Questions: Multiple Choice Question Which of the following is an expression that represents sampling error? s-s^2 μ-σ X̄-s X̄-μ

Multiple Choice Question Which of the following is an expression that represents sampling error? s-s^2 μ-σ X̄-s X̄-μ
Transcript text: Multiple Choice Question Which of the following is an expression that represents sampling error? $s-s^{2}$ $\mu-\sigma$ $\bar{X}$-s $\bar{X}-\mu$
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Solution

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Solution Steps

Step 1: Calculate the Population Mean

The population mean \( \mu \) is calculated using the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

For the given data, where \( \sum_{i=1}^N x_i = 35 \) and \( N = 5 \):

\[ \mu = \frac{35}{5} = 7.0 \]

Step 2: Calculate the Sample Mean

The sample mean \( \bar{X} \) is computed from the sample data, which results in:

\[ \bar{X} = 7.0 \]

Step 3: Calculate the Sampling Error

The sampling error is defined as the difference between the sample mean and the population mean:

\[ \text{Sampling Error} = \bar{X} - \mu \]

Substituting the values:

\[ \text{Sampling Error} = 7.0 - 7.5 = -0.5 \]

Final Answer

The expression that represents sampling error is \( \bar{X} - \mu \). Thus, the answer is:

\[ \boxed{\bar{X} - \mu} \]

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