Class 5 - hyp_test_demo

Class 5 - hyp_test_demo - Introduction The simulations on...

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Introduction Page 1 The simulations on the following sheets generate a sample of 9 observations from a standard normal distribution with standard deviation 1 and a mean value that can be changed on the sheet. The values for the 9 sample observations are indicated by the pink dots at the top of each chart. The null of μ =0 is tested with a specified α . The distribution of the Test Statistic, TS, when the null is true is in dark blue . When the phenomenon mean has the value specified, the actual distribution of the Test Statistic appears in yellow . The location of sample mean (the average of the 9 sample observations) is at the light blue diamond . The sample data are used to calculate the appropriate confidence interval assuming that the phenomenon standard deviation is unknown. The green line indicates the limit or limits for the appropriate confidence interval. A light green line indicates the critical value(s) on the null distribution of the TS. The location of the observed value of the Test Statistic, TS, is indicated by the medium blue line . The p-value is the area in red . A new set of observations is created each time the F9 function key is pushed.

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Confidence Interval Method for testing Critical Value Method for testing p-value Method for testing If the confidence interval contains the null hypothesized value, then H 0 is concluded as being true. If the confidence interval does not contain the hypothesized value then H 0 is rejected as being true. If the value of the test statistic computed from the sample data is beyond the critical value or values (is in the rejection region), then H 0 is rejected as being true. If the test statistic value is not in the rejection region, then H 0 is not rejected and is considered to be true . The p-value is the probability of obtaining by chance a sample result at least as extreme as the one observed in the actual sample assuming the null hypothesis is true. If the p-value < α , then H 0 is rejected as being true. However, if the p-value > α , H 0 is not rejected and H 0 is concluded as being true.
Test > Page 3 1 2 3 4 5 6 7 8 9 -2 -0.71 -0.07 0.03 1.23 1.26 1.26 1.49 2.22 < Ordered Sample Observations 99% 1-Sided Confidence Interval for the Phenomenon Mean 0.3 = Phenom Sample Mean - Table Value * Standard Error p-value = 0.13 0.01 0.52 - 2.9 * 1.31 1.2 = TS 0.52 - 1.26 = -0.74 = Confidence Limit 2.9 Accept the Null 1.26 -2 0.03 -0.07 1.49 2.22 1.23 -0.71 1.26 Height on Graph = 0.5 0.6 0.7 Rounded Value = 0.52 -0.74 5 X ution-TS on of TS Frequen Sample le Mean Confide p-valueCritical TS Lower Upper -2.5 0.03 0.02 0 -1 -1 -1 -1 -1 -1 Limit Limit -2.49 0.03 0.02 0 -1 -1 -1 -1 -1 -1 -0.74 5 -2.48 0.03 0.02 0 -1 -1 -1 -1 -1 -1 -2.47 0.03 0.02 0 -1 -1 -1 -1 -1 -1 95% 95% -2.46 0.03 0.02 0 -1 -1 -1 -1 -1 -1 Lower Upper -2.45 0.03 0.02 0 -1 -1 -1 -1 -1 -1 Limit Limit -2.44 0.03 0.02 0 -1 -1 -1 -1 -1 -1 -0.48 1.53 -2.43 0.03 0.02 0 -1 -1 -1 -1 -1 -1 -0.48 1.53 -2.42 0.03 0.02 0 -1 -1 -1 -1 -1 -1 -2.41 0.03 0.02 0 -1 -1 -1 -1 -1 -1 99% 99% -2.4 0.03 0.02 0 -1 -1 -1 -1 -1 -1 Lower Upper -2.39 0.03 0.02 0 -1 -1 -1 -1 -1 -1 Limit Limit -2.38 0.03 0.02 0 -1 -1 -1 -1 -1 -1 -0.94 1.99 -2.37 0.04 0.02 0 -1 -1 -1 -1 -1 -1 -0.94 1.99 -2.36 0.04 0.02 0 -1 -1 -1 -1 -1 -1 -2.35 0.04 0.02 0 -1 -1 -1 -1 -1 -1 -2.34 0.04 0.02 0 -1 -1 -1 -1 -1 -1 -2.33 0.04 0.02 0 -1 -1 -1 -1 -1 -1 -2.32 0.04 0.02 0 -1 -1 -1 -1 -1 -1 -2.31 0.04 0.02 0 -1 -1 -1 -1 -1 -1 -2.3 0.04 0.02 0 -1 -1 -1 -1 -1 -1 -2.29 0.04 0.02 0 -1 -1 -1 -1 -1 -1 -2.28 0.04 0.03 0 -1 -1 -1 -1 -1 -1 -2.27 0.04 0.03 0 -1 -1 -1 -1 -1 -1 -2.26 0.04 0.03 0 -1 -1 -1 -1 -1 -1 -2.25 0.04 0.03 0 -1 -1 -1 -1 -1 -1 -2.24 0.04 0.03 0 -1 -1 -1 -1 -1 -1 -2.23 0.04 0.03 0 -1 -1 -1 -1 -1 -1 -2.22

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