Unit 5 FRQ

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Auburn University *

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2010

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Statistics

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May 15, 2024

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Unit 5 Exam Producing Data Free Response Directions: Complete the assignment. Your answers for this assignment must include reasons; simply stating the answer without justification will earn partial credit. 1. A game of chance is based on spinning a 0-9 spinner like the one shown two times in succession. The player wins if the larger of the two numbers is greater than 5. a. What constitutes a single play of this game? What are the possible outcomes resulting in win or lose? (6 points) A single play of this game is when the player spins the spinner two times in succession. The outcome is a win if the larger of the two numbers is greater than five and a loss if the larger of the two numbers is less than or equal to 5. b. Describe a correspondence between the random digits from a Random Number Table and outcomes in the game. (6 points) The spinner aligns perfectly with the number table looking at one digit at a time, so the first digit on the number table is the first outcome. For example, Row 35 starts with 77800, so the first two consecutive spins would result in a 7 and a 7. Since 7 is equal to 7, it can be considered the larger of the two values and is greater than 5, so the first play would be a win. c. Use the Random Number Table to simulate 20 repetitions. Using the table, begin at line 37. Report each trial and the proportion of times you win the game. (6 points) 7, 2: Win 1 8, 9: Win 2 4, 0: Loss 5, 6: Win 3 4, 6: Win 4 8, 5: Win 5 4, 3: Loss 3, 2: Loss 0, 0: Loss 7, 1: Win 6 8, 9: Win 7 9, 1: Win 8 2, 9: Win 9 0, 8: Win 10 4, 8: Win 11 2, 0: Loss

9, 1: Win 12 8, 5: Win 13 3, 5: Loss 5, 1: Loss P(W)= 13/20= 0.65= 65% Row 35 77800 25734 09801 92087 02955 12872 89848 48579 06028 13827 24028 03405 01178 06316 81916 40170 53665 87202 88638 47121 Row 37 86558 84750 43994 01760 96205 27937 45416 71964 52261 30781 78545 49201 05329 14182 10971 90472 44682 39304 19819 55799 14969 64623 82780 35686 30941 14622 04126 25498 95452 63937 2. Bias is present in each of the following sampling designs. In each case, identify the * type of bias involved and state whether you think the sampling frequency obtained is lower or higher than the actual population parameter. a. A political pollster seeks information about the proportion of American adults that oppose gun control. He asks a SRS of 1000 American adults: “ Do you agree or disagree with the following statement: Americans should preserve their constitutional right to keep and bear arms. ” A total of 910, or 91%, said “ agree ” (that is, 910 out of the 1000 oppose gun control) (6 points: 2 points type of bias; 2 points explanation of bias; 2 points estimate higher/lower population parameter) • The bias involved here is wording bias . • The wording makes it obvious that the pollster is anti-gun control as they phrased the right to bear arms as a “ constitutional right ” that should be protected by the government. • This wording bias causes a higher percentage of people to agree with the statement that the right to bear arms is a “ constitutional right. ” b. A flour company in Minneapolis wants to know what percentage of local households bake at least twice a week. A company representative calls 500 households during the daytime and finds 50% of them bake at least twice a week. (6 points) • This is under-coverage bias : part of the population is excluded from the sample. • Since the company is only calling during the daytime, they are excluding the households who are unavailable during the day to take a call, maybe due to work, so the people who have work during the day, or other circumstances that would make them unavailable to take a call, are excluded, not representing the entire population well. • This under coverage results in the data having more people baking since the people who would answer to say that they are too busy are bake are unavailable due to more daytime commitments.

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