Exercise 4.2 #83-89 Exercise 4.3 #94,96

CHAPTER 4 COLLECTING DATA 308 Inference about a population requires that the individuals taking part in a study be randomly selected from the population. A well-designed experiment that randomly assigns experimental units to treatments allows inference about cause and effect. In the absence of an experiment, good evidence of causation requires a strong association that appears consistently in many studies, a clear explanation for the alleged causal link, and careful examination of other variables. Studies involving humans must be screened in advance by an institutional review board. All participants must give their informed consent before take ing part. Any information about the individuals in the study must be kept confidential. Section 4.3 Exercises 93. Tweet, tweet! What proportion of students at your in the sample, 24% were white. The margin of error for pg 299 school use Twitter? To find out, you survey a simple this estimate is 3.0 percentage points. random sample of students from the school roster. (a) Would you be surprised if a census revealed that 26% a) Will your sample result be exactly the same as the true of cars on I-195 in Miami on a weekday morning were population proportion? Explain your answer. white? Explain your answer. (b) Which would be more likely to produce a sample (b) Explain how the traffic analyst could decrease the result closer to the true population value: an SRS of margin of error. 50 students or an SRS of 100 students? Explain your 97. Kissing the right way According to a newspaper arti- answer. cle, "Most people are kissing the 'right way." That is, 94. Far from home? A researcher wants to estimate the according to a study, the majority of couples prefer to average distance that students at a large community tilt their heads to the right when kissing. In the study, a college live from campus. To find out, she surveys a researcher observed a random sample of 124 kissing cou- simple random sample of students from the registrar's database. ples and found that 83/124 (66.9%) of the couples tilted to the right. To determine if these data provide con- (a) Will the researcher's sample result be exactly the same vincing evidence that couples are more likely to tilt their as the true population mean? Explain your answer. heads to the right, 100 simulated SRSs were selected. (b) Which would be more likely to produce a sample result closer to the true population value: an SRS of 100 Each dot in the graph shows the number of couples students or an SRS of 50 students? Explain your answer. that tilt to the right in a simulated SRS of 124 couples, assuming that each couple has a 50% chance of tilting 95. Football on TV A Gallup poll conducted telephone to the right. interviews with a random sample of 1000 adults aged 18 and older. Of these, 37% said that football is their favorite sport to watch on television. The margin of error for this estimate is 3. 1 percentage points. (a) Would you be surprised if a census revealed that 50% of adults in the population would say their favorite 45 48 51 sport to watch on TV is football? Explain your answer. 54 57 60 72 (b) Explain how Gallup could decrease the margin of Simulated number of couples who tilt to the right 63 66 69 error. (a) Explain how the graph illustrates the concept of sam- 96. Car colors in Miami Using a webcam, a traffic analyst pling variability. selected a random sample of 800 cars traveling on 1-195 in Miami on a weekday morning. Among the 800 cars (b) Based on the data from the study and the results of the simulation, is there convincing evidence that couples prefer to kiss the "right way"? Explain your answer296 CHAPTER 4 COLLECTING DATA wood chips, pine needles, plastic) to determine which Multiple Choice Select the best answer for Exercises 83-90. combination produces the highest yield for a variety of 83. Can a vegetarian or low-salt diet reduce blood pressure? green beans. He has 60 green-bean plants to use in the Men with high blood pressure are assigned at random experiment. If he wants an equal number of plants to to one of four diets: (1) normal diet with unrestricted be assigned to each treatment, how many plants will be salt; (2) vegetarian with unrestricted salt; (3) normal assigned to each treatment? with restricted salt; and (4) vegetarian with restricted ( b ) 3 ( c ) 4 salt. This experiment has (a) I (d) 5 (e) 12 (a) one factor, the type of diet. (b) two factors, high blood pressure and type of diet. 87. Corn variety 1 yielded 140 bushels per acre last year at a research farm. This year, corn variety 2, planted in (c) two factors, normal/vegetarian diet and unrestricted/ the same location, yielded only 1 10 bushels per acre. restricted salt. Based on these results, is it reasonable to conclude that (d) three factors, men, high blood pressure, and type of diet. corn variety 1 is more productive than corn variety 2? (e) four factors, the four diets being compared. (a) Yes, because 140 bushels per acre is greater than 1 10 84. In the experiment of the preceding exercise, the bushels per acre. subjects were randomly assigned to the different (b) Yes, because the study was done at a research farm. treatments. What is the most important reason for this (c) No, because there may be other differences between random assignment? the two years besides the corn variety. (a) Random assignment eliminates the effects of other variables such as stress and body weight. (d) No, because there was no use of a placebo in the experiment. (b) Random assignment balances the effects of other variables such as stress and body weight among the four (e) No, because the experiment wasn't double-blind. treatment groups. 88. A report in a medical journal notes that the risk of (c) Random assignment makes it possible to make a developing Alzheimer's disease among subjects who conclusion about all men. regularly opted to take the drug ibuprofen was about (d) Random assignment reduces the amount of variation half the risk of those who did not. Is this good evidence in blood pressure. that ibuprofen is effective in preventing Alzheimer's disease? (e) Random assignment prevents the placebo effect from ruining the results of the study. (a) Yes, because the study was a randomized, comparative experiment. 85. To investigate if standing up while studying affects per- formance in an algebra class, a teacher assigns half of (b) No, because the effect of ibuprofen is confounded with the 30 students in his class to stand up while studying the placebo effect. and assigns the other half to not stand up while study- ing. To determine who receives which treatment, the (c) Yes, because the results were published in a reputable teacher identifies the two students who did best on the professional journal. last exam and randomly assigns one to stand and one to (d) No, because this is an observational study. An not stand. The teacher does the same for the next two experiment would be needed to confirm (or not highest-scoring students and continues in this manner confirm) the observed effect. until each student is assigned a treatment. Which of the following best describes this plan? chance. (e) Yes, because a 50% reduction can't happen just by (a) This is an observational study. (b) This is an experiment with blocking. 89. A farmer is conducting an exp which variety of apple tree, Fuji or Gala, will produce (c) This is a completely randomized experiment. more fruit in his orchard. 20 equally sized square plots. He had red is divided into (d) This is a stratified random sample. es of each (e) This is a systematic random sample. variety and randomly assigns each tree to a separate plot in the orchard. What are the experimental unitis in this study? 86. A gardener wants to try different combinations of fertilizer (none, 1 cup, 2 cups) and mulch (none, (a) The trees (d) The farmer (b) The plots (c) The apples (e) The orchard