W5 Lecture Part II-A Summary

# W5 Lecture Part II-A Summary - Week Five Lecture Part II A...

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Week Five Lecture Part II – A Summary Here is a summary of the statistical applications and their characteristics we have learned and used in RES/342. z Test Statistic The z test statistic is applied when we are testing the hypothesis of the difference between two population means, and the standard deviation is known. The z test statistic is based on a z score (measures the number of standard deviations that a data value is from the mean). The z test statistic assumes a normal distribution, thus measures of central tendency apply. In using the z test statistic we need a minimum of 30 observations from which the sample is selected. We refer this then to a large sample. Any number of observations less than 30 is referred to as a small sample. Finally, we apply the test statistic value to determine if our sample value is “statistically significant.” We must decide how statistically significant we want any sample to be. If we are ok with accepting that the sample is in 95% of the observations, then we would chose a 0.05 level of significance, which means, we accept the willingness to be wrong in the long run 5 % of the time. The level of significance then determines the rejection region where the null hypothesis is not supported. We use the standard normal table to determine those boundaries. At a level of significance of 0.05, that means the rejection region is + or – 1.96. Our decision to accept our null hypothesis is based on whether or not the test statistic value (of our sample) is inside the + and -1.96. Tailed- tests are involved with this test statistic. Here is a summary of the three possibilities: Two-tailed tests. Used when the test statistic could be a negative value or a positive value. The scenario situation is worded so that we are interested in only determining if one population is different than another. The word different means that the value of one could be higher or lower than the other. The hypothesis set up, therefore is: H O : μ 1 = μ 2 H A : μ 1 μ 2 Lower-tail test . Used when the test statistic is testing the mean of one population sample to determine if it is less than the other parameter. The hypothesis set up, therefore is: H O : μ 1 μ 2 H A : μ 1 < μ 2

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Upper-tail test . Used when the test statistic is testing the mean of one population sample to determine if it is greater than the other parameter. The hypothesis set up, therefore is: H O : μ 1 μ 2 H A : μ 1 > μ 2 Although we are attempting to prove support for the null hypothesis, we can see
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