1) Sam computed a 90% confidence interval for from a specific random sample of size n. He claims that at the 90% confidence level, his confidence interval contains . Is this claim correct? Explain. No. The probability that this interval contains is either 0 or 1. No. The proportion of all confidence intervals based on random samples of size n that contain is 0.10. Yes. 90% of all confidence intervals will contain . Yes. The proportion of all confidence intervals based on random samples of size n that contain is 0.90. 2) Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther. Suppose a small group of 12 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with = 0.30 gram. (a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) a. is unknown b. is known c. uniform distribution of weights d. normal distribution of weights e. n is large (c) Give a brief interpretation of your results in the context of this problem. a. The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20. b.There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region. c. The probability to the true average weight of Allen's hummingbirds is equal to the sample mean. d. The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80. e. There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region. (d) Find the sample size necessary for an 80% confidence level with a maximal error of estimate E = 0.14 for the mean weights of the hummingbirds. (Round up to the nearest whole number.) ________hummingbirds 3) Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken nine blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with = 1.93 mg/dl. (a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) uniform distribution of uric acid is known n is large normal distribution of uric acid is unknown (c) Give a brief interpretation of your results in the context of this problem. a. There is a 5% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient. b. There is not enough information to make an interpretation. c. The probability that this interval contains the true average uric acid level for this patient is 0.05. d. There is a 95% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient. e. The probability that this interval contains the true average uric acid level for this patient is 0.95. (d) Find the sample size necessary for a 95% confidence level with maximal error of estimate E = 1.16 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.) _______blood tests 4) Consider a 90% confidence interval for . Assume is not known. For which sample size, n = 10 or n = 20, is the critical value tc larger? 20 10 neither 5) How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains gave the following weights (pounds): 75 105 126 129 60 64 Assume that the population of x values has an approximately normal distribution. (a) Use a calculator with mean and sample standard deviation keys to find the sample mean weight x and sample standard deviation s. (Round your answers to one decimal place.) x lb = s lb = (b) Find a 75% confidence interval for the population average weight of all adult mountain lions in the specified region. (Round your answers to one decimal place.) lower ______lb limit upper ______lb limit 6) For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 22 out of 824 fish died when caught and released using barbless hooks on flies or lures. All hooks were removed from the fish. (a) Let p represent the proportion of all pike and trout that die (i.e., p is the mortality rate) when caught and released using barbless hooks. Find a point estimate for p. (Round your answer to four decimal places.) (b) Find a 99% confidence interval for p. (Round your answers to three decimal places.) lower limit upper limit Give a brief explanation of the meaning of the interval. Choose one from the following. 99% of all confidence intervals would include the true catch-andrelease mortality rate. 99% of the confidence intervals created using this method would include the true catch-and-release mortality rate. 1% of the confidence intervals created using this method would include the true catch-and-release mortality rate. 1% of all confidence intervals would include the true catch-andrelease mortality rate. (c) Is the normal approximation to the binomial justified in this problem? Explain. Which one is correct? Yes; np > 5 and nq > 5. No; np > 5 and nq < 5. No; np < 5 and nq > 5. Yes; np < 5 and nq < 5. 7) For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. A random sample of medical files is used to estimate the proportion p of all people who have blood type B. (a) If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 85% sure that the point estimate p will be within a distance of 0.04 from p? (Round your answer up to the nearest whole number.) _________medical files (b) Answer part (a) if you use the preliminary estimate that about 12 out of 90 people have blood type B. __________medical files