A psychologist is interested in people\'s views on various crimes. She has produ

Question

A psychologist is interested in people's views on various crimes. She has produced videotaped re enactments of four different, non-violent crimes -jewelry theft, credit card fraud, embezzlement, and tax evasion and has asked viewers to give the length of the prison sentence (in months) the perpetrator should get as punishment. The psychologist is looking at differences in the perceived seriousness of the crimes and also at whether there is an influence of the viewer's self-reported political position as conservative or liberal She randomly selected 80 conservatives and 80 liberals. She divided the conservatives at random into four groups of 20. For each crime, she had a different group of conservatives watch the re-enactment. She did the same for the liberals. After collecting the participants' prison sentence judgments, she computed the group mean judgment for each of the eight groups. These means are shown in the graph below 24 23 21 20 18 ewelry Credit card Embezzlement Tax theft fraud evasion After checking that the assumptions for the test were satisfied, the psychologist performed a two-way ANOVA test. (The dependent variable was prisonn sentence judgment, and the factors were politicaí position and type of crime.) Her partially filled ANOVA table is shown below. Complete the table, and then answer the questions after the table. Do not round any values in the table except the F statistic values, which you should round to at least three decimal places Source of Degrees ofSum of freedom Mean F statistic varation squares Political 44.1 Type of 45.9 15.3 1287 Interaction 32.3 1807.65 11.892 Total 159 2029.95 At the 0.05 significance level, what is the critical value for the test for an interaction between the two factors? Round to at least three decimal At the 0.05 significance level, can the psychologist conclude that there is an interaction O No If your response above was No, answer the following: At the 0.05 level, for which factor(s) can the psychologist conclude that there is a significant main effect? Political o Type of crime Both Neither

Explanation / Answer

From the given data

Correct answer: 3.9033

Correct answer: option (A) YES

ANOVA Table Source df Sum of square Mean Square F-ratio F-critical P-value Political 1 44.1 44.1 3.708251 3.903366 0.056 Type Crime 3 45.9 15.3 1.286536 2.664107 0.2811 Interaction 3 132.3 44.1 3.708251 2.664107 0.013 Error 152 1807.65 11.8924 Total 159 2029.95

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