Macmillan Learning Stacked The Graduate Management Admission Test (GMAT) is taken by individuals interested in pursuing graduate management education. GMAT scores are used as part of the admissions process for more than 6000 graduate management programs worldwide. The mean sore for all test takers is 563, with a standard deviation of 118. A researcher in the Philippines is concerned about the performance of undergraduates in the Philippines on the GMAT. She believes that the mean scores for this year's college seniors in the Philippines who are interested in pursuing graduate management education will be less than 563. She has a random sample of 250 college seniors in the Philippines interested in pursuing graduate management education that take the GMAT. Suppose we know that GMAT scores are Normally distributed with standard deviation o= 118. The null and alternative hypotheses are Ho: μ = 563 versus Ha: μ< 563. Data on scores on the GMAT can be found at www.gmac. com/gmat/learn-about-the-gmat-exam, www.gmac.com/gmat-other-assessments/ accessing-gmat- exam-scores-and-reports/gmat-scoring-by-exam-section-normal-view, and www.gmac.com/market-intelligence-and-research/assessment-data/ about-the- geographic-trend-reports. The mean and standard deviation for the GMAT scores is based on data from 2015-2018 and is based on the results of 739, 752 tests. Another sample of 250 students had x = 540. Use the applet to find the P-value for this outcome. Give your answer to four decimal places. Ⓒ P-value:

A psychologist has designed an index to measure the social perspectives of elementary school children.  The index is based on ratings of a child’s responses to questions about a set of photographs showing different social situations.  The following are the indices measured on a random sample of 16 children attending elementary school in a particular district. 48, 75, 69, 58, 60, 68, 59, 66, 71, 52, 49, 60, 54, 55, 70, 57   For the data the mean index is 60.69 and the standard deviation is 8.26. Perform a statistical test to determine if the population mean index is greater than 50. a) Name of hypothesis test:   b) H0:   c) HA:   d) Test Statistic:   e) Rejection region:   f) Decision in the context of the problem:

Secretary of State Roxana Tillerson is worried about malpractice at the 4 processing centers for Green Cards in the country. Green Card applications are given a grade g on a scale 0-100. They are assigned randomly to different centers and thus Tillerson expects all centers to have similar mean scores. She collects the data in the table. #applications 9360 67.27 15.29 1 9870 66.74 14.64 7020 66.94 15.14 3 5040 67.02 14.84 4 rows x 3 columns At this point she just wants to decide whether or not to initiate a deeper investigation into malpractice at all sites. Does she have sufficient evidence for this, at 6% significance? SSTT number (rtol=0.01, atol=0.0001) SSE number (rtol=0.01, atol=0.0001) F. number (rtol=0.01, atol=0.0001) P-val number (rtol=0.01, atol=0.0001) O (a) No, she cannot make a conclusion O (b) Yes, she has enough evidence Select the key assumptions in the test you used. O (a) The populations are independent and therefore their covariances are zero. O (b) All sample sizes…

In a small company, the median salary is significantly lower than the mean salary. What does this indicate about the salary distribution in the company? What might be some possible reasons for this pattern?