A special academic program for skilled students conduct an admission exam to select their new cohort. The admission exam is known to have a mean score of 63. An examiner thinks that the actual mean score for the most recent applicants is lower than 63. He randomly samples the scores of 17 recent applicants and obtains the average scores as 60.0 with a standard deviation of 5.7. He performs a hypothesis test using a 5% level of significance to reach an appropriate conclusion. a. Calculate the value of the the appropriate test statistic for this test. Answer rounded to at least 2 decimal places. b. Determine the tabulated critical value for this test. Only write the absolute value (without +/- sign) Answer rounded to at least 3 decimal places. c. Determine the p-value for this test. Answer in exact fraction, or rounded to at least 4 decimal places.

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