PSY 201 1 Introduction to Statistics in Psychology PSY 201 Greg Francis PhD Department of Psychological Sciences Psychological Sciences Building Room 3174 765 494 6934 email gfrancis purdue edu http www1 psych purdue edu gfrancis Classes PSY201 Homework 11 Due 8 November 2009 Hand 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 X 1 X 2 is 8 points is this enough to indicate a significant difference for a two tailed test at the 05 level d If the sample mean difference X 1 X 2 is 12 points is this enough to indicate a significant difference 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 your gender In a study of American college students Rozin Bauer and Catanese 2003 examined the importance of food as a source of pleasure versus concerns about food associated with weight gain and health The following results are similar to those obtained in the study The scores are a measure of concern about the negative aspects of eating Males Females n 6 n 9 X 31 X 45 s 9 9 s 9 2 Based on these results is there a significant difference between the attitudes for males and for females Use a two tailed test with 0 05 Assume homogeneity of variance 3 When people learn a new task their performance usually improves when they are tested the next 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 a visual discrimination task on one day and then were tested on the task the following day Half of the participants were allowed to have at least 6 hours of sleep and the other half were kept awake all night Is there a significant difference between the two conditions Use a two tailed test with 0 05 Since the sample sizes are the same you can assume homogeneity of variance 6 hours Sleep No Sleep n 8 n 8 X 72 X 61 s 7 93 s 8 07 PSY 201 2 4 An automobile manufacturer wants to know if its new model has better gasoline performance than the old model A random sample of 30 new model cars is selected and the gasoline performance is determined These data are then compared with data on 25 randomly selected old model automobiles The means and variances are given in the table Old model New model n 25 n 30 X 52 X 56 s2 220 s2 210 a Test the homogeneity of variance assumption What is the conclusion about this assumption Use 0 10 b Test the null hypothesis H0 1 2 0 against Ha 1 2 Use 0 05 What do you conclude about the gas mileage of the different models 5 Given the following pairs of sample variances from independent samples test the homogeneity of variance assumption for each pair Use 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 to ask a question can influence eyewitness memory In the study college students watched a film of an automobile accident and then were asked questions about what they saw One group was asked About how fast were the cars going when they smashed into each other Another group was 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 the following results with means of estimated speeds Smashed into Hit n 15 n 18 X 40 8 X 34 0 s 6 04 s 5 44 a Test the homogeneity of variance assumption What is the conclusion about this assumption Use 0 10 b Do the results indicate a significantly higher mean for the smashed into group Use a one tailed test with 0 01 PSY 201 3 7 Two random independent samples of high school seniors are selected and administered a mathematics exam The information abut the samples and the test scores is as follows Group 1 Group 2 n 41 n 50 X 70 0 X 62 1 s2 200 s2 220 a Test the homogeneity of variance assumption What is the conclusion about this assumption Use 0 10 b Test the null hypothesis H0 1 2 0 against Ha 1 2 6 0 Use 0 1 8 The stimulant Ritalin has been shown to increase attention span and improve academic performance in children with ADHD Evans et al 2001 To demonstrate the effectiveness of the drug a researcher selects a sample of n 25 children diagnosed with the disorder and measures each child s attention span before and after taking the drug The data show an average increase of attention span of X 1 X 2 6 8 minutes and a standard deviation of sd 5 5 Is this result sufficient to conclude that Ritalin has a significant effect on attention span Test H0 0 against Ha 6 0 with 0 01 9 Eagly et al 1991 reported that physically attractive people are also perceived as being more intelligent As a demonstration of this phenomenon a researcher obtained a set of 10 photographs 5 showing 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 asked to rate the intelligence of the person in the photo on a scale from 1 to 10 For each student the researcher determined the average rating for the 5 attractive photos and the average for the 5 unattractive photos and then computed the difference between the scores For the entire sample the average difference was X 1 X 2 2 7 attractive photos rated higher with sd 2 0 Are the data sufficient to conclude that there was a significant difference in perceived intelligence for the two sets of photos Use a two tailed test with 0 05 PSY 201 4 10 One of the primary advantages of a repeated measures design compared to independentmeasures is that it reduces the overall variability by removing variance caused by individual differences The following data are from a research study comparing two treatment conditions Treatment 1 Treatment 2 Difference 10 13 3 12 12 0 8 10 2 6 10 4 5 6 1 7 9 2 n 6 n 6 n 6 X1 8 X 2 …