Graphical Analysis In Exercises 9–12, use the values on the number line to find the sampling error.

Verified step by step guidance

1. Step 1: Understand the concept of sampling error. Sampling error is the difference between the sample mean (denoted as x̄) and the population mean (denoted as μ). It is calculated as: Sampling Error = x̄ - μ.
2. Step 2: Identify the values provided in the problem. From the number line, the sample mean x̄ is given as 3.8, and the population mean μ is given as 4.27.
3. Step 3: Write the formula for sampling error using MathML: $\mathrm{Sampling}\mathrm{Error}=\mathrm{x̄}-\mu$
4. Step 4: Substitute the values into the formula. Replace x̄ with 3.8 and μ with 4.27 in the formula.
5. Step 5: Perform the subtraction to find the sampling error. The result will be the difference between 3.8 and 4.27, which represents the sampling error.

Key Concepts

Sampling Error

Sampling error refers to the difference between the sample mean (x̄) and the population mean (μ). It occurs because a sample is only a subset of the population, and thus may not perfectly represent the entire population. In this case, the sampling error can be calculated by subtracting the population mean from the sample mean, providing insight into the accuracy of the sample's estimate.

Sample Mean (x̄)

The sample mean, denoted as x̄, is the average value of a set of observations drawn from a population. It is calculated by summing all the sample values and dividing by the number of observations. In the context of the question, the sample mean is given as 3.8, which serves as a point of comparison against the population mean to assess sampling error.

Population Mean (μ)

The population mean, represented by μ, is the average of all possible values in a population. It is a fixed value that describes the entire group being studied. In this scenario, the population mean is 4.27, and understanding its relationship to the sample mean is crucial for evaluating the sampling error and the representativeness of the sample.