A sample of 36 students was randomly divided into six groups. Each group was assigned to view one of six slides showing a person making a facial expression. The six expressions are listed in the table below. After viewing the slides, the students rated the degree of dominance they inferred from the facial expression (on a scale ranging from -10 to +15). The data are listed below. Using the given ANOVA table to conduct a test to determine whether the mean dominance ratings differ among the six facial expressions. Use α = 0.1. angry disgusted fearful happy sad neutral 2.1 0.4 0.82 1.71 0.74 1.69 0.64 0.73 -2.93 -0.04 -1.26 -0.6 0.47 -0.07 -0.74 1.04 -2.27 0.55 0.37 -0.25 0.79 1.44 -0.39 0.27 1.62 0.89 -0.77 1.37 -2.65 0.57 -0.08 1.93 -1.6 0.59 -0.44 -2.16
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6. RUNNING R CODES The simulated data set below is based on an experiment reported in the Journal of Nonverbal Behavior (Fall 1996). A sample of 36 introductory psychology students was randomly divided into six groups. Each was asked to view one of six slides showing a person making either an angry, disgusted, fearful, happy, sad, or neutral face. After viewing the slides the students rated the degree of dominance they inferred from the facial expression (a higher score indicating more dominance). Angry 2.10 Angry 0.64 Angry 0.47 Angry 0.37 Angry 1.62 Angry -0.08 Disg 0.40 Disg 0.73 Disg -0.07 Disg -0.25 Disg 0.89 Disg 1.93 Fear 0.82 Fear -2.93 Fear -0.74 Fear 0.79 Fear -0.77 Fear -1.60 Happy 1.71 Happy -0.04 Happy 1.04 Happy 1.44 Happy 1.37 Happy 0.59 Sad 0.74 Sad -1.26 Sad -2.27 Sad -0.39 Sad -2.65 Sad -0.44 Neut 1.69 Neut -0.60 Neut -0.55 Neut 0.27 Neut -0.57 Neut -2.16 a) Write down the equation of the one-way ANOVA model that is described by this set-up. Be sure to clearly identify each parameter and the sample sizes. b) Check that the assumptions for performing a one-way ANOVA hold, including using Levene's test. c) What hypothesis is being tested by the F-statistic in the ANOVA table? Carefully state your conclusion at the α=0.05 level. d) Use the Tukey's multiple comparison procedure with an experiment-wise (family-wise) αT=0.05 level to test all of the pairwise differences, and make a display showing the ranking in which the different facial expressions reflect dominance. e) Use a contrast to make a 95% confidence interval for the difference in dominance between the average of the two strong negative emotions (Angry and Disgusted) and the positive emotion (Happy). Be sure to be clear about what the sign of the values in your interval means about the emotions (e.g. does a positive value mean negative emotions were more dominant or less dominant?). Use t .025 = 2.042.
Shaiju T.
Extra Practice: An experiment compares the leniency scores assigned to students charged with a disciplinary infraction in which subjects are shown a picture of the alleged wrongdoer randomly selected to show either a smiling or a neutral pose. A sample of n=34 that were smiling had a mean leniency score of 4.91 with standard deviation 1.68. A sample of n=34 with neutral poses had a mean leniency score of 4.12 with standard deviation 1.52. Test whether the mean leniency score for smiling students is higher than the mean score for students with a neutral expression. a). State the hypotheses using relevant parameters. b). Give notation and calculate the difference in sample means. c). Calculate the standard error. d). Calculate the t-test statistic. e). Using the t-distribution, we find a p-value = 0.025, but what are the degrees of freedom? df =_______ f). Use a 5% level. What generic conclusion do we make about the null hypothesis? g). State the conclusion of the test in the context of the situation.
Lucas F.
In a study to determine whether counseling could help people lose weight, a sample of people experienced a group-based behavioral intervention which involved weekly meetings with a trained interventionist for a period of six months. The following data are the numbers of pounds lost for 14 people. Assume the population is approximately normal. Perform a hypothesis test to determine whether the mean weight loss is greater than 20 pounds. Use the a=0.10 level of significance and the P-value method with the TI-84 Plus calculator: 22.5, 28.5, 7.6, 24.1, 21.5, 12.9, 17.3, 21.2, 37.6, 33.8, 12.1, 36.3, 24.1, 19.4. Part 1 of 4: (a) State the appropriate null and alternate hypotheses. H0: μ = 20 H1: μ > 20 This hypothesis test is a right-tailed test. Part 2 of 4: (b) Compute the P-value. Round the answer to at least four decimal places. P-value =
Supreeta N.
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