One Management professor adopted a crossword puzzle exercise in his introductory management information systems (MIS) class, because he believes that the most important effects of engaging in a crossword exercise is the great workout it gives one's brain- solving crossword puzzles requires several skills, such as spelling, reasoning, making inferences, evaluating choices, and drawing conclusions. That is, the exercise may enhance one's ability to memorize words. He wants to know whether or not the crossword puzzle can accelerate the learning of MIS vocabulary and terms. A total of 109 students in his two sections of MIS class in fall 2019 participated in an experiment involving students learning and retention of MIS terms using the group. one day about two weeks before the end of semester, students in the control group were given a list of terms taken from the text book used in the course; students in the experimental group were given a crossword puzzle exercise containing terms and phrases taken from the same text book and based on the same list of terms given to the control group. Before an in-class quiz, both groups had fourty minutes to use their handouts to prepare; after fourty minutes, both groups were given the same quiz. To ensure that experimental subjects worked the crossword puzzle, they had to submit a complete puzzle to the professor prior to the quiz. After the quiz, the professor computed the proportion of students who received A and B grades of the wuiz for these two groups. If the proportion of A and B grades is significantly high, it implies that the crossword puzzle exercise may accelerate students learning. The proportion of the experiment group 0.7547, while the proportion of the control group is 0. 6429. He then developed a two-tailed test. The null hypothesis is: the proportion of A and B grades in the experiment group that used the crossword puzzle handout as an aid in studyying for their quiz is not different from the proportion of A and B grades in the control group that did not have that handlut. The alternative hypothesis is: the proportion of A and B grades in the control group that did not have that handout. since he did not have any further information about the population, he used t test statistic. Did the professor develop a correct hypothesis test and hypothesis formulation, and use a correct test statistic? If you think yes, explain why you think yes; if no, explain why not and how to develope a correct hypothesis test and hypothesis formulation. Also, explain what it will happen(including the test statistic and p-value) if the professor developed a wrong hypothesis test and hypothesis formulation? Discuss and explain your reason. You must provide your statistical analysis and reasons.