. Calculate a test Statistic In order to determine whether Ho should be rejected or not, we need to compete a test statistic SEm - Standard error of mean The test statistic would be = 2.50 4. Deciding about Ho 18 n SE H SE x x x and true is assuming mean population where z 0 0 0 stat

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19 | P a g e This is stating whether we can reject or cannot reject Ho. if our test statistic is ≥ 1.96 , then we reject the null hypothesis at alpha ( )= 0.05 5. Interpreting the result Describe the results and state correct statistical conclusions If Ho is rejected, accepted Ha is explained. i.e . the population mean is different from the estimated mean ( o) at 5% level of significance.
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