RVHS 2023 T4 Session 1 (Solution for SelfMark)

1    2023 Term 4 Timed Practice (Structured Remedial Session 1) Question 1. [N13/9740/P2/Q6] The continuous random variable Y has the distribution N(µ, σ2). It is known that P(Y < 2a) = 0.95 and P(Y < a) = 0.25. Express µ in the form ka, where k is a constant to be determined. [4]

2    Question 2. [N16/9740/P2/Q6(modified)] The Company Secretary obtains a suitable sample of 80 employees in order to carry out a hypothesis test of the Managing Director’s belief that the mean age of the empl oyees now is less than 37 years. You are given that the population variance of the ages is 140 years2. (i) Write down appropriate hypot heses to test the Managing Director’s belief, defining any symbols you use. You are given that the result of the test, using a 5% sign ificance level, is that the Managing Director’s belief should be accepted. Determine the set of poss ible values of the mean age of the sample of employees. [4]

3    (ii) You are given that the mean age of the sample of employees is 35.2 years, and that the result of a test at α% significance level is that the Managing Directo’s belief should not be accepted. Find the set of possible values of α. [3]