𝑨 𝒓𝒂𝒏𝒅𝒐𝒎 𝒔𝒂𝒎𝒑𝒍𝒆 𝒐𝒇 15 𝒂𝒅𝒖𝒍𝒕 𝒎𝒂𝒍𝒆 𝒘𝒐𝒍𝒗𝒆𝒔 𝒇𝒓𝒐𝒎 𝒕𝒉𝒆 𝑪𝒂𝒏𝒂𝒅𝒊𝒂𝒏 𝑵𝒐𝒓𝒕𝒉𝒘𝒆𝒔𝒕 𝑻𝒆𝒓𝒓𝒊𝒕𝒐𝒓𝒊𝒆𝒔 𝒈𝒂𝒗𝒆 𝒂𝒏 𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒘𝒆𝒊𝒈𝒉𝒕 𝒙1 = 96.2 𝒑𝒐𝒖𝒏𝒅𝒔 𝒘𝒊𝒕𝒉 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆𝒅 𝒔𝒂𝒎𝒑𝒍𝒆 𝒔𝒕𝒂𝒏𝒅𝒂𝒓𝒅 𝒅𝒆𝒗𝒊𝒂𝒕𝒊𝒐𝒏 𝒔1 = 6.8 𝒑𝒐𝒖𝒏𝒅𝒔. 𝑨𝒏𝒐𝒕𝒉𝒆𝒓 𝒔𝒂𝒎𝒑𝒍𝒆 𝒐𝒇 29 𝒂𝒅𝒖𝒍𝒕 𝒎𝒂𝒍𝒆 𝒘𝒐𝒍𝒗𝒆𝒔 𝒇𝒓𝒐𝒎 𝑨𝒍𝒂𝒔𝒌𝒂 𝒈𝒂𝒗𝒆 𝒂𝒏 𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒘𝒆𝒊𝒈𝒉𝒕 𝒙2 = 88.8 𝒑𝒐𝒖𝒏𝒅𝒔 𝒘𝒊𝒕𝒉 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆𝒅 𝒔𝒂𝒎𝒑𝒍𝒆 𝒔𝒕𝒂𝒏𝒅𝒂𝒓𝒅 𝒅𝒆𝒗𝒊𝒂𝒕𝒊𝒐𝒏 𝒔2 = 6.7 𝒑𝒐𝒖𝒏𝒅𝒔. (𝒃) 𝑳𝒆𝒕 𝜇1 𝒓𝒆𝒑𝒓𝒆𝒔𝒆𝒏𝒕 𝒕𝒉𝒆 𝒑𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 𝒎𝒆𝒂𝒏 𝒘𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝒂𝒅𝒖𝒍𝒕 𝒎𝒂𝒍𝒆 𝒘𝒐𝒍𝒗𝒆𝒔 𝒇𝒓𝒐𝒎 𝒕𝒉𝒆 𝑵𝒐𝒓𝒕𝒉𝒘𝒆𝒔𝒕 𝑻𝒆𝒓𝒓𝒊𝒕𝒐𝒓𝒊𝒆𝒔, 𝒂𝒏𝒅 𝒍𝒆𝒕 𝜇2 𝒓𝒆𝒑𝒓𝒆𝒔𝒆𝒏𝒕 𝒕𝒉𝒆 𝒑𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 𝒎𝒆𝒂𝒏 𝒘𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝒂𝒅𝒖𝒍𝒕 𝒎𝒂𝒍𝒆 𝒘𝒐𝒍𝒗𝒆𝒔 𝒇𝒓𝒐𝒎 𝑨𝒍𝒂𝒔𝒌𝒂. 𝑭𝒊𝒏𝒅 𝒂 95% 𝒄𝒐𝒏𝒇𝒊𝒅𝒆𝒏𝒄𝒆 𝒊𝒏𝒕𝒆𝒓𝒗𝒂𝒍 𝒇𝒐𝒓 𝜇1 – 𝜇2. (𝑼𝒔𝒆 1 𝒅𝒆𝒄𝒊𝒎𝒂𝒍 𝒑𝒍𝒂𝒄𝒆.)
Added by Margaret P.
