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Purdue PSY 20100 - Homework 11

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PSY 201 1Introduction to Statistics in Psychology: PSY 201Greg Francis, PhDDepartment of Psychological SciencesPsychological Sciences Building, Room 3174(765) 494-6934email: [email protected]://www1.psych.purdue.edu/∼gfrancis/Classes/PSY201/Homework 11Due: 8 November 2009Hand in your answers on a separate sheet of paper.(1) One sample has n1= 15 with s1= 10.7, and a second sample has n2= 15 with s2= 11.0.[Since the sample sizes are the same, you can assume homogeneity of variance.]a) Find the pooled variance for the two samples.b) Compute the estimated standard error for the sample mean difference.c) If the sample mean difference, X1− X2is 8 points, is this enough to indicate a significantdifference for a two-tailed test at the .05 level?d) If the sample mean difference, X1− X2is 12 points, is this enough to indicate a significantdifference for a two-tailed test at the .05 level?(2) Do you view a chocolate bar as delicious or as fattening? Your attitude may depend on yourgender. In a study of American college students, Rozin, Bauer and Catanese (2003) examined theimportance of food as a source of pleasure versus concerns about food associated with weight gainand health. The following results are similar to those obtained in the study. The scores are ameasure of concern about the negative aspects of eating.Males Femalesn = 6 n = 9X = 31 X = 45s = 9.9 s = 9.2Based on these results, is there a significant difference between the attitudes for males and forfemales? Use a two-tailed test with α = 0.05. Assume homogeneity of variance.(3) When people learn a new task, their performance usually improves when they are tested thenext day, but only if they get at least 6 hours of sleep (Stickgold, Whidbee, Schirmer, Patel, &Hobson, 2000). The following data demonstrate this phenomenon. The participants learned avisual discrimination task on one day, and then were tested on the task the following day. Half ofthe participants were allowed to have at least 6 hours of sleep and the other half were kept awakeall night. Is there a significant difference between the two conditions? Use a two-tailed test withα = 0.05. [Since the sample sizes are the same, you can assume homogeneity of variance.]6-hours Sleep No Sleepn = 8 n = 8X = 72 X = 61s = 7.93 s = 8.07PSY 201 2(4) An automobile manufacturer wants to know if its new model has better gasoline performancethan the old model. A random sample of 30 new-model cars is selected, and the gasoline perfor-mance is determined. These data are then compared with data on 25 randomly selected old-modelautomobiles. The means and variances are given in the table:Old model New modeln = 25 n = 30X = 52 X = 56s2= 220 s2= 210a) Test the homogeneity of variance assumption. What is the conclusion about this assumption?Use α = 0.10.b) Test the null hypothesis H0: µ1− µ2= 0 against Ha: µ1< µ2. Use α = 0.05. What do youconclude about the gas mileage of the different models?(5) Given the following pairs of sample variances from independent samples, test the homogeneityof variance assumption for each pair. Use α = 0.10.a) s21= 80.6, s22= 23.0, n1= 21, n2= 10.b) s21= 50, s22= 100, n1= 19, n2= 43.c) s21= 90.6, s22= 25.3, n1= 61, n2= 16.(6) In 1974, Loftus and Palmer conducted a classic study demonstrating how language used toask a question can influence eyewitness memory. In the study, college students watched a filmof an automobile accident and then were asked questions about what they saw. One group wasasked, “About how fast were the cars going when they smashed into each other?” Another groupwas asked the same question except the verb was changed to “hit” instead of “smashed into.”The “smashed into” group reported significantly higher estimates of speed than the “hit” group.Suppose a researcher repeats this study with a sample of today’s college students and obtains thefollowing results with means of estimated speeds.Smashed into Hitn = 15 n = 18X = 40.8 X = 34.0s = 6.04 s = 5.44a) Test the homogeneity of variance assumption. What is the conclusion about this assumption?Use α = 0.10.b) Do the results indicate a significantly higher mean for the “smashed into” group? Use aone-tailed test with α = 0.01.PSY 201 3(7) Two random, independent samples of high school seniors are selected and administered amathematics exam. The information abut the samples and the test scores is as follows.Group 1 Group 2n = 41 n = 50X = 70.0 X = 62.1s2= 200 s2= 220a) Test the homogeneity of variance assumption. What is the conclusion about this assumption?Use α = 0.10.b) Test the null hypothesis H0: µ1− µ2= 0 against Ha: µ1− µ26= 0. Use α = 0.1.(8) The stimulant Ritalin has been shown to increase attention span and improve academic perfor-mance in children with ADHD (Evans et al., 2001). To demonstrate the effectiveness of the drug, aresearcher selects a sample of n = 25 children diagnosed with the disorder and measures each child’sattention span before and after taking the drug. The data show an average increase of attentionspan of X1− X2= 6.8 minutes and a standard deviation of sd= 5.5. Is this result sufficient toconclude that Ritalin has a significant effect on attention span? Test H0: δ = 0 against Ha: δ 6= 0with α = 0.01.(9) Eagly et al. (1991) reported that physically attractive people are also perceived as being moreintelligent. As a demonstration of this phenomenon, a researcher obtained a set of 10 photographs, 5showing men who were judged to be attractive and 5 showing men who were judged as unattractive.The photographs were shown to a sample of n = 25 college students and the students were askedto rate the intelligence of the person in the photo on a scale from 1 to 10. For each student, theresearcher determined the average rating for the 5 attractive photos and the average for the 5unattractive photos, and then computed the difference between the scores. For the entire sample,the average difference was X1− X2= 2.7 (attractive photos rated higher) with sd= 2.0. Are thedata sufficient to conclude that there was a significant difference in perceived intelligence for thetwo sets of photos? Use a two-tailed test with α = 0.05.PSY 201 4(10) One of the primary advantages of a repeated-measures design compared to independent-measures, is that it reduces the overall variability by removing variance caused by individual dif-ferences. The following data are from a research study comparing two treatment conditions.Treatment


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