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Alaboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with milligrams. Construct a contidence interval for the true
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D.

To create a 95% confidence interval for the true mean cholesterol level in chicken eggs, you would start with the formula:

Here, mg, mg, and . For a 95% confidence level, the z-value is approximately 1.96. Plugging in the values, the standard error (SE) is calculated as:

Now, calculate the margins:

Finally, constructing the interval gives:

Thus, the correct confidence interval rounded to two decimal places is approximately:

B.

Ever wonder where the concept of confidence intervals originated? It can be traced back to the early 20th century when statisticians like Ronald Fisher began developing statistical methods for inference. Fisher’s work laid the foundation for how we can estimate population parameters based on sample data, which is foundational to modern statistics.

If you want to dive deeper into the statistical world, books like “Statistical Inference” by George Casella and Roger L. Berger or “The Elements of Statistical Learning” by Trevor Hastie, Robert Tibshirani, and Jerome Friedman are fantastic reads. They cover topics ranging from basic statistics to advanced data analysis, helping you get a solid grip on the principles of inference and model fitting.