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 70. An examiner thinks that the actual mean...

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 70. An examiner thinks that the actual mean score for the most recent applicants is lower than 70. He randomly samples the scores of 10 recent applicants and obtains the average scores as 65.0 with a standard deviation of 9.8. 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.

b. Determine the tabulated critical value for this test. Only write the absolute value (without +/- sign)

c. Determine the p-value for this test.