The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size n = 500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, X, in Lance's sample who regularly skip breakfast is greater than 126. You may find table of critical values helpful. Express the result as a decimal precise to three places.

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 = 50 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 α = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ho: P = 0.301; H₁: p = 0.301 Ho: P 0.301 Ho: P = 0.301; H₁: p 5 and nq > 5. O The Student's t, since np 5 and nq > 5. What is the value of the…

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 the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank. You draw a random sample of n = 226 numbers from this file and r = 87 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1. 1) Test the claim that p is more than 0.301. Use α = 0.10. 2) What is the value of the sample test statistic? (Round your answer to two decimal places.)  3) Find the P-value of the test statistic. (Round your answer to four decimal places.)  4) If p is in fact larger than 0.301, it would seem there are too many numbers in…

The 2006 Statistical Abstract of the United States reports on a survey that asked a national sample of 80,000 American households about pet ownership. Suppose (for now) that one-third of all American households own a pet cat. Still supposing that one-third of all American households own a pet cat, between what two values do you expect 95% of all sample proportions to fall?