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Tests of Significance How to put them in writing. As with confidence intervals, it is helpful to have a format to follow to see that all steps are included. Being able to write good answers to these questions is one of the major goals of this course. Once you learn this process, you will have to make only small changes when we learn a new test, the framework will remain the same. The assumptions for confidence intervals are the same as those for tests of significance. Are you ready? First we list the steps: Step 1: Null and alternate hypotheses Step 2: Assumptions Step 3: Formula and calculations Step 4: Graph Step 5: P-value Step 6: Reject/fail to reject and explain P-value. Step 7: Conclusion We consider the problem of finding whether the average weight of an ICR white laboratory mouse is the value we believe it to be. We read that the mean and standard deviation are 37g and 3.2g, respectively. We collect a sample of 10 mice and record these weights (in grams): {35, 42, 41, 34, 38, 36, 37, 39, 34, 36}. Like many other measurements, the weights of the mice follow a normal distribution. The question we are asked is whether the mean weight is 37g. Now we will write an answer to this question, following the 7 steps. We give more detail as we work: Step 1: Write the null and alternate hypotheses in symbols, then in sentences, so that variables are explained. Write an extra sentence or make a legend if needed. H0: =37g Ha: 37g H0: The mean weight for an adult ICR mouse is 37g. Ha: The mean weight for an adult ICR mouse is not 37g. For our problem, Step 2: Assumptions: meet every assumption for the test. We are given an SRS, a normal population, and is known. Step 3: Formula and calculations: Write the formula for the calculation of the test statistic (Z) and show the values substituted into the equation. Solve for Z. Z x 0 n 37.2 37 .2 .1976 3.2 1.01192 10 n.b., 37.2 was found by calculating the mean of the data. Step 4: Graph the test statistic. Step 5: Calculate the probability of the shaded region of the graph. Write a statement using Z. P-value = P(Z .1976 or Z .1976) 2(.42166) .8433 Step 6: Reject or fail to reject H0, followed by an explanation of the meaning of the p-value. Fail to reject H0, a test statistic this extreme will occur by chance alone 84% of the time. n. b., if you have trouble deciding whether to reject, ask yourself if the result is surprising? Are you surprised that we could get a mean of 37.2 when the true mean is 37? I’m not! Step 7: Write a conclusion in terms of the original problem. I usually start with “We have evidence of…” or “We lack evidence of…,” and modify appropriately. We lack evidence that the mean weight of ICR mice is not 37 grams. n.b., We either reject or fail to reject, but we never attempt to prove that the null hypothesis is true! Think about this for a minute. We will have many variations, but the basic process will be the same now for all tests of significance. Remember the 7 steps: Step 1: Null and alternate hypotheses Step 2: Assumptions Step 3: Formula and calculations Step 4: Graph Step 5: P-value Step 6: Reject/fail to reject and explain P-value. Step 7: Conclusion THE END