Complete problems 2, 4, 14, 18, and 20 on pages 254257 of your text.Use Word to record your answers. For problems which require calculations please show your work in order to receive full credit. Please copy and paste the SPSS output into Word as well as write out the answers for the question which calls for SPSS use. Please show all work done in IBM SPSS thank youPage 254 Problem # 2Given: independent samples with Sy = 10. (a) Calculate Sx y from formula 14. 2b, assuming nx = ny = 30. (b) Recalculate Compare the two values of y. What principle does this outcome illustrate?Page 255 Problem # 4You are given the following scores from two randomly drawn independent samples:X: 6,7,8,8,11 Y: 3,4,4,7,7(a)State formally the hypotheses necessary to conduct a non directional test of no difference between the two population means. (b) Complete the test at the .05 abd .01 levels of significance, and state your conclusions.Page 257 Problem # 14In reference to Problem 13, what should the sample size be if the psychologist feels that: (a) She should choose power = .80? (b) Is it important to know whether the difference between the means is .15 grade point (or More) and power = .95?Writer Question # 13 Information is needed for Question 14.A psychologist wonders whether mid semester warning notices affect performance. She decides to select a sample of delinquent students and, at random, to send such notices to half of them and no notices to the other half. Experience suggest that among such delinquent students, GPA = .30. She decides to adopt = .05 and power = .95. If the difference between the warned and unwarned students is as great as .075 grade points, she would want to know it. (a) State the null hypothesis and th alternative hypothesis for a two tailed test. (b) What should the size of the sample be to test this null hypothesis? Use Cohens power curves.Page 257 Problem # 18Professor Smith wishes to compare the performance of students in her class on multiple choice and fill in the blank exams. She randomly chooses half the class for each test. If each test has a standard deviation of 10, what is the probability of detecting a true difference (of 5 points with a two-tailed test,Page 257 Problem # 20Self fulfilling prophecies refer to beliefs or expectations that can bring about enhanced (or impaired) performance. Research by Eden (2003) and his colleagues have demonstrated how self-fulfilling prophecies can affect actual job performance. For example, Eden and Zuk (1995) randomly assigned naval cadets to control and experimental condition, with those in the experimental condition led to believe that they could overcome seasickness and perform well even during rough seas. Their results showed that those in the experimental condition actually reported less seasickness and performed better than candets who were assigned to the control condition. Suppose you replicated their study. Below are performance scores from the experimental (X) and conrol (Y) conditions. (a) Use IBM SPSS to conduct a two-tailed hypothesis test with