p.230, p 4In two separate studies, the actual difference between the means of a treated group and untreated group is 3 points.  However, in one study, the σ           is very large                                                                                  M1-M2     and so the 3 points is not found to be significant.   In the other study, the σ                                                                                                M1-M2is very small and so the 3 points id found to be significant.  What might have caused this big difference in the σ         for the two studies?                                  M1-M2p.231, p8In the study of the effect of a new drug on the alleviation of asthma symptoms, the σM for symptom relief in the patient group that received the new drug is 1.45, and the σM for symptom relief in the group that did not receive the new drug 1.22.  Calculate σ               M1-M2 p.241, p2A large furniture store stations salespeople near its entrance to greet customers and offer assistance in shopping.  The salespeople, who work commission basis, tell the customer their name and hand them a business card.  A psychologist thinks that the salesperson’s intrusiveness might cause customers to buy less furniture rather than more furniture.  She convinces the store’s management to let her study the issue.  Customers are randomly selected to either receive or not receive a salesperson’s offer assistance immediately on entering the store.  The amount of customers’ purchases are then logged as they leave the store.  Here is the data                                          Amount of Purchase, in U.S. DollarsImmediate Assistance                                               No Assistance Unless Requested0                                                                                                                           7612,274                                                                            00                                                                                                                            2,5920                                                                                                                            00                                                                                                                            1,037       362                                                                                 0      855                                                                       84       0                                                                                     0       0                                                                                     672       1,273                                                                              0 a.     What are the independent and dependent variables in this study?b.     State the null hypothesis and the directional (one-tailed) research hypothesis.c.      Calculate τand compare it with the tabled critical τ at the .01 and .05 α levels. Can you reject the null hypothesis?  p. 264, 4State whether the investigator used independent samples, repeated measures, or matched samples:a.     An investigator wants to know if elementary-age children who have experienced the death of a parent are helped by a counseling group consisting of other children who have experienced a death in the family. He randomly selects  children for this special counseling group, comparing their emotional adjustment at the beginning of treatment with their emotional adjustment following a year of the specialized group counseling.b.     An investigator wants to know if elementary-age children who have experienced the death of a parent are better helped by a counseling group consisting only of other children who have experienced a death in the family or by a counseling group consisting of children demonstrating a wide range of behavioral and emotional issues.  He randomly assigns children to the two groups and compares each group’s emotional adjustment following a year of group counseling. p. 271, p 7The following data are from a study of aggression in 40 children (20 pairs) after viewing either violent film or an educational film.  Participants were first matched on gender and their typical aggression level.  Here are participants’ scores on the aggression test given after viewing the film.  Higher scores indicate more aggression. Pair                                                     Violent Film                            Educational Film1                                                          26                                           182                                                          24                                           123                                                          18                                           144                                                          27                                           225                                                          19                                           136                                                          14                                           157                                                          24                                           208                                                          12                                           99                                                          21                                           1210                                                       15                                           1811                                                       11                                           712                                                       23                                           2713                                                       23                                           1414                                                       18                                           815                                                       17                                           2016                                                       12                                           1217                                                       25                                           1718                                                       28                                           2019                                                       13                                           1020                                                       22                                           14 Calculate t and compare it with the one-tailed critical t at the .01 a level.  Did the children who viewed the violent film show significantly more aggression? Two-Sample T TestThink about a study you would like to explore in our future or current career that could be analyze with a two-sample t test.  To help design the study, answering the following:             – Is it an independent group t test matched groups t test or repeated measures t test, and why?            – What is the independent variable?            – What is the dependent variable?             – What do you expect to find if you ran the study? List this out both in statistical language (feel free to make up some number for the results) as well as real-world language.