Final answer:
To calculate the mean absolute deviation (MAD) for a 3-year moving average, you need specific data on actual and forecasted values to find the average of absolute deviations. Specific data is also required to calculate the standard error of the sample mean and to determine the distribution of the sample mean.
Step-by-step explanation:
To calculate the mean absolute deviation (MAD) of forecasts made using a 3-year moving average, one must use the actual data and the forecast data to find the deviations. Unfortunately, the provided question does not contain any specific data to compute MAD. MAD is typically found by calculating the average of the absolute deviations of each data point from the forecasted values.
For example, if we had a data set and forecast values:
- Actual data: 100, 110, 120
- Forecasted data: 105, 115, 125
The absolute deviations would be: |100 - 105| = 5, |110 - 115| = 5, |120 - 125| = 5. MAD would then be the average of these values, which is (5 + 5 + 5) / 3 = 5.0.
To answer questions 1 and 2 which are related to the standard error of the sample mean and the distribution of the sample mean, we would also need specific sample data including the sample mean and the sample size. The standard error of the mean is typically computed by dividing the sample standard deviation (sx) by the square root of the sample size (n).
Once we have computed the standard error, the distribution of the sample mean would typically be normal or approximately normal, especially if the sample size is large, due to the Central Limit Theorem. This theorem states that the sampling distribution of the sample mean will tend to be normal regardless of the shape of the population distribution as the sample size becomes larger.