Question

you and your classmates are conducting a simulation study to estimate the average time ninth-grade students at your school spend playing video games per day. after collecting the data, you find that the mean time spent playing video games is 3.2 hours, with a standard deviation of 1.5 hours. you randomly select 150 students.

using the formula for calculating the margin of error for a sample mean at a 95% confidence level:
\me_{95\\%} = cv \cdot \frac{s}{\sqrt{n}}\\

what is the margin of error for their estimate of the average daily time spent playing video games?

use the keypad to enter your answer in the box. more symbols can be found using the drop-down arrow in the top-left corner. round your answer to two decimal places.

margin of error:
\me_{95\\%} \approx \text{ hours}\\

Explanation:

Identify the given parameters

We extract the values from the problem statement:

• Sample mean \(\bar{x} = 3.2\) hours
• Sample standard deviation \(s = 1.5\) hours
• Sample size \(n = 150\)
• Confidence level = \(95\%\)

Determine the critical value

Using the Critical Value knowledge point

$$ CV = z^* = 1.96 $$

Calculate the margin of error

Using the Margin of Error and Confidence Interval knowledge points

$$
LATEXBLOCK0
$$

Round to two decimal places

Rounding the calculated value to two decimal places:

$$ ME_{95\%} \approx 0.24 $$

Answer:

\(ME_{95\%} \approx\) <blank>0.24</blank> hours