Stat individual Assignment.docx

On the other hand if our question is whether mr bonds

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On the other hand, if our question is whether Mr. Bonds is better than chance at determining whether a martini is shaken or stirred, we would use a one-tailed probability. What would the one-tailed probability is the probability of the right hand tail, it would be the probability and the null hypothesis would not be rejected. The null hypothesis for the two-tailed test is n=0.5. By contrast, the null hypothesis for the one tailed test is n< 0.5. Accordingly, we reject the two tailed hypothesis if the sample proportion deviates greatly from 0.5 in either direction. The one tailed hypothesis is rejected only if the sample proportion is much greater than 0.5. The alternative hypothesis in the two tailed test is n 0.5 . In the one tailed test it is n>0.5. You should always decide at the data. Statistical tests that compute one tailed probability before looking at the data. Statistical tests that compute one tailed probabilities are called one tailed tests: those that compute two tailed probabilities are called two tailed tests. Two tailed tests are much more common than one tailed tests in scientific research because an outcome signifying that something other than chance is operating is usually worth nothing. One tailed tests are appropriate when it is not important to distinguish between no effect and an effect in the unexpected direction. For example, consider an experiment designed to test the efficacy of a treatment for the common cold. The researcher would only be interested in whether the treatment was better than a placebo control. It would not be worth distinguishing between the case in which the treatment was worse than a placebo and the case in which it was the same because in both cases the drug would be worthless. Some have argued that a one tailed test is justified whenever the researcher predicts the direction of an effect. The problem with this argument is that if the effect comes out strongly in the non-
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predicted direction, the researcher is not justified in concluding that the effect is not zero. Since this is unrealistic, one tailed tests are usually viewed skeptically if justified on this basis alone. 4. TYPE I AND TYPE II ERRORS No hypothesis test is 100% certain. Because the test is based on probabilities, there is always a chance of making an incorrect conclusion. When you do a hypothesis test, two types of errors are possible type I and type II. The risks of these two errors are inversely related and determined by the level of significance and the power for the test. Therefore, you should determine which error has more severe consequences for your situation before you define their risks. TYPE I ERRORS When the null hypothesis is true and you reject it, you make a type I error. The probability of making a type I error is α , which is the level of significance you set for your hypothesis test. An α of 0.05 indicates that you are willing to accept a 5% chance that you are wrong when you reject the null hypothesis. To lower this risk, you must use a lower value for α . However, using a lower value for alpha means that you will be less likely to detect a true difference if one really exists.
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