Ch. 1 - Introduction to Statistics

Larson - Elementary Statistics: Picturing the World 8th Edition

Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo

Larson 8th Edition

Ch. 1 - Introduction to Statistics

Problema 1.3.27

Capitolo 1, Problema 1.3.27

Identify the sampling technique used, and discuss potential sources of bias (if any). Explain.
Soybeans are planted on a 48-acre field. The field is divided into one-acre subplots. A sample is taken from each subplot to estimate the harvest.

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The sampling technique used in this scenario is **stratified sampling**. This is because the 48-acre field is divided into one-acre subplots (strata), and a sample is taken from each subplot to estimate the harvest.

Stratified sampling involves dividing the population into distinct subgroups (strata) that share similar characteristics. In this case, the subplots are the strata, and the sampling ensures representation from each subplot.

Potential sources of bias could arise if the samples taken from each subplot are not representative of the entire subplot. For example, if the samples are taken only from areas of the subplot that are more fertile or accessible, the results may overestimate or underestimate the harvest.

To minimize bias, it is important to ensure that the samples within each subplot are selected randomly and cover the entire subplot uniformly. This helps in obtaining a more accurate estimate of the harvest.

Additionally, environmental factors such as soil quality, irrigation, or pest infestation that vary across subplots could introduce variability. These factors should be accounted for when analyzing the results to avoid misleading conclusions.

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Sampling Technique

The sampling technique refers to the method used to select a subset of individuals or observations from a larger population. In this case, the technique used is stratified sampling, where the 48-acre field is divided into one-acre subplots, and a sample is taken from each subplot. This approach ensures that each section of the field is represented in the sample, which can lead to more accurate estimates of the overall harvest.

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05:11

Sampling Distribution of Sample Proportion

Bias in Sampling

Bias in sampling occurs when certain members of a population are systematically more likely to be selected than others, leading to an inaccurate representation of the population. Potential sources of bias in this scenario could include variations in soil quality or moisture levels across the subplots, which might affect the yield but are not accounted for if the sampling does not consider these factors.

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05:11

Sampling Distribution of Sample Proportion

Estimation of Harvest

Estimation of harvest involves using sample data to make inferences about the total yield of the entire field. By analyzing the yields from the sampled subplots, one can extrapolate to estimate the total harvest. However, the accuracy of this estimation depends on the sampling technique and the absence of bias, as any skewed data can lead to incorrect conclusions about the overall productivity of the field.

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06:33

Introduction to Confidence Intervals

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