Dr. Bailey's Math Class



Statistical ReasoningName ______________________________Part I: Short answer questions.What is the difference between an experiment and an observational study?What methods of sampling are considered unbiased? State each type, and give an example.What type of sampling errors can exist? (What methods of sampling are biased?) State each type, and give an example.What other type of errors can occur that would result in biased data? (nonsampling errors-we discussed four of these)To reduce bias in a survey, participants should be selected by _____________________________________.How can we reduce variability? On January 6, just after the National Basketball Association labor dispute was settled, the Gallup Poll asked a random sample of 671 adults “How much have you missed watching NBA basketball since the dispute started?" 60% answered “Not at all." Gallup says that the margin of error for this result is plus or minus 4 percentage points with a 95% confidence interval. This means that we can be 95% confident that between ____ and ____ of all adults did not miss watching NBA games.In March of this year, the postmaster for a medium-sized city of 100,000 people wanted to plan for the expected crowds filing their tax returns at the last minute. Using a random-digit dialing technique, a group of 1000 tax filers were interviewed, revealing that 10% of them said it was likely that they would not file until the last day. Based on this information, a 95% confidence statement indicated that the percentage of tax filers who would file on the last day was estimated to be between 8% and 12% of all tax filers in the city would file on the last day. In this problem, What is the margin of error?What is the population?What is the sample?What sampling method was used?What is the sample statistic?In a recent survey of 1500 randomly selected U.S. adults, 68% of the respondents agreed with the statement, “I should exercise more than I do.” For this study, state one source of potential bias and how it would affect the estimate of the proportion of adults who would agree with the statement, “I should exercise more than I do.”Your school principal has decided to grant four special “sleep in” days during the upcoming 180-day school year. She wants to select these days at random, but is not quite sure how to do this so she comes to you for advice. Tell the principal how to go about obtaining an SRS of 4 days using the partial random digits table below. Be very specific so she can follow your instructions with ease. 15099 40192 77011 14459 31901 21491 14873 04197 45740 41807 07051Use the partial table of random digits below to select an SRS of 4 days using the method you described in the previous question. Mark directly on the table to show your process clearly.Would you advise the principal to take a stratified random sample? Why or why not?Part II: Multiple-Choice. Circle the letter corresponding to the best answer choice.1.A recent study was conducted to see if a soy-protein powder would be effective in increasing bone density in 200 randomly selected women aged 60 to 75 who lived in Canada. Which of the following represents the population? (a) All women who would use this soy-protein powder. (b) All women in Canada who would use this soy-protein powder.(c) All women who are between 60 and 75 years of age who would use this soy-protein powder. (d) All women in Canada who are between 60 and 75 years of age who would use this soy-protein powder.(e) No one, since the women volunteered to be part of the study.2. A table of random numbers is used to select 30 students from a large college statistics class to rate a statistics video on a integer scale of 1 to 5 These 30 students are(a) the sampling frame(b) the population(c) a simple random sample of the class(d) a census(e) a voluntary response sample3. In the previous problem, the ratings that these students give are used to estimate the ratings that would be given if the entire class were asked to rate the video. The average of the ratings of all students in the class is(a) a population parameter(b) a convenience sample(c) a census(d) the population(e) a statistic that is an unbiased estimate of the class rating4. Suppose that many of the households asked their income by the Census Bureau give an answer that is too low because they fear that their answer will go to the Internal Revenue Service.(a) This is a sampling error that causes bias.(b) This is a sampling error that increases variability.(c) This is a nonsampling error that causes bias.(d) This is a nonsampling error that increases variability.5. A radio station is interested in predicting the proportion of registered voters who support an increase in the state sales tax to construct additional regional parks across the state. Listeners of the station’s programs were asked to go to the station’s Web site and indicate whether they favored or opposed such an increase. 1744 listeners logged on and 922 (53%) were against the increase. Which one of the following is NOT a correct statement about possible bias in the sampling procedure? (a) Only people with Internet access would be counted. (b) Those who responded may not even be registered voters. (c) Only people listening to the station would be counted. (d) 1744 is quite a large sample, so any bias that might have occurred can be overcome. (e) It is likely that only those who feel passionately about the proposal would respond. 6.For which of the following purposes would it be most unreasonable to use a census?(a) To determine the proportion of students with a learning disability in a small rural are high school.(b) To determine the proportion of red snappers with a high mercury level in the Gulf of Mexico.(c) To determine the difference between the proportion of engineering professors and the proportion of business professors in favor of a new teaching initiative at a large university.(d) To determine the mean wage earned by construction workers in a small town.(e) To determine the mean selling price of houses in your neighborhood.7. Gallup conducts its polls by telephone, so people without phones are always excluded from the Gallup sample. What type of nonsampling error was commited?(a) nonresponse(b) response bias(c) wording of questions(d) undercoverage8. A national retail chain wants to test-market a new product line: bed and bath accessories created by a nationally known clothing designer. The chain has approximately 1500 stores across the country. The locations of these stores are downtown in urban cities, are in suburban shopping malls, or are stand-alone stores in medium-size cities. The chain decides to randomly select 5% of its downtown stores, 10% of its suburban stores, and 5% of its small-city stores in which to test the product line. What type of sampling method did the retail chain use? (a) Simple random sample.(b) Systematic sample.(c) Convenience sample.(d) Cluster sample.(e) Stratified sample.9.Which of the following is not a source of bias in sample surveys?(a) non-response(b) wording of questions(c) voluntary response(d) use of a telephone survey(e) all are sources of bias ................
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