Question

If the weight of cereal in a particular packet is less than 14 ounces the packet is considered nonconforming. Each week, the manufacturer randomly selects 1,000 cereal packets and determines the number that nonconforming. The results for 12 consecutive weeks are shown below. {46, 32, 21, 30, 47, 31, 32, 52, 48, 45, 62, 58) To answer this exercise, read carefully and follow the following instructions. a) Use Minitab and the given process data (above) to construct a control chart for p b) Copy and paste the control chart on a Word document, c) Determine whether the process is within statistical control and write your determination beneath the chart on your Word document

Answer 1

The student's question involves using statistical methods to analyze quality control in different manufacturing scenarios, including creating control charts, hypothesis testing for weight tolerances, and assessing the need for recalibration based on standard deviation.

Step-by-step explanation:

The question provided discusses several scenarios that require statistical analysis to determine the quality and consistency of production in different contexts. The student is asked to use process data to construct a control chart for p using Minitab, assess whether the weight of cereal packets is within statistical control, and determine if the process of packing Class A apples meets the weight tolerance requirements by conducting a hypothesis test. Additionally, it covers evaluating whether a machine needs recalibration due to weight fluctuations in cereal boxes by comparing the measured standard deviation against a specified threshold. Lastly, it mentions the probability and percentile problems associated with the total weight of open boxes of cereal and the calculation of uncertainty in apple bag weights.

Answer 2

To address your exercise, we need to follow a series of steps involving statistical analysis and the use of software like Minitab. Here's how you can proceed:

a) Constructing a Control Chart for p in Minitab

1. Input Data: First, input the given data into Minitab. This data represents the number of nonconforming packets each week.

2. Set Up Control Chart: In Minitab, you'll need to select the appropriate control chart for the data type. Since you are dealing with proportions (the number of nonconforming packets out of a total of 1,000), you'll use a `p-chart` (control chart for proportions).

3. Specify Parameters: Specify the sample size (1,000 packets each week) and enter the data for the 12 weeks.

4. Create the Chart: Minitab will calculate the control limits and plot the data points, creating the p-chart.

b) Copy and Pasting the Control Chart into a Word Document

After creating the chart in Minitab:

1. Copy the Chart: Right-click on the chart in Minitab and select "Copy" or use the software's export feature.

2. Paste in Word: Open a Word document and paste the chart there.

c) Determining Whether the Process is Within Statistical Control

1. Analyze the Chart: Look for any signs that the process is out of control, such as data points outside the control limits, a run of points on one side of the center line, or a pattern within the points.

2. Write Your Determination: Underneath the chart in your Word document, write your analysis. If the data points are mostly within the control limits and show no non-random pattern, the process can be considered in control. If there are signs of the process being out of control (like points outside the control limits), you should note that and suggest investigating the cause.