stats hw review

Directions: The purpose of Project 8 is to prepare you for the final, comprehensive exam and is set up EXACTLY the same. Questions 1 and 2 are not graded in this exercise, but are on the final. Be sure to answer them still so you can receive feedback. Once done with these, move into the calculation questions. Be advised that you will need to decide which type of test to use in most of the problems. Please write out all pertinent information for each of the 4 steps of hypothesis testing. For the calculations, you only need to provide the values of all statistics for that test. There is no need to show work.List the four Steps of the Hypothesis test:Step 1 –Step 2 –Step 3 –Step 4 –This semester we have discussed the following statistical analyses.Z-test               One-Sample t-test                    Independent Groups t-test                   Repeated Measures t-testOne-Way ANOVA                 Repeated Measures ANOVA             CorrelationWhen do you use them? Please type your answer in the Test Used column.ơ is givenµ is givenGroups ComparedTest UsedNoNoLooks at the same group at 2 different times or across two different conditionsYesYesSample against populationExamines the degree to which two variables relate to one anotherNoNoLooks at the same group at 2 or more times or across 2 or more conditionsNoNoExamines mean differences between two different groupsNoYesSample against populationNoNoExamines mean differences between 2 or more groups1. A researcher for a cereal company wanted to demonstrate the health benefits of eating oatmeal. A sample of 9 volunteers was obtained and each participant ate a fixed diet without any oatmeal for 30 days. At the end of the 30-day period, cholesterol was measured for each individual. Then the participants began a second 30-day period in which they repeated exactly the same diet except that they added 2 cups of oatmeal each day. After the second 30-day period, cholesterol levels were measured again and the researcher recorded the difference between the two scores for each participant. For this sample, cholesterol scores average M = 16 points lower with the oatmeal diet with SS = 538 for the difference scores.                                                      10 points·      Are the data sufficient to indicate a significant change in cholesterol level? Use a two-tailed test with α = .01.·      Compute r2 to measure the size of the treatment effect.2. One possible explanation for why some birds migrate and others maintain year round residency in a single location is intelligence. Specifically, birds with smaller brain, relative to their body size, are not simply smart enough to find food during the winter and must migrate to warmer climates where food is easily available. Birds with bigger brains, on the other hand, are more creative and can find food even when the weather turns harsh. Following are hypothetical data similar to the actual results. The numbers represent relative brain size for the individual birds in each sample.                                                                                                        10 pointsNon-MigratingShort-Distance MigrantsLong Distance Migrants1864131191975N = 181296G = 1801685ΣX2 = 215012137M = 15M = 9M = 6T = 90T = 54T = 36SS = 48SS = 34SS = 16·      Determine whether there are any significant differences among the three groups of birds.·      Compute the effect size for these data.3. In 1974, Loftus and Palmer conducted a classic study demonstrating how the 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 reportedly 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.                                                                                                                 10 pointsEstimated SpeedSmashed IntoHitn = 15n = 15M = 40.8M = 34.0SS = 510SS = 414·      Do the results indicate a significantly higher estimate for speed for the “smashed into” group? Use a one-tailed test with α = .01.·      Calculate the effect size.4. For the following set of scores, compute the Pearson correlation. Then, state whether or not you can reject the null hypothesis assuming a one-tailed test with α = .05.                                                                     10 pointsXY6431506742645. In a study examining the effect of alcohol on reaction time, researchers found that even moderate alcohol consumption significantly slowed response time to an emergency situation in a driving simulation. In a similar study, researchers measured reaction 30 minutes after participants consumed one 6-ounce glass of wine. Again, they used a standardized driving simulation task for which the regular population averages u = 400 msec. The distribution of reaction times is approximately normal with σ = 40. Assume that the researcher obtained a sample mean of M = 422 for the n = 25 participants in the study.                                                          5 points·      Are the data sufficient to conclude that the alcohol has a significant effect on reaction time? Use a two-tailed test with α = .05.·      Do the data provide evidence that the alcohol significantly increased (slowed) reaction time? Use a one-tailed test with α = .05.·      Compute Cohen’s d to estimate the size of the effect.6. The following data are from an experiment comparing three different treatment conditions for each of 5 people (i.e. each person was exposed to condition A, B, and C during the study):                                10 pointsABC012255N = 15126549ΣX2 = 354288T = 10T = 20T = 30SS = 14SS = 30SS = 30·      Using an α = .05, determine whether there are significant mean differences among the three conditions.·      Computer the effect size for the study.7. Researchers report that students who were given questions to be answered while studying new material had better scores when tested on the material compared to students who were simply given an opportunity to reread the material. In a similar study, an instructor in a large psychology class gave one group of students questions to be answered while studying for the final exam. The overall average for the exam was µ = 73.4, but the n = 16 students who answered questions had a mean of M = 78.3 with a standard deviation of s = 8.4. For this study, did answering           questions while studying produce significantly higher exam scores? Use a one-tailed test with    α = .01.                                                                                                                                             5 pointsExtra CreditComplete the following ANOVA summary table.                                                                              2 pointsn = 6;   k = 4SourceSSDfMSFBetween60WithinBetween SubjectsError14Total122For the following test statistics that you obtained in Step 3 of the Hypothesis test, state whether the score falls in the critical region or not. Note that to receive credit for these problems you MUST give the critical value you used to make your decision in the appropriate column. No calculations are needed for this question. I want you to demonstrate that you know how to use the tables and understand how to make a correct decision.                                          2 pointsTest Statistic ObtainedInformation needed to determine Critical valuesCritical Value from the appropriate tableShould you RETAIN or REJECT the null by stating either word.z = +2.65α = .05; two=tailedt = +3.15α = .01, two-tailed; df = 3r = .619α = .01, one-tailed; df =14Examine the following decisions researchers have made about their experiments. Was the correct decision made? If not, did they commit Type I or Type II error? You may want to check to make sure they looked up the correct critical value first.                                                                                                                                      2 pointsTest Statistic Obtained by the ResearcherCritical Value He/She Looked UpThe Decision They MadeIs the decision correct?If not, did they make a Type I or Type II error. You cannot answer no without indicating which type of error first.t = 1.95α = .05, one-tailed; df = 19tcrit = 1.729Retain the null orFail to reject the nullF (4,10) = 5.86, α = .01Fcrit = 5.99Reject the nullEnd Project 8:Remember that Exam 5 will look exactly like this. Use it to prepare and do other practice problems from each chapter.

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