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Statistics Worksheet #1 Writing HYPOTHESES Name ______________________________ 1. The claim being tested in a significance test is the ………………… hypothesis. (null/alternative) 2. A test of significance is designed to assess the strength of evidence against the ………………… hypothesis. (null/alternative) 3. A test of significance is trying to find evidence for the ………………… hypothesis. (null/alternative) 4. Hypotheses for significance tests must always be expressed in terms of the ……………… (parameter/statistic) 5. Which of these could be possible hypotheses for a significance test? A H0: p̂ = 0.5 B H0: p < 0.5 C Ha: p ≥ 0.5 Ha: p̂ > 0.5 H0: p > 0.5 D Ha: p = 0.5 H0: p = 0.5 Ha: p > 0.5 6. Which of these could be possible hypotheses for a significance test? A H0: p > 0.3 Ha: p < 0.3 B H0: p = 0.3 Ha: p ≠ 0.3 C H0: p = 0.3 Ha: p > 0.3 D H0: p ≠ 0.3 Ha: p = 0.3 For #7 – 10, write only the hypotheses for each problem. 7. According to M&M/Mars Company, 20% of all Plain M&M’s produced are orange. You buy one large 56 oz bag of Plain M&M’s and find that it contains 355 orange M&M’s out of a total of 1,858 M&Ms. Do we have evidence that the company is lying about the proportion of orange M&M’s? H0: …………………Ha: ………………… 8. You’ve been using the Random Digit Table all year, but one day you decide to check out its randomness. You count the number of times the digit “9" occurs in the last four rows of the table and find that there only 12 “9"'s in the last 160 digits. You suspect that the table is flawed by having fewer “9"’s then it should and decide to do a significance test. H0: …………………Ha: ………………… 9. The White House press secretary comments that the president currently has a 72% favorable job approval rating. A pollster challenges this claim as being too high. His polling service has just conducted a random survey of 1000 people (calling both landline and cell phone numbers) and 660 people gave the president a favorable job approval rating. Do we have reason to doubt the press secretary? H0: …………………Ha: ………………… 10. A 2009 nationwide random survey of 1500 adults asked the open-ended question, “What do you think is the most important problem facing this country today?” Sixty-nine percent responded with some form of economic problems (such as economy in general, unemployment/jobs, etc). Do these data provide good evidence that more than 2/3 of all adults believe that economic problems is the most important problem facing this country today? H0: …………………Ha: ………………… 11. If a die is fair, then the number 5 should occur 1/6 of the time. You have a die that you suspect is loaded so that the number 5 lands face up more often then expected. You roll the die 200 times and get 44 5's. Do we have evidence that the die is unfair (i.e. loaded)? a. Write the hypotheses for a significance test. H0: …………… and Ha: …………… b. What are the mean and standard deviation of the sampling proportion of 5's on the roll of a die? c. For the sampling distribution at the right, mark the mean of the sampling proportion, the mean ± 1 standard deviation, mean ± 2 standard deviations, and the mean ± 3 standard deviations. d. What is the value of p̂ ? …………… Mark this value on the horizontal axis of your sketch. Shade the area to the right of this value. e. Is getting 44 5's or more in 200 rolls of the die usual or unusual? ……………… 12. According to the 2000 U.S. Census, 80.4% of all U. S. residents 25 years old or older have at least a high school diploma. In 2005, a random sample of 3,000 residents 25 years old or older found that 2,365 had at least a high school diploma. Is there is evidence to suggest that the number of high school graduates is lower than reported in the Census? a. Write the hypotheses for a significance test. H0: …………… and Ha: …………… b. What are the mean and standard deviation of the sampling proportion? c. For the sampling distribution at the right, mark the mean of the sampling proportion, the mean ± 1 standard deviation, mean ± 2 standard deviations, and the mean ± 3 standard deviations. d. What is the value of p̂ ? …………… Mark this value on the horizontal axis of your sketch. Shade the area to the left of this value. e. So is getting 2,365 out of a sample of 3,000 usual or unusual? …………………