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A random sample of :11 = 16 communities in western Kansas gave the following information for people under 25 years of age. x1: Rate of hay fever per 1090 population for people under 25 100 39 122 130 91 123 112 93 125 95 125 117 97 122 127 83 A random sample of :12 = 14 regions in western Kansas gave the following information for people over 50 years old. x2: Rate of hay fever per 1090 population for peopEe over 5|] 93 108 99 98 110 88 110 79 115 100 89 114 85 96 IE USE SALT (i) Use a calculator to calculate x1, 51' x2, and 52. (Round your answers to four decimal places.) _=: (ii) Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use a = 0.05. (a) What is the level of signicance? :| State the null and alternate hypotheses. O HO: 5'1 = #2; H1: 311 > :12 O H0: 511 = 512; H1: p1 :12; H1: :11 = :12 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with known standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The standard non'nal. We assume that both population distributions are approximately normai with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with known standard deviations. What is the value of the sample test statistic? [Test the difference :11 312. Round your answer to three decimal places.) :I Letx be a random variable that represents the pH of arterial plasma (Le.r acidity of the blood). For healthy adulls, the mean of the xdistributionis y. = 7.4.? A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients wlth arthritis took the drug for 3 months. Blood tests showed thatx = 8.8 with sample standard deviation 5 = 3.3. Use a 5% level of signicance to test me claim that the dmg has changed (either way) the mean pH level of the blood. Ia USE (a) What is the level of signicance? E State the null and alternate hypotheses. O HO: pl : 7.4; H1: p 7.4 O HO: p > 7.4; H1: _u : 7.4 0 Ha: p: 7.4-, HI: p = 7.4 O HO: y. = 7.4,- H]: p t 7.4 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distributlon. O The standard normal, since the sample size is large and a is known. 0 The Student's t, since the sample size is large and o' is unknown. 0 The standard normal, since the sample size is large and a is unknown. 0 The Student's t, since the sample size is large and o' is known. What is the value of the sample test statistic? (Round your answer to three decimal places.) E Weatherwise is a magazine published by the American Meteorological Society. One issue gives a rating system used to classify Nor'easter storms that frequently hit New England and can cause much damage near the ocean. A severe storm has an average peak wave height of p : 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rang. Peak wave heights are usually measured from land (using binoculars) off fixed cement piers. Suppose that a reading of 39 waves showed an average wave height of; = 16.7 feet. Previous studies of severe storms indicate that 0' = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily] increasing above the severe Eating? Use a = 0.01. (a) What is the level of signicance? State the null and alternate hypotheses. H\": ,u : 15.4 ft; H1: L! > 15.40: 0 H0: ,0 : 15.4 ft; H1: 1:: 15.4ft O H\": ,u 15.4 ft; H1: 1': 15.41% (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. 0 The Student's t, since the sample size is large and a is unknown. The standard normal, since the sample size is large and o' is known. 0 The Student's t, since the sample size is large and o' is known. 0 The standard normal, since the sample size is large and o is unknown. What is the value of the sample test statistic? (Round your answer to two decimal places.) :| (c) Estimate the Pvalue. O Pvalue > 0.250 O 0100 H2 (b) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations. What is the value of the sample test statistic? (Test the difference u, - #2. Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)For one binomial experiment, n, = 75 binomial trials produced r, = 30 successes. For a second independent binomial experiment, n, = 100 binomial trials produced , = 50 successes. At the 5% level of significance, test the claim that the probabilities of success for the two binomial experiments differ. LA USE SALT (a) Compute the pooled probability of success for the two experiments. (Round your answer to three decimal places.) (b) Check Requirements: What distribution does the sample test statistic follow? Explain. O The standard normal. We assume the population distributions are approximately normal. Rectangular Snip The Student's t. We assume the population distributions are approximately normal. O The Student's t. The number of trials is sufficiently large. O The standard normal. The number of trials is sufficiently large. (c) State the hypotheses. O Ho: P1 = P2i Hi: P1 P2 (d) Compute p1 - P2. P1 - P2 = Compute the corresponding sample distribution value. (Test the difference p, - P2 . Do not use rounded values. Round your final answer to two decimal places.) (e) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. Is fishing better from a boat or from the shore? Pyramid Lake is located on the Paiute Indian Reservation in Nevada. Presidents, movie stars, and people who just want to catch fish go to Pyramid Lake for really large cutthroat trout. Let row B represent hours per fish caught fishing from the shore, and let row A represent hours per fish caught using a boat. The following data are paired by month from October through April. Oct Nov Dec Jan Feb March April B: Shore 1.5 1.9 2.1 3.2 3.9 3.6 3.3 A: Boat 1.4 1.3 1.7 2.2 3.3 3.0 3.8 LO USE SALT Use a 1% level of significance to test if there is a difference in the population mean hours per fish caught using a boat compared with fishing from the shore. (Let d = B - A.) (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: u = 0; H: u = 0; two-tailed O Ho: ud = 0; Hj: u 0; right-tailed OH: ud # 0; H,: My = 0; two-tailed (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that o has an approximately uniform distribution. The Student's t. We assume that d has an approximately normal distribution. The Student's t. We assume that d has an approximately uniform distribution. O The standard normal. We assume that d has an approximately normal distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.)In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at row B, the annual company percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose a random sample of companies yielded the following data: B: Percent increase 24 25 27 18 6 21 37 for company A: Percent increase 21 for CEO 23 26 14 10 15 30 In USE SALT Do these data indicate that the population mean percentage increase in corporate revenue (row B) is different from the population mean percentage increase in CEO salary? Use a 5% level of significance. (Let d = B - A.) (a) What is the level of significance? State the null and alternate hypotheses. OH: 4 = 0; H : 40 OH: u > 0; H : ud = 0 OH: Hy = 0; H1: ud>0 OH: My = 0; Hug 0.67 What sampling distribution will you use? 0 The Studenfs t, slnue \"D > 5 and my > 5. O The standard normal. since an > 5 and an > 5. O The Student's t, since no 0.7 OHU:p 5 and no > 5. O The standard normal, since np > 5 and not > 5. O The standard normal, since np 19 in; H: / = 19 in O Ho: M = 19 in; Hj: u = 19 in O Ho: M 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since the sample size is large and o is known. The standard normal, since the sample size is large and o is unknown. The Student's t, since the sample size is large and o is unknown. The standard normal, since the sample size is large and o is known. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. O P-value > 0.010 0.0010 1.75 yr 0 H\": u > 1.75 yr; H1: 1:: 1.75 yr 0 H0: pr 0.250 O 0.100