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Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).T Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows. 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean is ; = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that X has a normal distribution and a = 0.64 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is p = 4.40 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.40 grams? Use at = 0.01. 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 th 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 corpor report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 223 numerical entries from the file and r = 50 of the entries had a first n 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 = 0.10. In USE SALT (a) What is the level of significance? .10 State the null and alternate hypotheses. O Ho: p = 0.301; H, : p > 0.301 O Ho: p 5 and nq > 5. O The standard normal, since np 5 and nq > 5. O The Student's t, since np 0.7 O HO: p: 0.7; H1:p = 0.7 J (b) What sampling distribution will you use? O The standard normal, since rip > 5 and nq > 5. O The Student's t, since no > 5 and nq > 5. O The Student's t, since np 0; H 1 : Hd = 0 O Ho: Mld = 0 ; H 1: ud o (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that d has an approximately normal distribution. The Student's t. We assume that d has an approximately uniform distribution. The Student's t. We assume that d has an approximately normal distribution. The standard normal. We assume that d has an approximately uniform distribution