Question

a group of students is conducting a simulation study to estimate the average score on a standardized test for high school students in their district. they randomly select 200 students from their district and administer the test. after collecting the data, they find that the mean score on the test is 85, and the standard deviation of the scores is 10.

using the formula for calculating the margin of error for a sample mean at a 95% confidence level, what is the margin of error for their estimate of the average score on the standardized test?

\\\text{margin of error} = \text{critical value} \cdot \frac{\text{standard deviation}}{\sqrt{\text{sample size}}}\\

• 2.58
• 1.96
• 1.39
• 0.98

Explanation:

Identify the given parameters

Using the Sample Mean and Sample Standard Deviation knowledge points

$$
LATEXBLOCK0
$$

Calculate the margin of error

Calculate the margin of error using the provided formula:

$$ \text{Margin of Error} = z^* \cdot \frac{s}{\sqrt{n}} $$

$$ \text{Margin of Error} = 1.96 \cdot \frac{10}{\sqrt{200}} $$

$$ \text{Margin of Error} = 1.96 \cdot \frac{10}{14.1421} \approx 1.96 \cdot 0.7071 \approx 1.386 $$

Rounding to two decimal places yields \(1.39\).

Answer:

• 2.58
• 1.96
• 1.39 (Correct answer)
• 0.98