2. A plaintiff filed a complaint in a federal district court. The complaint asserted a state law claim based on a breach of contract against an individual defendant from whom \$50,000 in damages was sought. The individual defendant was the majority shareholder of the corporate defendant. None of the parties was a citizen of the same state. Does the federal court have jurisdiction over this action? a. Yes, because the defendant and plaintiff are from different states. b. No, because the plaintiff's breach of contract claim would not win anyway. c. No, because the amount-in-controversy requirement is not met. d. Yes, because the claim raises a federal question. 3. A man liked to exercise late at night in the gym located in his condominium. As he entered the gym one night, he heard a woman screaming for help. The man rushed over to the woman, who was trapped under an 80-pound barbell. The man lifted the barbell off the woman, but injured his back in his rush to help the woman. The woman thanked the man, and told him that she knew she should not have been lifting the barbell by herself because it was too heavy for someone her size. The man has brought a negligence action against the woman to recover for his back injury. Will he prevail? a. Yes, because the man's actions were reasonable given the woman's need for help. b. Yes, because the woman failed to exercise reasonable care. c. No, because the man had no affirmative duty to help the woman. d. No, because the man's own negligence was the cause of his injury. 4. An inexperienced unicycle rider takes a test run on the city streets. He tries to stop for a red light but his balance is so unsteady that he continues through the ready light and into the intersection. A vehicle is approaching from an intersecting street and has a full green light. The driver sees the unicycle ahead in the intersection but figures that the unicycle will be through the intersection by the time he gets there. He keeps driving and runs over the unicycle rider. The rider files a claim for negligence against the driver. What happens? a. The rider will win because the driver was more negligent than the rider. b. The driver will win because the rider was assuming the risk by entering the intersection against the light. c. The rider will win, but his award will be reduced because he was contributorily negligent. d. The driver will win because the rider went through the red light.
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In this case, it is stated that none of the parties is a citizen of the same state. This means that there is diversity of citizenship. Show moreā¦
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Compare statistical testing with legal methods used in a U.S. court setting. Then discuss the following topics in class or consider the topics on your own. Please write a brief but complete essay in which you answer the following questions. (a) In a court setting, the person charged with a crime is initially considered to be innocent. The claim of innocence is maintained until the jury returns with a decision. Explain how the claim of innocence could be taken to be the null hypothesis. Do we assume that the null hypothesis is true throughout the testing procedure? What would the alternate hypothesis be in a court setting? (b) The court claims that a person is innocent if the evidence against the person is not adequate to find him or her guilty. This does not mean, however, that the court has necessarily proved the person to be innocent. It simply means that the evidence against the person was not adequate for the jury to find him or her guilty. How does this situation compare with a statistical test for which the conclusion is "do not reject" (i.e., accept) the null hypothesis? What would be a type II error in this context? (c) If the evidence against a person is adequate for the jury to find him or her guilty, then the court claims that the person is guilty. Remember, this does not mean that the court has necessarily proved the person to be guilty. It simply means that the evidence against the person was strong enough to find him or her guilty. How does this situation compare with a statistical test for which the conclusion is to "reject" the null hypothesis? What would be a type I error in this context? (d) In a court setting, the final decision as to whether the person charged is innocent or guilty is made at the end of the trial, usually by a jury of impartial people. In hypothesis testing, the final decision to reject or not reject the null hypothesis is made at the end of the test by using information or data from an (impartial) random sample. Discuss these similarities between statistical hypothesis testing and a court setting. (e) We hope that you are able to use this discussion to increase your understanding of statistical testing by comparing it with something that is a well-known part of our American way of life. However, all analogies have weak points, and it is important not to take the analogy between statistical hypothesis testing and legal court methods too far. For instance, the judge does not set a level of significance and tell the jury to determine a verdict that is wrong only $5 \%$ or $1 \%$ of the time. Discuss some of these weak points in the analogy between the court setting and hypothesis testing.
Hypothesis Testing
Testing the Mean $\mu$
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