Conduct a hypothesis test for the following scenarios. You may compute the p-value either by simulation or test-statistic 1) 2) 3) at least one problem must be done by test-statistic conversion a...
Conduct a hypothesis test for the following scenarios. You may compute the p-value either by simulation or test-statistic 1) 2) 3) at least one problem must be done by test-statistic conversion at least one problem must be done by simulation simulation should involve at least 10,000 trials. The grading scheme is as follows: Identify and describe the parameter of interest. State the null and alternative hypotheses, using correct notation. Be specific with your parameters. 2pts State the value of the relevant sample statistic, and identify it with its correct symbol. Compute a p-value 1 pt [1 pt] 3 pts If done by simulation, include a screen shot. If done by test-statistic conversion (the z-score), show the converted test statistic, and verify that the normality conditions are met. State, in no uncertain terms, your conclusion in the context of the original problem. Use alpha 0.05. 3 pts It is not enough to say "reject the null or fail to reject the null. You should not say "such and such is likely" or "such and such probably isn't true. Give a clear decision. Consider the population to which you feel comfortable extrapolating your results. 1. A team of eye surgeons has developed a new technique for risky eye operations to restored the sight of people blind from a certain disease. Under the old method, it is known that only 30% of the patients who undergo this operation recover their eyesight. Under the new method, 88 of 225 operations have successfully recovered people's eyesights Can you justify the claim that the new method is better than the old one? (i.e. -carry out a hypothesis test) People spend a lot of money on bottled water. But do they really prefer bottled water to ordinary tap water? Researchers at Longwood University (Lunsford and Dowling Fink, 2010) investigated this question by presenting people who came to a booth at a local festival with four cups of water. Three cups contained different brands of bottled water, and one cup was filled with tap water. Each subject was asked which of the four cups of water they most preferred. Researchers kept track of how many people chose tap water in order to see whether tap water was chosen significantly less often than would be expected by random chance. Researchers found that 3 of 27 people chose the tap water. Prose rhythm is defined the occurrence of five-syllable sequences in long literature pieces; authors typically use the same prose rhythm in their writings. After analyzing Plato's Republic, D. Wishart and S. Leach reported that 26.1% of the five-syllable word sequences exhibited a "two-short, three-long pattern. Suppose an ancient writing dating back to Plato's time is found and the five-syllable word sequences are analyzed. If 61 of 317 randomly-selected sequences show the "two-short, three-long" pattern, does this give convincing evidence that Plato is NOT the author? (Plato will not be the author if the "two-short, three-long" pattern proportion is different from that found in Platos' Republic.) 2. 3.
Conduct a hypothesis test for the following scenarios. You may compute the p-value either by simulation or test-statistic 1) 2) 3) at least one problem must be done by test-statistic conversion at least one problem must be done by simulation simulation should involve at least 10,000 trials. The grading scheme is as follows: Identify and describe the parameter of interest. State the null and alternative hypotheses, using correct notation. Be specific with your parameters. 2pts State the value of the relevant sample statistic, and identify it with its correct symbol. Compute a p-value 1 pt [1 pt] 3 pts If done by simulation, include a screen shot. If done by test-statistic conversion (the z-score), show the converted test statistic, and verify that the normality conditions are met. State, in no uncertain terms, your conclusion in the context of the original problem. Use alpha 0.05. 3 pts It is not enough to say "reject the null or fail to reject the null. You should not say "such and such is likely" or "such and such probably isn't true. Give a clear decision. Consider the population to which you feel comfortable extrapolating your results. 1. A team of eye surgeons has developed a new technique for risky eye operations to restored the sight of people blind from a certain disease. Under the old method, it is known that only 30% of the patients who undergo this operation recover their eyesight. Under the new method, 88 of 225 operations have successfully recovered people's eyesights Can you justify the claim that the new method is better than the old one? (i.e. -carry out a hypothesis test) People spend a lot of money on bottled water. But do they really prefer bottled water to ordinary tap water? Researchers at Longwood University (Lunsford and Dowling Fink, 2010) investigated this question by presenting people who came to a booth at a local festival with four cups of water. Three cups contained different brands of bottled water, and one cup was filled with tap water. Each subject was asked which of the four cups of water they most preferred. Researchers kept track of how many people chose tap water in order to see whether tap water was chosen significantly less often than would be expected by random chance. Researchers found that 3 of 27 people chose the tap water. Prose rhythm is defined the occurrence of five-syllable sequences in long literature pieces; authors typically use the same prose rhythm in their writings. After analyzing Plato's Republic, D. Wishart and S. Leach reported that 26.1% of the five-syllable word sequences exhibited a "two-short, three-long pattern. Suppose an ancient writing dating back to Plato's time is found and the five-syllable word sequences are analyzed. If 61 of 317 randomly-selected sequences show the "two-short, three-long" pattern, does this give convincing evidence that Plato is NOT the author? (Plato will not be the author if the "two-short, three-long" pattern proportion is different from that found in Platos' Republic.) 2. 3.
