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Elementary Statistics Written Homework Unit 3C: Sections 6.1 & 6.3 No software output is required for this assignment. 1. 6.58 Multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E. A random sample of the correct choice on 400 multiple-choice questions on a variety of AP exams shows that B was the most common correct choice, with 90 of the 400 questions having B as the answer. Does this provide evidence that B is more likely than 20% to be the correct choice? a. State hypotheses, and calculate the sample statistic. b. Are conditions met for using a Normal distribution for this test? Explain. c. Calculate the standard error and z-test statistic, assuming a Normal distribution is appropriate. d. Find the p-value and draw a Normal curve with appropriate shaded region. p-value: e. State the conclusion of the test in context, using nontechnical language. f. Find a 95% confidence interval for the proportion of questions on all AP exams having B as the correct choice using the normal distribution and the formula for standard error. Show your calculations. Sections 6.1 & 6.3 MATH 1342 Page 1 of 22. 6.148 Metal Tags on Penguins and Survival Data were collected over a 10-year timespan from a sample of 100 penguins that were randomly given either metal or electronic tags. One variable examined is the survival rate 10 years after tagging. The scientists observed that 10 of the 50 metal tagged penguins survived, compared to 18 of the 50 electronic tagged penguins. a. State hypotheses in terms of the parameters given to test whether the survival rate is lower among metal-tagged penguins than among electronic-tagged penguins. b. Calculate the sample statistic PE - PM c. Use Normal distribution methods to calculate a z-test statistic, given SE = 0.090. d. Find the p-value and draw a Normal curve with appropriate shaded region. p-value: e. State the conclusion of the test in context, using nontechnical language. f. Find a 90% confidence interval for this difference in proportions, given SE = 0.088. g. Interpret the confidence interval. Page 2 of 2 Sections 6.1 & 6.3 MATH 1342