Control Limits In constructing a control chart for the proportion...

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1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- Introduction to Confidence Intervals
  15m
- Confidence Intervals for Population Mean
  48m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample1h 1m
- Steps in Hypothesis Testing
  1h 1m
10. Hypothesis Testing for Two Samples2h 8m
11. Correlation48m
- Scatterplots & Intro to Correlation
  26m
- Correlation Coefficient
  21m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

1. Intro to Stats and Collecting Data

Intro to Stats

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1. Intro to Stats and Collecting Data

Intro to Stats

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2:02 minutes

Problem 14.2.3

Textbook Question

Control Limits In constructing a control chart for the proportions of defective dimes, it is found that the lower control limit is -0.00325. How should that value be adjusted?

Verified step by step guidance

Understand that control limits in a control chart are used to determine the range of acceptable variation in a process. The lower control limit (LCL) should not be negative, as proportions cannot be negative.

Recognize that the LCL is calculated using the formula: LCL = p̂ - z * sqrt((p̂(1-p̂))/n), where p̂ is the sample proportion, z is the z-score corresponding to the desired confidence level, and n is the sample size.

Since the calculated LCL is negative, it indicates that the process variation is too small or the sample size is too small. In practice, a negative LCL is adjusted to zero because a proportion cannot be less than zero.

Adjust the LCL to zero to reflect the realistic lower bound for proportions. This adjustment ensures that the control chart accurately represents the process capability.

Re-evaluate the control chart with the adjusted LCL to ensure that it accurately reflects the process stability and identify any out-of-control signals based on the new limits.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Control Limits

Control limits are boundaries set within a control chart to determine the acceptable range of variation in a process. They are calculated using statistical methods and help identify when a process is out of control. Typically, control limits are set at three standard deviations from the process mean, indicating the expected range of variation.

Proportions of Defective Items

Proportions of defective items refer to the fraction or percentage of items in a sample that do not meet quality standards. In statistical quality control, this measure is used to monitor and control the quality of a production process. It is essential to ensure that the proportion remains within the control limits to maintain process stability.

Adjustment of Control Limits

Adjusting control limits involves recalculating them to ensure they are meaningful and applicable. If a control limit is negative, as in the case of a lower control limit for proportions, it should be adjusted to zero because proportions cannot be negative. This adjustment ensures the control chart accurately reflects the process's capability and quality standards.

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