Business Context

FreshCart forecasts weekly order volume for staffing and inventory. Over the last month, the operations team noticed actual demand drifting away from the forecast and wants to determine whether the misses are just normal randomness or evidence that the forecasting process has become unreliable.

Problem Statement

Use the recent forecast performance data to quantify forecast accuracy and identify the most likely reasons the forecast became inaccurate.

Given Data

FreshCart tracked forecasted and actual weekly orders for 8 weeks:

Assume the historical forecasting process was designed to be unbiased, with mean error 0. The historical standard deviation of weekly forecast errors was 300 orders. Use a significance level of 0.05.

Requirements

1. Compute the weekly forecast errors, where error = actual  forecast.
2. Calculate the mean forecast error and sample standard deviation of the 8 recent errors.
3. Test whether the recent mean error is significantly different from 0 using a one-sample t-test.
4. Calculate the z-score of the recent error volatility relative to the historical standard deviation.
5. Based on the numbers, identify common reasons the forecast may have become inaccurate.
6. Give a business recommendation on whether the model should be recalibrated immediately.

Assumptions

• Weekly errors are independent.
• The 8-week sample is representative of current operating conditions.
• Historical error standard deviation of 300 orders is a valid benchmark for comparison.