1. Describe what is measured by the estimated standard error (Sx̅) in the denominator of the t test. How is this different than Sx (the sample standard deviation of the x scores) 2. Single Sample...

1. Describe what is measured by the estimated standard error (Sx̅) in the denominator of the t test. How is this different than Sx (the sample standard deviation of the x scores) 2. Single Sample T-test Confidence Interval Questions a. For a two-tailed, single sample t test with n = 61 individuals in the study and alpha set to .05, what are the critical values? [0.5 points] b. What proportion of possible random samples are contained within the critical values stated above if the null hypothesis is true? In other words what proportion of true null values are in the area of rejection? [0.5 points] c. If the mean of a certain sample of n = 61 scores is x̅ = 15, and the standard error of x̅ is Sx̅ = 1.5 what two x values make up the 95% confidence interval around this sample score? [2 points] 3. One sample of n1 = 14 individuals (group 1) receive a drug therapy intervention for anxiety. The sum of the squared deviations for the anxiety scores of group 1 was SS1 = 180. Another group (group 2) of n2 = 11 individuals received a pet therapy treatment for anxiety and the sum of the squared deviations for their group SS2 = 120. a. What is the pooled variance (S2 pooled ) of these two samples? [1 points] b. What is the standard error of the difference between these two samples (Sxଵ̅− xଶ̅) [1 points] 4. A scientific paper reports an independent samples (aka 2 sample) t test with the statement: “t(334) = 2.54, p = .002”. a. Did the paper find a significant result according to the typical standards in psychology? [0.5 points] b. What was the sample size in the study? [0.5 points] 5. There is an adage that what does not kill us makes us stronger. Anecdotes from clinical therapists suggest there may be some truth to this, in that people with some history of overcoming adversity tend to have better coping skills. To test this a researcher wants to compare the resiliency of those who have a history of major negative life events (neg events) vs those who do not have a history of negative life events (no neg events). The researcher hypothesizes that there will be some difference in the resiliency of those who have a negative history vs those who don’t. If resiliency is not affected by a history of negative life events, there is no reason to expect that the two populations should differ in their resiliency.  The researcher collects two samples of nno neg events = 13 and nneg events = 12  She measures each sample’s resiliency scores using a questionnaire that ranges from 1(low resiliency) to 100 (high resiliency) and finds x̅no neg event = 76 and x̅neg event = 84  The sample sums of squared deviations for the two groups are SSno neg event = 140 and SSneg event = 260 a. Find the T value for this independent groups t test. [2 points] b. Find the critical value or values for this test[1 points] c. What do you conclude from this test? [1 points] d. Report the estimated Cohen’s D for this test. [1 points] 6. An education researcher is examining the effects of after-school programs that help elementary students with homework. She Hypothesizes that schools with an afterschool program will get higher grade averages than those without. The education researcher has access to two schools: Small Mountain Central (SMC) and Big Lake Elementary (BLE). She randomly selects Small mountain central to receive a pilot after school program. Big Lake Elementary has no current after school program and will serve as the control group. This researcher is clever and realizes that these two schools may not be perfectly equal comparisons. Checking before the study launches, she finds that on average students at Big Lake Elementary tend to get higher grades on average already, likely due in part to their larger budget.  Historyically, students at Big Lake Elementary get a class average about 5 points higher than those at small mountain central. Thus, even if after school programs have no effect, there should be an expected difference in grades of (μSMC - μBME) = -5.  Big mountain central has a class size of nbmc = 120 ; Small mountain central has a class size of nsmc = 100  After launching the afterschool program at Small Mountain Central, their average class grade was x̅smc = 84. That same year, Big mountain elementary had an average score of x̅bmc = 83  The pooled variance for the two samples is S2 pooled = 200. a. Report the t value for this test [2 points] b. Using a 1 tailed test with alpha set to .05, indicate whether this after school program results in a significant improvement above what we would expect for the cognitive therapy alone. If the degrees of freedom for this test do not appear exactly on the t critical value table, use the critical value for whatever listed degrees of freedom are closest [1 points] 7. How is a within subjects experiment different from a between subjects experiment? [1 points]