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3. [0.6/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 8.3.007.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 221 numerical entries from the file and r = 49 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. (i) Test the claim that p is less than 0.301. Use a = 0.05. LA USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Hoip = 0.301; Hip > 0.301 O Hoip 5 and nq > 5. The Student's t, since np 5 and nq > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.4. [0.48/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 8.3.010.MI.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Women athletes at a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of 38 women athletes at the school showed that 23 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 10% level of significance. In USE SALT (a) What is the level of significance? b) State the null and alternate hypotheses. O Ho:p 5 and nq > 5. O The standard normal, since np 5 and ng > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic. (Round your answer to four decimal places.)5. [0.48/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 8.3.012.5. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color.t Suppose = 58 college students were sur r = 8 of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use a = 0.05. LA USE SALT a) What is the level of significance? State the null and alternate hypotheses. D Hoip = 0.24; H,: p > 0.24 O Hoip = 0.24; Hip 5 and nq > 5. The standard normal, since np 5 and nq > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.6. [0.48/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 8.3.013.5. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The following is based on information from The Wolf in the Southwest: The Making of an Endangered Species, by David E. Brown (University of Arizona Press). Before 1918, the proportion of female wolves in the general population of all southwestern wolves was about 50%. However, after 1918, southwestern cattle ranchers began a widespread effort to destroy wolves. In a recent sample of 37 wolves, there were only 11 females. One theory is that male wolves tend to return sooner than females to their old territories, where their predecessors were exterminated. Do these data indicate that the population proportion of female wolves is now less than 50% in the region? Use a = 0.01. LO USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Hoip = 0.5; Hip = 0.5 Hoip = 0.5; Hjip 5 and nq > 5. The standard normal, since np > 5 and nq > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic. (Round your answer to four decimal places.)7. [0.48/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 8.3.016.MI.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leacht found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 490 five-syllable sequences from this manuscript showed that 127 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use a = 0.01. LA USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Hip 0.214 O Ho: p = 0.214; Hip 0.214; H1: p = 0.214 (b) What sampling distribution will you use? O The Student's t, since np > 5 and nq > 5. The standard normal, since np > 5 and ng > 5. The standard normal, since np 0.47; Hip = 0.47 O Hoip = 0.47; Hip 0.47 (b) What sampling distribution will you use? The Student's t, since np > 5 and nq > 5. The standard normal, since np > 5 and nq > 5. The Student's t, since np