Scores on a certain test for students are normally distributed. A local college student believes that the average score for students at a certain state college (let's call it XY college) is less than a score of 105, and so wants to test the hypothesis. The student has a friend at XY college who will obtain a SRS of 64 XY college student scores and found the mean of the 64 results was 103 with a sample standard deviation of 24. The level of significance (alpha) used for this problem is 0.05. [20 pts] a) State the pair of Hypothesis using proper notation and mathematical symbols(or full correct wording) for testing the this student's belief as stated above.. [4 pts] b) What are the assumptions required to be valid for the hypothesis tests to be valid? Note: When making a statement involving the random variable, it must be put in actual context and be specific. [3pts]. c)What is the appropriate test statistic (Student must complete by O A 1 F4 F5 F6 F7 F8 F9 F10c)What is the appropriate test statistic (Student must complete by showing by formula using the appropriate values in that formula "showing work" and the final answer and appropriate label)? [4 pts] d) Find/Calculate the P-value for this hypothesis test (show full calculator syntax) [3 pts] e) What is the decision (Reject Ho or Fail to Reject Ho (Retain Ho)? Give full supporting statistical reasoning to your decision by comparing the two appropriate values necessary. [2 pts] f) Give the statistical and real-world conclusions corresponding this hypothesis test and put in context to the random variable involved. [4 pts] Label each answer (Part A, part B etc and if not answering a part, make sure to label and put "no answer" so it is easy to read). Edit View Insert Format Tools Table O