Step 1
Given: \( x_1 = 96.2 \) pounds (mean weight of wolves from the Canadian Northwest Territories) \( x_2 = 88.8 \) pounds (mean weight of wolves from Alaska) Calculate: \( \bar{x}_1 - \bar{x}_2 = 96.2 - 88.8 = 7.4 \) pounds Show more…
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𝘈 𝘳𝘢𝘯𝘥𝘰𝘮 𝘴𝘢𝘮𝘱𝘭𝘦 𝘰𝘧 15 𝘢𝘥𝘶𝘭𝘵 𝘮𝘢𝘭𝘦 𝘸𝘰𝘭𝘷𝘦𝘴 𝘧𝘳𝘰𝘮 𝘵𝘩𝘦 𝘊𝘢𝘯𝘢𝘥𝘪𝘢𝘯 𝘕𝘰𝘳𝘵𝘩𝘸𝘦𝘴𝘵 𝘛𝘦𝘳𝘳𝘪𝘵𝘰𝘳𝘪𝘦𝘴 𝘨𝘢𝘷𝘦 𝘢𝘯 𝘢𝘷𝘦𝘳𝘢𝘨𝘦 𝘸𝘦𝘪𝘨𝘩𝘵 𝘹1 = 96.2 𝘱𝘰𝘶𝘯𝘥𝘴 𝘸𝘪𝘵𝘩 𝘦𝘴𝘵𝘪𝘮𝘢𝘵𝘦𝘥 𝘴𝘢𝘮𝘱𝘭𝘦 𝘴𝘵𝘢𝘯𝘥𝘢𝘳𝘥 𝘥𝘦𝘷𝘪𝘢𝘵𝘪𝘰𝘯 𝘴1 = 6.8 𝘱𝘰𝘶𝘯𝘥𝘴. 𝘈𝘯𝘰𝘵𝘩𝘦𝘳 𝘴𝘢𝘮𝘱𝘭𝘦 𝘰𝘧 29 𝘢𝘥𝘶𝘭𝘵 𝘮𝘢𝘭𝘦 𝘸𝘰𝘭𝘷𝘦𝘴 𝘧𝘳𝘰𝘮 𝘈𝘭𝘢𝘴𝘬𝘢 𝘨𝘢𝘷𝘦 𝘢𝘯 𝘢𝘷𝘦𝘳𝘢𝘨𝘦 𝘸𝘦𝘪𝘨𝘩𝘵 𝘹2 = 88.8 𝘱𝘰𝘶𝘯𝘥𝘴 𝘸𝘪𝘵𝘩 𝘦𝘴𝘵𝘪𝘮𝘢𝘵𝘦𝘥 𝘴𝘢𝘮𝘱𝘭𝘦 𝘴𝘵𝘢𝘯𝘥𝘢𝘳𝘥 𝘥𝘦𝘷𝘪𝘢𝘵𝘪𝘰𝘯 𝘴2 = 6.7 𝘱𝘰𝘶𝘯𝘥𝘴. (𝘢) 𝘊𝘢𝘵𝘦𝘨𝘰𝘳𝘪𝘻𝘦 𝘵𝘩𝘦 𝘱𝘳𝘰𝘣𝘭𝘦𝘮 𝘣𝘦𝘭𝘰𝘸 𝘢𝘤𝘤𝘰𝘳𝘥𝘪𝘯𝘨 𝘵𝘰 𝘱𝘢𝘳𝘢𝘮𝘦𝘵𝘦𝘳 𝘣𝘦𝘪𝘯𝘨 𝘦𝘴𝘵𝘪𝘮𝘢𝘵𝘦𝘥, 𝘱𝘳𝘰𝘱𝘰𝘳𝘵𝘪𝘰𝘯 𝘱, 𝘮𝘦𝘢𝘯 𝜇, 𝘥𝘪𝘧𝘧𝘦𝘳𝘦𝘯𝘤𝘦 𝘰𝘧 𝘮𝘦𝘢𝘯𝘴 𝜇1 – 𝜇2, 𝘰𝘳 𝘥𝘪𝘧𝘧𝘦𝘳𝘦𝘯𝘤𝘦 𝘰𝘧 𝘱𝘳𝘰𝘱𝘰𝘳𝘵𝘪𝘰𝘯𝘴 𝘱1 – 𝘱2. 𝘛𝘩𝘦𝘯 𝘴𝘰𝘭𝘷𝘦 𝘵𝘩𝘦 𝘱𝘳𝘰𝘣𝘭𝘦𝘮. (𝘣) 𝘓𝘦𝘵 𝜇1 𝘳𝘦𝘱𝘳𝘦𝘴𝘦𝘯𝘵 𝘵𝘩𝘦 𝘱𝘰𝘱𝘶𝘭𝘢𝘵𝘪𝘰𝘯 𝘮𝘦𝘢𝘯 𝘸𝘦𝘪𝘨𝘩𝘵 𝘰𝘧 𝘢𝘥𝘶𝘭𝘵 𝘮𝘢𝘭𝘦 𝘸𝘰𝘭𝘷𝘦𝘴 𝘧𝘳𝘰𝘮 𝘵𝘩𝘦 𝘕𝘰𝘳𝘵𝘩𝘸𝘦𝘴𝘵 𝘛𝘦𝘳𝘳𝘪𝘵𝘰𝘳𝘪𝘦𝘴, 𝘢𝘯𝘥 𝘭𝘦𝘵 𝜇2 𝘳𝘦𝘱𝘳𝘦𝘴𝘦𝘯𝘵 𝘵𝘩𝘦 𝘱𝘰𝘱𝘶𝘭𝘢𝘵𝘪𝘰𝘯 𝘮𝘦𝘢𝘯 𝘸𝘦𝘪𝘨𝘩𝘵 𝘰𝘧 𝘢𝘥𝘶𝘭𝘵 𝘮𝘢𝘭𝘦 𝘸𝘰𝘭𝘷𝘦𝘴 𝘧𝘳𝘰𝘮 𝘈𝘭𝘢𝘴𝘬𝘢. 𝘍𝘪𝘯𝘥 𝘢 95% 𝘤𝘰𝘯𝘧𝘪𝘥𝘦𝘯𝘤𝘦 𝘪𝘯𝘵𝘦𝘳𝘷𝘢𝘭 𝘧𝘰𝘳 𝜇1 – 𝜇2. (𝘜𝘴𝘦 1 𝘥𝘦𝘤𝘪𝘮𝘢𝘭 𝘱𝘭𝘢𝘤𝘦.) 𝘭𝘰𝘸𝘦𝘳 𝘭𝘪𝘮𝘪𝘵 - 𝘶𝘱𝘱𝘦𝘳 𝘭𝘪𝘮𝘪𝘵 - (𝘤) 𝘌𝘹𝘢𝘮𝘪𝘯𝘦 𝘵𝘩𝘦 𝘤𝘰𝘯𝘧𝘪𝘥𝘦𝘯𝘤𝘦 𝘪𝘯𝘵𝘦𝘳𝘷𝘢𝘭 𝘢𝘯𝘥 𝘦𝘹𝘱𝘭𝘢𝘪𝘯 𝘸𝘩𝘢𝘵 𝘪𝘵 𝘮𝘦𝘢𝘯𝘴 𝘪𝘯 𝘵𝘩𝘦 𝘤𝘰𝘯𝘵𝘦𝘹𝘵 𝘰𝘧 𝘵𝘩𝘪𝘴 𝘱𝘳𝘰𝘣𝘭𝘦𝘮. 𝘋𝘰𝘦𝘴 𝘵𝘩𝘦 𝘪𝘯𝘵𝘦𝘳𝘷𝘢𝘭 𝘤𝘰𝘯𝘴𝘪𝘴𝘵 𝘰𝘧 𝘯𝘶𝘮𝘣𝘦𝘳𝘴 𝘵𝘩𝘢𝘵 𝘢𝘳𝘦 𝘢𝘭𝘭 𝘱𝘰𝘴𝘪𝘵𝘪𝘷𝘦? 𝘢𝘭𝘭 𝘯𝘦𝘨𝘢𝘵𝘪𝘷𝘦? 𝘰𝘧 𝘥𝘪𝘧𝘧𝘦𝘳𝘦𝘯𝘤𝘦 𝘴𝘪𝘨𝘯𝘴? 𝘈𝘵 𝘵𝘩𝘦 95% 𝘭𝘦𝘷𝘦𝘭 𝘰𝘧 𝘤𝘰𝘯𝘧𝘪𝘥𝘦𝘯𝘤𝘦, 𝘥𝘰𝘦𝘴 𝘪𝘵 𝘢𝘱𝘱𝘦𝘢𝘳 𝘵𝘩𝘢𝘵 𝘵𝘩𝘦 𝘢𝘷𝘦𝘳𝘢𝘨𝘦 𝘸𝘦𝘪𝘨𝘩𝘵 𝘰𝘧 𝘢𝘥𝘶𝘭𝘵 𝘮𝘢𝘭𝘦 𝘸𝘰𝘭𝘷𝘦𝘴 𝘧𝘳𝘰𝘮 𝘵𝘩𝘦 𝘕𝘰𝘳𝘵𝘩𝘸𝘦𝘴𝘵 𝘛𝘦𝘳𝘳𝘪𝘵𝘰𝘳𝘪𝘦𝘴 𝘪𝘴 𝘨𝘳𝘦𝘢𝘵𝘦𝘳 𝘵𝘩𝘢𝘯 𝘵𝘩𝘢𝘵 𝘰𝘧 𝘵𝘩𝘦 𝘈𝘭𝘢𝘴𝘬𝘢 𝘸𝘰𝘭𝘷𝘦𝘴?
Ivan K.
For one binomial experiment, n1 = 75 binomial trials produced r1 = 45 successes. For a second independent binomial experiment, n2 = 100 binomial trials produced r2 = 65 successes. At the 5% level of significance, test the claim that the probabilities of success for the two binomial experiments differ. (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. (c) State the hypotheses. (d) Compute p̂1 - p̂2. Compute the corresponding sample distribution value. (Test the difference p1 − 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.) (f) Conclude the test. (g) Interpret the results.
Sheryl E.
Education influences attitude and lifestyle. Differences in education are a big factor in the "generation gap." Is the younger generation really better educated? Large surveys of people age 65 and older were taken in n1 = 32 U.S. cities. The sample mean for these cities showed that x1 = 15.2% of the older adults had attended college. Large surveys of young adults (age 25 - 34) were taken in n2 = 31 U.S. cities. The sample mean for these cities showed that x2 = 17.8% of the young adults had attended college. From previous studies, it is known that σ1 = 6.2% and σ2 = 5.2%. Does this information indicate that the population mean percentage of young adults who attended college is higher? Use α = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. (b) What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? (e) Interpret your conclusion in the context of the application.
Kirsty G.
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