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She can say, based on the sample statistics, there is only a 1.47% chance that a score, as extreme as her score, would be observed when the assumed mean is 145. So, Melinda can state that she has outperformed her goal with “statistical significance”. The p-value is 0.015, below the significance level (α) of 0.05, so it falls into the rejection region and can thereby be qualified as “significant” compared to the mean of the 145: This will occur if her result falls into the rejection area which will be calculated through the test statistics: Melinda hopes that the statistician will prove that she’s done “significantly” better than the 145 points and therefore that the null hypothesis will be rejected.
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The score is an average calculation of the total of 15 sales of the product, so the sample size (n) is 15 and the sample standard deviation (s) is in this case calculated to be 8.8. The statistician sets up a hypothesis test through a one-sided test whereas the result that she is testing for is greater than assumed mean of 145: She asks her statistician colleague to test her results. She scores 150.51 and wishes to prove that her score is ‘significantly’ greater than the set goal of the 145. Say that Melinda is a portfolio manager in an investment firm and is supposed to score the average of 145.00 points on some point scale for ROI for a given product. For two-tailed tests the statistician will apply the alpha-level divided by two (one half of the alpha-level on each side of the mean estimate in the density curve). The formula is the same as for when using the z-statistics, but the t-table returns greater values than the z-tables, as the it works with a greater degree uncertainty.įor one-tailed tests the statistician will apply the entire alpha-level when looking up in the respective z or t-table. The formulas for a one-tailed test for one mean:Īs shown, for small samples with unknown sigma, the Student’s t-distribution is applied. To the right tail for the positive values and to the left tail for the negative values:įirst step in any hypothesis testing, whether it’s a one-tailed test or a two-tailed test, the statistician will set the hypotheses and significant level (α). ‘Different from’ means that it can be both ‘greater than’ or ‘less than’, and the analyst therefore will look to both sides of the mean. When an analyst wishes to test whether a sample mean is different from the assumed mean, it is a two-tailed test. If the new finding falls into the rejection area, the analyst will reject the null hypothesis (H 0 ) as there is sufficient evidence to support the alternative hypothesis. The same method is applied for less than examples where we will look to the left for values less than the mean estimate:Īs with hypothesis test in general the rejection area is in the smaller area under the tails. This “ greater than” example is also called a right-tailed test as it looks to the right for values greater than the mean. The analyst wishes to test whether this is finding can be concluded as “significantly” greater and thereby if the null hypothesis, that claims a smaller value, can be rejected. Right-tailed test (greater than), left-tailed test (less than)Īn example of a one-tailed test can be that an analyst run a sample and find a sample mean that seems “relatively much” larger than the assumed mean. Alpha (α) is not divided by two when looking up the z-score or t-score, as it is only looked for in one side.If we are analyzing for the question that the findings are different from the assumed mean, we are talking two-tailed tests.One-tailed tests are applied to answer for the questions: Is our finding significantly greater than our assumed value? Or: Is our finding significantly less than our assumed value?.