Z- procedure, sample size, confidence Interval, and hypothesis test. Please read all the questions carefully and answer all the questions step by step. Please show the workings. If you use the Ti calculator to do it, please write the calculator workings (that is how you enter it into the calculator. 1. The mean length of a random sample of 12 trout from lake Lugo is 14.3 inches with a standard deviation of 1.5 inches. Compute the 90% confidence interval estimate for the length of trout in Lake Lugo. Also, provide an interpretation in words. 2. PCB contamination of a river by a manufacturer is being measured by amounts of the pollutant found in fish. A company scientist claims that the fish contain only 5 parts per million, but an investigator believes the true figure is higher. What is the conclusion if six fish are caught and show the following amounts of PCB (in parts per million) 6.8,5.6,5.6, 5.2, 4.7, 6.3, and 5.4. Test 50% significance level. In addition to your conclusions, you must provide the null and alternative hypothesis, alpha, and the p-value.3. A government agency claims that 60% of Americans agree that oil exploration in our national parks is necessary. A geologist wants to test this claim. In a survey of 1945 Americans, 1215 said they agree that oil exploration is needed. Use a 5% significance level.a. Write the null and alternative hypotheses and the alpha risk.b. What is the p-value of the test and what conclusion is reached? 4. From the population of secondary school students in the state, a random sample of 60 indicated that they watch an average of 2.8 hours of television per day with a standard deviation of 0.8 hours. Use a Z procedure for this problem. a. What is the 99% confidence interval estimate for the hours of television watched for all children in the state? b. What size sample would we need to reduce the margin of error by 50%?
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