It is thought that 20% of Annual Tax returns to the Australian Tax Office (ATO) contain errors of one kind or another. An auditor in the ATO investigating the number of returns with errors in a particular industry takes a sample of 25 returns and classifies each return as being “in error” or “not in error”. i. If the variable X is used to represent the number of returns in the sample that are in error, and assuming this industry is no different to other industries in terms of the error rate, then state: • the values that X may take; • the distribution of this variable; and • the parameter/s of this distribution. ii. Determine the probability that 6 or less returns in this sample are in error. The auditor found that there were 13 tax returns with errors in this sample. iii. Determine the probability of finding 13 or more returns with errors if indeed the error rate was 20%. iv. Based upon your answer for part iii., what conclusion might the auditor make about this particular industry in terms of the error rate of returns. Say in a full sentence exactly what led you to this conclusion.
2b. It is thought that 20% of Annual Tax returns to the Australian Tax Office (ATO) contain
errors of one kind or another. An auditor in the ATO investigating the number of returns
with errors in a particular industry takes a sample of 25 returns and classifies each return as
being “in error” or “not in error”.
i. If the variable X is used to represent the number of returns in the sample that are in
error, and assuming this industry is no different to other industries in terms of the error
rate, then state:
• the values that X may take;
• the distribution of this variable; and
• the parameter/s of this distribution.
ii. Determine the probability that 6 or less returns in this sample are in error.
The auditor found that there were 13 tax returns with errors in this sample.
iii. Determine the probability of finding 13 or more returns with errors if indeed the error
rate was 20%.
iv. Based upon your answer for part iii., what conclusion might the auditor make about this
particular industry in terms of the error rate of returns. Say in a full sentence exactly
what led you to this conclusion.
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