Name: . Blaine Nowak Date: 11/9/ 22 PSYC 3402 Take-home Exam 3 Part I: Determine the best hypothesis test to recommend for each scenario presented below. Use the following tests as recommendations: One sample z test, One sample / test, Independent samples t test, Dependent samples t test. (1 point each): 1) A study was performed to test whether cars get better mileage on premium gas than on regular gas. Each of 10 cars was first filled with either regular or premium gas, decided by a coin toss, and the mileage for that tank was recorded. The mileage was recorded again for the same cars using the other kind of gasoline. Dependent Samples t test 2) A researcher predicted that the Dunder Mifflin Paper Company makes more sales than the average paper company in the United States. To test this, the researcher collects the sales data from a small sample of 6 Dunder Mifflin employees and compares this to the national average of sales from similar paper companies. One Sample I test 3) The campus board wants to observe two groups of students who are going to be registering for classes to see if there's a difference in time efficiency between those who use an advisor before registering and those who don't. The first group of 10 students meets with an advisor before their registration. The second group of 10 students doesn't meet with an advisor before their registration. Did the students who met with an advisor before registering experience shorter registration times? Dependent Samples t-test 4) A study was performed to test eyewitness accuracy. Pairs of participants entered a room believing they would be participating in a gambling experiment. Each participant was given $10 in coins to play poker with. The participants were randomly seated near the door or away from the door. After 15 minutes, an actor dressed in street clothes burst into the room, and stole the money from the participant near the door. The "thief" was later caught, and both participants were asked to identify him in a line-up. Eyewitness accuracies from the participants were then compared. independent samples t- test 5) To test the effects of cartoons on cognitive functioning, a researcher assigns 15 children to watch 30 minutes of Spongebob Squarepants, and 15 more children to color for 30 minutes. The research then tests all children on the same cognitive functioning task. independent sampost test 6) A researcher who studies the amount of hours that students get a day wanted to know if college students who had an assignment due would sleep less than if they did not have any assignments due. The researcher picked 7 random students from the PSYC 3402 class and had them write down the amount of sleep they got (in hours) when they did not have an assignment due, and then the amount of sleep they got (in hours) when they were given an assignment, which had to be completed the same day it was given out. Dependent: Samples t test 7) A statistics student is curious about what kind of dessert to make for a family get-together, but can't decide between making a traditional dessert or a Greek dessert. She believes the traditional dessert will be liked better, but decides to use her newfound knowledge to determine if this is truly the case. She collects a group 23 of friends and neighbors to try the two desserts and determine which one is more preferred. First, the sample a chocolate cheesecake and then baklava. After trying each desert the friends and neighbors rate the dessert on a preference scale. t test 8) The average price for turnips in Animal Crossing: New Horizons is 95 bells (this distribution is not normal). Samantha believes that selling on Tuesday mornings will sell for more than average. To test this, she sells her turnips on Tuesday mornings for 20 weeks, noting the average price during this time. one sample 2 test 9) A dog breeding enthusiast argues that Chiweenie (Chihuahua dachshund hybrid) are the most adorable dogs. Her colleague claims that Pomsky (Pomeranian husky hybrids) are the cutest. To test this, they collect one sample to rate both dog breeds by cuteness. t test 10) A parakeet breeder believes that she raises healthier and longer-lived parakeets than those bought from pet stores. After contacting the pet stores to determine the average lifespan of store bought parakeets, she then determines the average lifespan of a sample of 18 of her own birds. testPart II: Free response For problems 11 through 15, Sele 1 1) What are the risks e risks associated with running the same test multiple times? Is there any way to calcula What is the associated error of running S tests using the standard alpha level? 12) What are the two types of independent variable manipulations? Describe each. Which test is appropriate for each type? How are degrees of freedom affected? 13) What are the three cases of the central limit theorem? What is the standard error of the mean? What is a sampling distribution? How is "Plinko" (or Pachinko, Quincunx, or the bean machine) related to the central limit theorem? 14) What is effect size? How is it related to hypothesis testing? How do we interpret effect sizes? Provide an example of an effect size technique to apply when only one sample is studied. What about two samples? 