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Type I errors and Type II errors

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9.13 In the U.S. legal system, a defendant is presume innocent until proven guilty. Consider a null hypothesis H o. that the defendant is innocent, and an alternative hypothesis H 1 that the defendant is guilty. A jury has two possible decisions: Convict the defendant(i.e., do not reject the null hypothesis). Explain the meaning of the risks of committing either a Type I or a Type II error in this example.

9.14 Suppose the defendant in problem 9.13 is presumed guilty until proven innocent as in some other judicial systems. How do the null and alternative hypotheses differ from those in 9.13? What are the meanings of the risks of commiting either a Type I or Type II here?

Answer:H o: defendant is guilty, H 1:defendant is innocent. A type I error would be not convicting a guilty person. A type II error would be convicting an innocent person.

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9.13 In the U.S. legal system, a defendant is presumed innocent until proven guilty. Consider a null hypothesis H0: that the defendant is innocent, and an alternative hypothesis H1 that the defendant is guilty. A jury has two possible decisions: Convict the defendant (i.e., do not reject the null hypothesis). Explain the meaning of the risks of committing either a Type I or a Type II error in this example.
It appears that there is an error in your problem as stated. The problem states that if you convict the defendant it means you do not reject the null hypothesis. In fact, it you convict the defendant you do reject the ...

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This is a 450 word solution explaining Type I and Type II errors in the context of the U.S. legal system.

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Inferences based on Single Samples

A consumer protection group is concerned that a ketchup manufacturer is filling its 20-ounce family-size containers with less than 20 ounces of ketchup. The group purchases 10 family-size bottles of this ketchup, weighs the contents of each, and finds that the mean weight is equal to 19.86 ounces, and the standard deviation is equal to 0.22 ounces.

-Do the data provide sufficient evidence for the consumer group to conclude that the mean fill per family-size bottle is less than 20 ounces? Test using alpha=0.05.

- If the test in part a were conducted on a periodic basis by the company's quality control department, is the consumer more concerned about making a Type I or Type II error? (consumer's risk)

-The ketchup company is also interested in the mean amount of ketchup per bottle. It does not wish to overfill them. For the test conducted in a, which type error is more serious from the company's point of view-Type I or Type II error? (producer's risk)

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