ETX2121 Data Analysis in Business Sample Exam 3 Solutions Question 1 a) ˆ i) X = 196.6 ; T = NX = 500 × 196.6 = $98 300

ii)

n = 20; s = 91.480; 1 − α = 0.95 ⇒ α = 0.05 ⇒ α 2 = 0.025 , t α 2,n −1 = t 0.025,19 = 2.093

Since n/N = 20/500 = 0.04 < 0.05, not required to use the fpc. 95% confidence interval estimate of the total accounts receivable
⎛ s ⎞ N ⎜ X ± tα 2 ,n −1 ⎟ ⎜ ⎟ n⎠ ⎝ ⎛ ⎛ 91.480 ⎞ ⎞ = 500⎜196.6 ± 2.093⎜ ⎟⎟ ⎜ ⎟⎟ ⎜ ⎝ 20 ⎠ ⎠ ⎝ = 500(196.6 ± (2.093 × 20.4556)) = 500(196.6 ± 42.8136) = 500[153.7864; 239.4136] = [76893.20; 119706.80] For 95% of the time over repeated sampling, we estimate the total accounts receivable to be between $68,609 and $127,991 iii) A point estimate is a single value whereas an interval estimate which specifies a range of values within which the population total probably lies gives us information about the accuracy of the estimate of the population total.

iv)

6 = 0.3 . 20 When nπ and n (1 − π ) are at least 5, the sampling distribution of p approaches a normal distributed as a consequence of the central limit theorem. Hence π(1 − π ) ⎞ ⎛ p ~ N ⎜ π, ⎟ n ⎠ ⎝ Implying that p−π ~ N(0,1). Z= π(1 − π ) n p=

b) Calculate the cumulative amount corresponding to each account. Select 5 random numbers between 1 and 3932. Match each random number with the next largest cumulative amount Select the account corresponding to this cumulative amount.
((1 + 4 + 2 + 3) + 4 = 14 marks) 1

Question 2 a) • Clearly identify the purpose of the survey • Clearly identify the output that is required from the analysis of the questions • Ensure that the structure of the questions and questionnaire satisfies the requirements of the analysis procedures that are to be applied. • The workability of a questionnaire may be checked by independent scrutiny, that is by a person not involved in drawing up the questions, but familiar with the