15) Explain who "Student," Fisher, and Pearson are. List one reason why each is important to statistics. Why did "Student" develop his distribution and test? Part III Hypothesis testing: For problems 16 through 22 select only three (3) problems to solve. For problems 16 through 21 please address the following (9 points each): . Please state the null and alternative hypotheses. Using an alpha level of .05, please test the null hypothesis (what is the appropriate test, what is the critical value?). Draw the rejection region. Calculate the test statistic State the conclusion you are entitled to draw as a result of this test. Calculate the effect size as appropriate for the hypothesis test used. 16) A researcher believes that table-top role-playing games (TTRPGs) can change creative intelligence through problem solving. To test this, the researcher recruits 5 participants from a university who have never played a TTRPG before and instructs them to play Dungeons and Dragons (D&D) weekly for two months. An experienced Game Master (GM) is recruited as a confederate for the participants. This confederate runs the campaign, and helps the participants understand the mechanics for the game. The participants are then tested using Sternberg's test for creative intelligence. Their data is compared to the population average of 100.5. Did D&D demonstrate a difference in creative intelligence (this question may be completed in Excel)? Was this difference meaningful? Participants Creative IQ: 96, 103, 113, 119, 129 17) An outbreak of Salmonella-related illness was attributed to ice cream produced at a certain factory: a) Scientists initially measured the level of Salmonella in 7 randomly sampled batches of ice cream. The average level (in MPN/g) was 0.698 with a standard deviation of 0.39. Is there evidence that the mean level of Salmonella in the ice cream is greater than the accepted population average of 0.37 MPN/g? b) After media outcry, a second sample was taken of 36 randomly sampled batches, with average level of 0.54 MPN/g. Is there evidence that this sample is greater than the accepted population average 0.37 and standard deviation of 0.32 MPN/g? 18)/A researcher believes that dogs will learn to do tricks for peanut butter more quickly than compared to Milkbones. The researcher selects a sample of dogs from a local animal training school, and randomly separates them into two groups. Sixteen dogs received peanut butter after completing a trick and took an average of 1 14 trials (SD = 17) to learn the trick, while the remaining 16 dogs took an average of 125 trials (SD = 21) with Milkbones to learn the trick. Is there evidence to support the researcher's prediction? Where these results meaningful? 19) A recent study on the effects of Tamiflu looked into whether the antiviral medication can reduce the duration of the flu or not. To test this, researchers selected sample of 32 individuals recently diagnosed with the flu. Sixteen of these individuals were given a placebo, and their average flu durations was 12.7 days (SD = 1.82). The remaining16 subjects were given Tamiflu, and their average flu duration was 1 1.4 days (SD - 1.63). Did Tamiflu make reduce the duration of the flu? What was the effect size for Tamiflu? 20) The video game speed running community has many different completion categories. Amongst them, tool- assisted speed runs use third party software to assist the player in completing a run. A new tool has been developed for Metroidvania style games. To test if this software is effective, a speed runner collects 5 of his peers to run an experiment. Each speed runner completes the game Castlevania: Symphony of the Night with a glitchless any % completion. They then repeat this game using the new tool. Did the tool improve the speed run time? Was the difference meaningful? Glitchless any % 35.2 Tool Assist 34.5 34.J 35.9 33.9 31.7 34.6 32.3 31.5 31.9 21) A researcher believes that the type of syndicated comedy may affect an individuals' humor style. To test this, the research begins a pilot study with 7 individuals. Each participant watches 4 hours of The Office and then takes the Multidimensional Sense of Humor Scale (this scale ranges from 4 to 96). Each participant then returns to the study one week later and watches 4 hours of Friends before taking the Multidimensional Sense of Humor Scale again. Did the type of show cause a difference in their humor scores? Does the difference matter? The Office Friends 76 69 73 61 55 59 88 80 43 47 62 52 54 46 22) A potent pugilist recently empowered his unarmed strike to deal increased damage. His adventuring ally, a mighty mage, also levelled up. Along with the rest of his companions, a braggadocios bard and refined rogue, the four adventurers decide to compare their damage output. Using the sample summary and t-test calculations, determine answer the following questions: a) Assuming a critical value of 2.145, which comparisons listed below are significant? (Hypothesis test step 4) b) State the test statistic for each significant comparison. C ) Determine the effect size for each comparison listed below d) What is the family wise error for this experiment, considering four t-tests were run? Pugilist Mage Bard Rogue t-tests Comparison Observed t-value Pugilist vs Mage t = 1.57786 Mean 12.4 15.5 10 8.2 Pugilist vs Bard t= 1.762135 SD 4.2 4.8 3. 5 13 Pugilist vs Rogue t= 2.894831 N 18 18 14 8 Mage vs Rogue t = 3.64772 Extra Credit (1 point each, maximum 2 points) 1) What is homogeneity of variance? How does it influence Student's t-test and Welch's t-test? 2) What is the strength and weakness of running t-tests? 3) What does it mean to defenestrate? 4) How is flat earth related to science denial