1. Tests of Significance -how to put them in writing

2. First we list the steps: Step 1: Null and alternate hypotheses Step 2: Conditions Step 3: Formula and calculations Step 4: Graph of Z Step 5: P-value Step 6: Compare p and α, then reject/fail to reject Step 7: Conclusion in context

3. 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 of the population of all mice in our university laboratories is 37g, the same as the known value for ICR whites. Carry out a test of significance at α = 0.05. Now we will write an answer to this question, following the 7 steps.

4. We give more detail as we work: Step 1: Write the null and alternate hypotheses in symbols. H 0 : μ = 37g H a : μ ≠ 37g

5. Step 3:Step 2: 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. Conditions: meet every condition required for the test. We are given an SRS, and a normal population. n.b., 37.2 was found by calculating the mean of the data.

6. Step 4: Graph the test statistic.

7. Step 5: Calculate the probability of the shaded region of the graph. Write a statement using Z. P-value = Step 6: Compare to alpha, then reject or fail to reject H 0. Fail to reject H 0, 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!

8. 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 our university laboratory mice is different from 37 grams. n.b., We either reject or fail to reject, but we never attempt to prove that the null hypothesis is true!

9. Step 1: Null and alternate hypotheses Conditions Step 2: Formula and calculations Step 3: Graph Step 4: P-value Step 5: Reject/fail to reject and explain P-value. Step 6: Conclusion Step 7: We will have many variations, but the basic process will be the same now for all tests of significance. Remember the 7 steps:

10. THE END