Question
5.A recent study by the Center for Disease Control claims that a new super-contagious virus will impact a population in which it is found if left unchecked. A recent occurrence this virus happened on a very isolated island nation with over 500,000 inhabitants. In randomly testing 2500 residents of this island after the virus outbreak, a research team found 1560 tested positive for having been infected by the virus. a What was the sample's proportion measure of those having been infected by the virus? That is, determine the sample measure designated as p-hat. a Is the above information sufficient for you to be certain that the percentage of all in a population who contracted the virus is the same as the value computed inpart a above? Why or why not? b. The CDC claims that this virus tends to impact over 60% of any population in which it is found and left unchecked. The researchers wish to use the island nation results to test the CDC claim. In establishing a statistical hypothesis testing of this situation, give the required null and alternative hypotheses for a test of the claim made by the CDC.H: C. Based on your answer in part b, should you use a right-tailed, a left-tailed, or a two-tailed test? Briefly explain how one determines which of the three possibilities is to be used. d.Describe the possible Type I error for this situation--make sure to state the error in terms of the percentage of a population infected by the virus. е.Describe the possible Type Il error for this situation--make sure to state the error in terms of the percentage of a population infected by the virus. f. Determine the appropriate critical value(s) for this situation given a 19% significance level. g. Determine lcalculate the value of the sample's test statistic. h. Determine the P-value. i Based upon your work above, should you "Reject the null hypothesis" or "Fail to reject the null hypothesis?" Explain why. I- Based upon the work above (and assuming requirements of the hypothesis tests are met), is there statistically sufficient evidence in this sample to support the daim that the percentage of a population that will be infected by the virus if left unchecked will be over 60%? Explain your reasoning.
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