Question 4 a. A large accountancy firm finds that over the long run 10% of its statements for clients are in error in some way. A quality assurance officer at the firm investigating the source of the errors takes a sample of 20 statements produced by a single employee and classifies each as being “in error” or “not in error”. i. If the variable X is used to represent the number of statements in the sample that are in error, and assuming the error rate is the firm’s level of 10% then state: • the type of distribution this variable has; and • the parameter/s of this distribution. ii. Determine the probability that 2 or less returns in this sample are in error. The quality assurance officer found that there were 5 statements in the sample that were in error. iii. Determine the probability of finding 5 or more returns in error if indeed the error rate was 10%.
Question 4
a. A large accountancy firm finds that over the long run 10% of its statements for clients are in error in some way. A quality assurance officer at the firm investigating the source of the errors takes a sample of 20 statements produced by a single employee and classifies each as being “in error” or “not in error”.
i. If the variable X is used to represent the number of statements in the sample that are in error, and assuming the error rate is the firm’s level of 10% then state:
• the type of distribution this variable has; and
• the parameter/s of this distribution.
ii. Determine the probability that 2 or less returns in this sample are in error.
The quality assurance officer found that there were 5 statements in the sample that were in error.
iii. Determine the probability of finding 5 or more returns in error if indeed the error rate was 10%.
iv. Based upon your answer for part iii., what conclusion might the quality assurance office make about this employee in terms of the error rate of statements.
b. A process that cuts lengths of metal with high precision aims to produce metal rods with length of 600 millimetres (mm). Management at the factory is concerned that after an adjustment to the machine the mean length of the rods being produced is less than the required 600 mm. The production line manager tasked with investigating the issue finds that a (random) sample of 15 rods yielded a mean length of 596 mm and a sample standard deviation of 3 mm.
i. Say whether the information from the sample would prompt the production line manager to continue the investigation. Justify your decision.
ii. State the null and alternate hypotheses for this situation.
iii. Use the Excel macro provided this session to test the hypothesis you have stated above using a 5% level of significance. You must show the Excel output, the rejection criterion, relevant numbers from the output, the test result and a conclusion in terms of the original problem.
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