A researcher is studying the impact of "daylight shifting" (Group 1 (treatment): waking up and being active 1 hour early; Group 2 (control): normal waking and activity time) on cognitive performance. A sample of participants is recruited and each person is randomly assigned to either the treatment or control group. The following data are obtained for each participant on a test of visual working memory (how many shapes a person can recall after briefly being exposed to those shapes):

GROUP 1 (TREATMENT) GROUP 2 (CONTROL) 4 5 6 5 3 3 2 4 2 8 3 3 2 Missing 4 5 M1 = 3.2500 M2 = 4.7143 n: = 8 \"2 = 7 $51 = 13.5000 552 = 17.4285 52 = 1.9268 52 = 2.9048 Follow the steps below to test the null and alternative hypotheses with a t-test. a. Ifthe research hypothesis is that daylight shifting will impact visual working memory, state the null (H0) and alternative (H1) hypotheses in both words and symbols. Use a \"two-tailed\" (non-directional} test, with a 5% Type I error rate. (5 points) b. Determine dfmm; and tcritical for the research study. (2 points) c. Calculate each of the following for the dataset. Clearly show your work for each calculation. (7 points) dfl and dfz sz SMI-M2 tobserved d. Based on these data, what decision should the researcher make about the null hypothesis and why? (2 points) e. Calculate and interpret a measure of effect size for the data (report your answer to 3 decimal places}. (2 points) f. If in reality there is an effect of daylight shifting in the population (i.e., the null hypothesis is false), did the researcher make a correct decision, Type I error, or Type II error? (1 point)