1 Problem Set 7 1. In a study of the effect of anxiety on the need for affiliation, participants were told either that they would either be giving a speech to a large audience of peers (high anxiety) or that they would be speaking to one experimenter (low anxiety). Subjects were then given a choice between waiting alone before speaking or waiting in the company of others. Below are the number of participants who chose to wait alone or with others in the high and low anxiety conditions. Test the null hypothesis that anxiety had no effect on whether people chose to wait alone or with others. (34 points) Alone With others High anxiety 14 20 a. Research Problem b. Statistical Hypotheses c. Decision Rule d. Calculations e. Decision f. Interpretation Low anxiety 21 10 2 2. A purple skittles lover is interested in knowing whether skittle colors are equally distributed in each bag. They open up a bag of skittles and count each color. Their data are below. Test the null hypothesis that the probability of getting any color is equal. (34 points) Red 8 Orange 7 a. Research Problem b. Statistical Hypotheses c. Decision Rule d. Calculations e. Decision f. Interpretation Yellow 12 Green 14 Purple 9 3 For each of the following questions, please specify what statistical test should be used. The correct answer can be any test that we covered this semester from correlation through chi square. (4 points each) 3. In a test of the decay theory of memory, participants memorized a list of nonsense syllables and were tested for recall after one hour and then four hours. What statistical test should be used to test the null hypothesis that delay had no effect on their recall scores? 4. Researchers are interested in whether the way instructions are delivered to jurors affects their decision making. They have two groups. In one group the jurors are verbally given instructions from the judge. In the second group the jury is given written instructions to read. What test would the researchers use to test the null hypothesis that how the instructions are given does not affect the jury’s decision making process? 5. A teacher thinks that she has an especially gifted class. She wants to compare their standardized test scores to those for the entire population of 4th graders. She knows that district wide the average exam score was a 430 with a standard deviation of 12. Her class of 18 students scored a 495. What test would you use to test the null hypothesis that her class did not do score higher than the rest of the district? 6. An experimenter is interested in testing whether listening to music improves learning how to solve complex equations. She has a control group complete a learning task without music and then an experimental group that listens to current popular music while completing the same task. What test would you use to test the null hypothesis that music does not have an effect on learning? 7. A professor believes there is a relationship between attendance and test scores. What test would she use to test the null hypothesis that there is no link between attendance and performance on a test? 8. Administration at a university believe that students who live on campus during the semester have higher levels of satisfaction with their experience at the university than students living in different off campus options. They sample 20 students who live on campus, 20 who live with roommates in off campus housing, and 20 who live at home with their families while attending classes, and then measure their satisfaction with their experience as students at the university. What test would the researchers use to test their hypothesis about student satisfaction? 9. The director of a juvenile drug rehabilitation center wants to see how their relapse rates compare to the state average. She knows the state average, but does not know the standard deviation for the state’s relapse rate. What test would she use to test the null hypothesis that her facility does not differ from the state average? 10. The matching hypothesis states that partners in romantic relationships tend to be well matched for attractiveness. Researchers are interested in seeing if this hypothesis generalizes to same sex couples. The researchers collect pictures of the faces of both partners in 30 same sex relationships, and have a group of trained coders rate how attractive each partner is. What test would the researchers use to test the null hypothesis that there is no difference in the attractiveness of same sex partners? Problem Set 6 1. In an experiment designed to determine the effect of mood on perception of pain, subjects were induced to experience a good mood, a bad mood, or had no mood induction. Participants were then asked to rate the amount of pain they were currently experiencing. Below is a list of the pain ratings. Test the null hypothesis that mood has no effect on perception of pain. (35 points) Negative Mood Positive Mood Control Group 10 6 11 12 8 2 2 7 5 1 5 6 4 5 7 Research Problem: Is the perception of pain related to the experience of bad mood, good mood or no mood induction? Statistical Hypotheses: Null Hypothesis: Mood has no effect on the perception of pain µ1 = µ2 Alternative Hypothesis: Mood has a significant effect on the perception of pain µ1 ≠ µ2 Decision Rule: Reject the null hypothesis at the .05 level of significance if t is greater than or equal to 2.306 or less than or equal to -2.306, given 8 degrees of freedom. Use Jamovi to calculate the F value and post hoc tests if warranted. Copy and paste your outputs here or upload a separate file with your outputs to the assignment in Blackboard. Decision: t = -3.86 Since t < -2.306, Reject the null hypothesis Interpretation: 1 There is enough evidence to support the claim that mood has a significant effect on the perception of pain. 2 2. In a study of group productivity, participants worked alone or shared the responsibility for building widgets with one other, with three others, or with fifteen others. Below, are the data showing the number of widgets each group produced. Test the null hypothesis that group size had no effect on productivity. (35 points) Alone 9 10 12 9 Two-person group Four-person group 8 6 5 6 4 6 3 6 Sixteen-person group 5 8 3 6 Research Problem: Does group size affect productivity when building widgets? Statistical Hypotheses: Null Hypothesis: Group size has no effect on productivity µ1 = µ2 Alternative Hypothesis: Group size has a significant effect on productivity µ1 ≠ µ2 Decision Rule: Reject the null hypothesis at the .05 level of significance if t is greater than or equal to 3.182 or less than or equal to -3.182, given 3 degrees of freedom. Use Jamovi to calculate the F value and post hoc tests if warranted. Copy and paste your outputs here or upload a separate file with your outputs to the assignment in Blackboard. Decision: t = 3.00 Since t< 3.182, We Fail to Reject Null Hypothesis Interpretation: There is no enough evidence to support the claim that group size has a significant effect on productivity when building widgets. 3 3. Consider the following scores in an experiment involving three conditions; A B C 2 2 2 2 5 5 5 5 8 8 8 8 Without actually computing the sum of squares within, what must its value be? Why? (12 points) The sum of squares is 72. As evident from the table, the mean is 5. Values in conditions A and C deviate from the mean by a value of 3. Squaring the deviation we get 9. There are 8 values that deviate from the mean. Therefore, the sum of squares would be 9*8 = 72. 4. Insert the missing entries in the summary table for a one-way analysis of variance having three levels of the independent variable and n = 25. (Each answer is 3 points) Source SS df MS F Between 120 2 60 10.91 Within 121 22 5.5 Total 141 4
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