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To construct X bar and R chart from the given data.
Leggo Italian Foods is a 60-year-old family-owned firm producing a range of specialty Italian food products for sale online and through a network of neighborhood grocery stores and gourmet shops in major American cities. One extremely successful product is Leggo's pesto, a traditional Italian sauce used in pastas and other dishes. Leggo's pesto is made from a recipe brought to America by an immigrant ancestor the current generation refers to as Bisnonna Maria. Bisnonna Maria has long since passed away but her legacy remains in the pesto, which includes fresh basil and garlic, extra virgin olive oil, toasted pignolis, and finely grated pecorino romano cheese. Her original hand-written recipe is kept in a safe deposit box.
Leggo's main production plant outside Chicago produces Bisnonna Maria's pesto and bottles it in 10-ounce jars. The filling operation runs 18 hours per work day and produces thousands of jars. Obviously Leggo wants to make certain the filling process remains under control. To this end they monitor the process using control charts. During each hour of the day 25 jars are randomly sampled and the pesto in the jars is weighed and logged. Mean and Range Charts are plotted hourly to log the performance of the filling machine and determine if it's functioning properly. Embedded below is an Excel spreadsheet with one day's data. The spreadsheet shows the weights (in ounces) of pesto in each of 450 jars, taken in samples of 25 each operating hour of the day.
a. Use this data to construct Mean and Range charts for the pesto filling machines.
The χ 2 statistic from a contingency table with 6 rows and five columns will have:
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