Choose Any Two Classmates And Review Their Main Posts

Choose Any Two Classmates And Review Their Main Posts1 Review The St

Choose any two classmates and review their main posts. 1. Review the student’s response to numbers 1 and 2 above. Compare these answers to your answers. Create a paragraph that offers this comparison and better explains why samples can estimate population parameters but will never be 100% accurate.

2. Review the student’s responses to numbers 3 and 4. Evaluate their work and answer. What variable did they choose? What were their sample mean, sample standard deviation, and sample sizes? Is their margin of error E correct? If yes, what is their margin of error and what does it tell you? If not, correct it and show all the work and steps.

Paper For Above instruction

In the realm of statistical analysis, understanding the limitations and capabilities of sampling methods is crucial. The responses from both classmates shed light on fundamental concepts of population parameters, sampling error, and confidence intervals, illustrating both common misconceptions and accurate interpretations.

Both students correctly identified that estimating a population parameter using a sample inherently involves some degree of error. Person 1 emphasized that sampling provides estimates rather than exact values because surveying an entire population is often impractical due to costs and logistical constraints. For instance, estimating the average height of all 5th-grade children or the total number of pennies in the world are examples of parameters that cannot be precisely calculated but can be reasonably estimated through sampling. Person 2 echoed this perspective, explaining that it is nearly impossible to determine exact population parameters because of the large size and diversity of populations, but sample data allows for estimation within a confidence interval. Additionally, they appropriately highlighted that larger sample sizes typically reduce the margin of error, thereby increasing the precision of the estimate.

Both classmates addressed the concept of margin of error application in estimating population parameters. Person 1 used the formula E=1.96*s/sqrt(n) for means, and provided a numerical example involving data on children's heights to demonstrate how the margin of error can be computed and interpreted. The example reported a sample mean of 56.2 with a standard deviation of 2.78 and a sample size of 20, resulting in a margin of error of approximately 7.44, which implies that with 95% confidence, the true population mean height lies within about 7.44 units of the sample mean. Person 2 reinforced the same point, emphasizing that the margin of error reflects the range within which the true population parameter is expected to fall, considering sampling variability.

In evaluating their responses to the questions on the effect of sample size, both students correctly noted that larger samples tend to yield more accurate estimates by decreasing the margin of error. Person 1 succinctly summarized this by stating that increasing the sample size enhances the precision of the estimate and reduces errors, which aligns with the statistical principle that larger samples decrease sampling variability. Person 2 mentioned that increased sample size makes the estimate closer to the true population value and reduces the margin of error, thereby increasing confidence.

Regarding the question about the possibility of estimating population parameters with 100% accuracy, both students correctly acknowledged that this is impossible with sampling alone. Person 1 explained that errors always exist because samples do not include every element of the population, and outliers may skew results. Person 2 similarly clarified that some level of margin of error is unavoidable because sampling inherently involves some degree of uncertainty. Their explanations demonstrate a clear understanding that perfect accuracy would require measuring the entire population, which is generally infeasible or impractical.

In terms of the calculation of the margin of error, both students used appropriate formulas for mean estimates with 95% confidence intervals, incorporating the critical value of 1.96 (approximating the z-score for a 95% confidence level).

Person 1 created a variable, "Height of children in 5th grade," with 20 data points. They calculated a mean of 56.2 and a standard deviation of 2.78, leading to a margin of error of approximately 7.44 units. This example illustrates how sampling variability influences the estimate and how the margin of error provides a range for the population mean.

Person 2 invented a variable such as "Age," with a small dataset of 20 values and calculated a mean of 163 and a standard deviation of 19.83. Using the formula E=1.96*s/√n, they computed a margin of error of approximately 8.70, which results in a confidence interval from approximately 154.3 to 171.7. This practical demonstration reinforces the concept that the margin of error quantifies the uncertainty associated with sample estimates and that larger samples tend to narrow this interval.

In conclusion, both responses effectively illustrate that while samples are invaluable tools for estimating population parameters, there is always an associated margin of error. This inherent uncertainty prevents any sample-based estimate from being perfectly accurate, underscoring the importance of understanding and appropriately calculating confidence intervals and margins of error in statistical inference.

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