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- Do well-rounded people get fewer colds? A study on the Chronicle of Higher Education was conducted by scientist at Carnegie Mellon University, the University of Pittsburgh and the University of Virginia. They found that people who have only a few social outlets get more colds than those who are involved in a variety of social activities. Suppose that of the 276 healthy men and women tested, n1=96 had only a few social outlets and n2=105 were busy with six or more activities. When these people were exposed to a cold virus, the following results were observed: Construct a 99% confidence interval for the difference in the two population proportions.The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population. find the p valueA smartphone manufacturer is so certain of its quality control that it offers a complete replacement warranty if the smartphone fails within 3 years. Based upon compiled data, the company notes that there is a 2 percent chance that its smartphone will fail during the first year, a 10 percent chance that a smartphone that survives the first year fails during the second year, and a 20 percent chance that a smartphone that survives the first two years fails during the third year. The warranty does not cover replacement smartphones after the third year. (a) Formulate the evolution of the status of the smartphone as a Markov Chain whose states include two abosrbing states that involve needing to honor the warranty or having the smartphone survive the warranty period. Construct the transition probability matrix and draw the transition probability diagram. (b) Determine the probability that: (a) the manufacturer will have to honor the warranty and (b) the manufacturer will not…
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