Question

ESAND ABUSES 1 Uses Hypothesis Testing Hypothesis testing is important in many different fields because it gives a scientific procedure for assessing the validity of a claim about a population. Some of the concepts in hypothesis testing are intuitive, but some are not. For instance, the American Journal of Clinical Nutrition suggests that eating dark chocolate can help prevent heart disease. A random sample of healthy volunteers were assigned to eat 3.5 ounces of dark chocolate each day for 15 days, After 15 days, the mean systolie blood pressure of the volunteers ソ -was 64 millimeters of mercury lower. A hypothesis test could shov if this drop eful inferences must be made concerning the results. In another part or the stady, it was found that white chocolate did not result in similar benefits So, the inference of health benefits cannot be extended to all types of chocolate, Yog'also would not infer that you should eat large quantities of chocolate because the benefits must be weighed against known risks, such as weight gain, acne andacid reflux. Abuses Not Using a Random Sample Theentirotheory of hypothesis testing is based on the fact that the sample is randomly selected. If the sample is not random, then you cannot use it to infer anything aboys population parameter Attempting to Prove the Null Hypothesis ILtherR-value for a hypothesis test is greater than the level of significance, you hasenot proven the null hypothesis is true-only that there is not enough evidence to reject it. For instance, with a P-value higher than the level of significanice a researcher could not prove that there is no benefit to eating dark ch there is not enough evidence to support the claim that there is a benefit. that Making Type I or Type If Errors Remember that a type I error is rejecting a null hypothesis that is true and a type II error is failing to reject a null hypothesis that is false. You can decrease the probability of a type I error by lowering the level of significance. Generally, if you decrease the probability of making a type I error, you increase the probability of making a type II error. You can decrease the chance of making both types of errors by increasing the sample size. EXERCISES In Exercises 1-4, assume that you work in a transportation department.You are asked to write a report about the claim that 73% of US adults who fly at least once a year favor full body scanners at airports, (Adapted froim Rasmussen Reports t. Not Using a Random Sample How could you choose a random sample to Do You Favor the Use of Full-Body Scanners at Airports in the U.S.? test this hypothesis? No 2. Attempting to Prove the Nul Hypothesis What is the null hypothesis i this situation? Describe how your report could be incorrect by trying to prove the null hypothesis Don't know 11 3. Making a Type / Error Describe how your report could make a type l error 4. Making a Type I1 Error Describe how your report could make a type II Yes 73% error .137 authortzed to use unlil 600/2018 Uts beyond the authotized user or v alid s a copyright violation simin khosravani (simnkhos [email protected])on 478/2013 from 141.114 211 represents

Answer 1

1. We can use one sample Z test for proportion to test the hypothesis.

2. H₀ : p=0.73. The report can be incorrect if in reality, not 73% of U.S. adults who fly at least once a year favor full-body scanner at airports.

3. We make a type 1 error if we conclude that not 73% of U.S. adults who fly at least once a year favor full-body scanner at airports, but in reality above was true.

4. We make a type 2 error if we conclude that 73% of U.S. adults who fly at least once a year favor full-body scanner at airports, but in reality above was true.