Question 1

A college instructor would like to know if his calculus class has a good understanding of basic maths. He wants the class to be able to score above 75 on the test. Six students are chosen at random from his class and given a proficiency test. Their scores are 65, 94, 73, 67, 86 and

97 respectively. At the 10% level of significance, is there sufficient evidence to reveal that the mean score for the class on the test would be above 75? (Use the critical value approach.)

Question 2

a) Mr Wong gave the TOEFL test to a random sample of 525 Form 6 students in his tutorial class. These students had a mean score of 465. Perform an appropriate hypothesis test to determine whether there is evidence to reveal that the mean score for all Form 6 students who took the TOEFL test was greater than 455 with a standard deviation of 105 at the 5% level of significance. (Use the critical value approach.)

b Use the p-value approach to test the above hypothesis at the same level of significance.