EXAM 3 NAME Multiple Choice (2 points each) Provide your responses on the Datalink sheet 1. Which of the following statements is the most correct comparison between the Z and t distributions? a. The two distributions are exactly the same b. The Z distribution have fatter tails than the t distribution c. The t distribution is a family of distributions based on df, whereas Z is just one distribution d. The Z distribution is a family of distributions based on df, whereas t is just one distribution 2. In what situation would you use an independent samples t test? a. When you are comparing a sample mean to a known population mean prior to treatment b. When you are comparing two separate sample means c. When you have a repeated-measures research design d. When you have measured participants twice and comparing difference scores 3. What exactly do confidence intervals represent? a. A measure of effect size indicating with a certain percentage how confident we are that the true population mean is between two values b. A measure of effect size that indicates the amount of variability in scores that can be accounted for by the treatment c. A measure of effect size that indicates how strong an effect is based on the size of a mean difference in standard deviation units d. A measure of effect size that indicates a strong correlation between the independent variable and the dependent variable 4. What is an assumption to the independent sample's / test that requires an adjusted degrees of freedom if the assumption is violated? a. Normally distributed populations b. Independent observations c. Homoscedasticity d. Homogeneity of variance 5. Which of the following addresses an advantage of using repeated-measures designs? a. Variability is reduced b. Can look at changes over time c. Increased power d. All of the above End of Multiple Choice Section. Proceed to the computational questions below.6. A researcher named Yi, a master of meditation, hypothesized that meditation could help reduce people's perception of pain. Yi performed an experiment using the cold presser task in which participants submerge their hand in ice cold water. Longer amounts of time keeping their hands submerged under the ice water would indicate higher tolerance for pain. Master Yi randomly assigned participants for his study for two conditions: Control, in which they simply put their hand in the ice cold water for as long as they can stand; and Meditative Breathing, in which Master Yi taught the participants meditative breathing exercises and had them use this during the cold presser task. Yi yielded the results in seconds for how long each group could keep their hands submerged in the cold water is provided below. This is a two-tailed test a = .05 Control: M= 64.1, SS = 5468, n = 10 Meditative Breather: M= 71.6, SS = 5724, n = 10 Using an independent samples t test, at a = .05 two-tailed, compute the values below: dfTotal = (2 points) Critical value for t from the / distribution table = (2 points) pooled variance sp- = (3 points) estimated standard error S(MI-M2) = (3 points) test statistic / = (3 points) What is the correct decision regarding the null hypothesis? (3 points) Write a summary statement regarding the results, addressing the treatment, measurement, direction/pattern of results, and significance. (4 points)7. Now assume that Master Yi actually completed a repeated measures design in which he had the same two treatment conditions listed in the above example. but tested this on a single sample of participants, in which they got the control condition first, simply submerging their hands in the cold water for as long as they can stand, and the meditative breathing condition second, in which Master Yi taught the participants meditative breathing exercises and had them use this during the cold presser task for the second measurement. The raw data for this study is exactly the same as in the previous example, except this time Yi can use a related samples / test to see if there are differences in pain tolerance between the two conditions. The results demonstrated that, on average, participants showed increased pain tolerance after they had learned and used meditative breathing, as indicated by the mean of the difference scores: MD = 8.4. SSD = 1004, n = 10 Using a related-samples / test, at a = .05 two-tailed, compute the values below: df = (2 points) Critical value for / from the / distribution table = (2 points) sample variance s = (3 points) estimated standard error SMD (3 points) test statistic 1 = (2 points) What is the correct decision regarding the null hypothesis? (2 points) Write a summary statement regarding the results, addressing the treatment, measurement, direction/pattern of results, and significance. (4 points)Compute a 95% Confidence Interval for the mean difference score in question 7. Include Upper and Lower Intervals (1 point each) Upper Interval Lower Interval Bonus questions From Question 6, Compute the 95% Confidence Intervals for the difference between the means in score. Include Upper and Lower Intervals (1 points each) Upper Interval Lower Interval Based on the confidence intervals calculated in the first bonus question. explain what the intervals mean for the results of Question 6 study (3 points)