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Which Statement Is True About the Population Proportion of Defective Pieces in the 2000 Items?

In quality control and statistical analysis, understanding the population proportion of defective pieces is crucial to ensure the overall quality of a product. In this article, we will explore the possible statements regarding the population proportion of defective pieces in a sample of 2000 items and delve into the FAQs surrounding this topic.

Statement 1: The population proportion of defective pieces is exactly 0.05.

Statement 2: The population proportion of defective pieces is less than 0.05.

Statement 3: The population proportion of defective pieces is greater than 0.05.

To determine which statement is true, we need to gather data and perform statistical analysis. This is typically done by taking a sample from a larger population and calculating the proportion of defective pieces within that sample. However, it is important to note that the true population proportion can never be known with absolute certainty, as it is practically impossible to inspect every single item in a large population.

Frequently Asked Questions:

Q1: What is the population proportion?

A1: The population proportion refers to the proportion of defective pieces in the entire population of items being analyzed. It is a measure of the overall quality of the population.

Q2: Why is it important to know the population proportion?

A2: Knowing the population proportion allows companies to assess the quality of their products and make informed decisions regarding improvements, recalls, or other quality control measures.

Q3: How is the population proportion estimated?

A3: The population proportion is estimated by taking a sample from the population and calculating the proportion of defective pieces within that sample. This estimate is then used to make inferences about the true proportion in the entire population.

Q4: Can the true population proportion ever be known?

A4: No, the true population proportion can never be known with certainty unless every single item in the population is inspected, which is usually not feasible due to time and cost constraints.

Returning to the three statements:

Statement 1: The population proportion of defective pieces is exactly 0.05.

Given that we can never know the true population proportion with certainty, it is highly unlikely that the population proportion would exactly match the stated value of 0.05. Therefore, statement 1 is likely false.

Statement 2: The population proportion of defective pieces is less than 0.05.

This statement is plausible. If the sample of 2000 items reveals a proportion of defective pieces lower than 0.05, it is possible that the true population proportion is indeed less than 0.05. However, further analysis is required to confirm this statement.

Statement 3: The population proportion of defective pieces is greater than 0.05.

Similarly to statement 2, this statement is also plausible. If the sample of 2000 items indicates a proportion of defective pieces higher than 0.05, it is possible that the true population proportion is indeed greater than 0.05. Nonetheless, further analysis is necessary to validate this statement.

In conclusion, without performing statistical analysis on a sample of 2000 items, it is impossible to determine which statement is true about the population proportion of defective pieces. However, by calculating the sample proportion and using statistical methods, one can make informed inferences about the true population proportion, allowing businesses to take appropriate quality control measures.

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