## Question 214:

1

If you are assessing claimed versus actual the only reason it would be a one-sided hypothesis test would be if you only adjust down. That is, the amount paid can never be greater than the amount claimed?  If it can go both ways, then it is a two-sided issue.

If I understand the situation, you have a reasonable estimate of the standard deviation of the population, which would be the SD of the difference in actual expenses and claimed expenses.

If the 1st sample you took has an average difference of \$1 and you have the standard deviation of that sample, I would construct a confidence interval around that mean to give you an idea of the likely range of the true spread. The next question will help answer you sample size question: What is it you are trying to detect, if the mean difference of the entire T&E claims are less than \$5? If so, then one-sample 1-sided t-test testing against the mean of \$5 would be the next approach. If you have the mean and standard deviation of the sample I can calculate that for you or you can send me the data. Your data is also probably slightly skewed, as there will likely be some differences that are very large and there is a lower-limit (0) to other claims. For that reason, you could also paste your data in the Task-Time calculator which will generate the 95% CI interval after transforming the data.