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Quiz on Error Rates, Power, and Significance versus Importance I was considering doing a bungee jump. I asked the operator if it is safe. He said the following. There is no evidence that it is unsafe. I tested it 3 times with a 500 pound weight, and it worked perfectly each time. 1. 2. 3. The operator’s null hypothesis is A. It is safe B. It is unsafe The operator’s decision is to A. reject the null hypothesis B. not reject the null hypothesis In the bungee-jump example, a Type 1 error would be A. Deciding it is unsafe, when, in fact, it is unsafe. B. Deciding it is unsafe, when, in fact, it is safe. 4. C. Deciding it is safe, when, in fact, it is safe. D. Deciding it is safe, when, in fact, it is unsafe. I decide NOT to jump, because I am worried about A. a Type 1 error B. a Type 2 error C. a Type 3 error D. a Standard error E. A result that is statistically significant but not practically important 5. In the bungee-jump example, the reason that I am worried about an error is because A. the weight is too small (i.e., the effect is too small) B. the weight is too large (i.e., the effect is too large) C. the samples size is too small D. the sample size is too large E. None of the above children, there is highly Toothpaste Cost per 4 oz tube Sample Size Mean Cavities per Year per Child significant statistical Holtzman’s $19.99 6,000 0.48 evidence that the mean Competitor $1.99 6,000 0.61 Based on a study of 12,000 public school annual number of cavities is less for those using Holtzman’s new improved toothpaste (P < 0.0001). 6. A caring parent who is a wise consumer would see Holtzman’s toothpaste as not worth the cost because the study seems to have a 7. A. Type 1 error B. Type 2 error C. result that is statistically significant but not practically important If a result is statistically significant then A. the data confirm that the result is biologically important B. the effect of the treatment must have been very large C. we are sure that the true value of the population parameter is different from the hypothetical (null) value D. All of the above E. None of the above 8. If a result is not statistically significant then A. the data confirm that the result is not biologically important B. the effect of the treatment must have been negligible biologically C. we are not sure that the true value of the population parameter is actually different from the hypothetical (null) value. The difference observed between the estimate of the parameter and the hypothetical value of the parameter might just be due to natural, random variation 9. D. All of the above E. None of the above If the sample size is very large, and the P-value is very small, e.g., P < 0.001, and the underlying standard deviation is small, then which of the following is not true. A. We have the conditions under which statistical significance does imply practical, e.g., biological, e.g., clinical, importance. B. We have the conditions under which statistical significance may very well not imply practical, e.g., biological, e.g., clinical, importance. C. a very small, biologically unimportant effect could very easily be statistically significant. 10. In hypothesis testing, if the decision is to not reject the null hypothesis, then which of the following consequences is not possible? A. A Type 1 error B. A Type 2 error C. A correct decision D. A result that is statistically significant but not practically important E. Both choice A and choice D are not possible.