Questions: Administrators at a small school with 200 students want to estimate the average amount of time students spend looking at a screen (phone, computer, television, and so on) per day. The administrators select a random sample of 50 students from the school to ask. The administrators sampled % of the students from the school. (Do not round) The 10% condition is not met because 50 is less than 10% of all students at the small school.

Administrators at a small school with 200 students want to estimate the average amount of time students spend looking at a screen (phone, computer, television, and so on) per day. The administrators select a random sample of 50 students from the school to ask. The administrators sampled % of the students from the school. (Do not round) The 10% condition is not met because 50 is less than 10% of all students at the small school.
Transcript text: Administrators at a small school with 200 students want to estimate the average amount of time students spend looking at a screen (phone, computer, television, and so on) per day. The administrators select a random sample of 50 students from the school to ask. The administrators sampled $\square$ \% of the students from the school. (Do not round) The $10 \%$ condition is $\square$ not met because 50 $\square$ is less than $10 \%$ of all students at the small school.
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Solution

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Solution Steps

Step 1: Calculate the percentage of students sampled

The total number of students in the school is 200, and the sample size is 50. To find the percentage of students sampled, use the formula: \[ \text{Percentage sampled} = \left( \frac{\text{Sample size}}{\text{Total population}} \right) \times 100 \] Substitute the values: \[ \text{Percentage sampled} = \left( \frac{50}{200} \right) \times 100 = 25\% \]

Step 2: Check the 10% condition

The 10% condition states that the sample size should be less than 10% of the total population to ensure independence in sampling. Here, the total population is 200, so 10% of the population is: \[ 10\% \text{ of 200} = 0.10 \times 200 = 20 \] The sample size is 50, which is greater than 20. Therefore, the 10% condition is not met.

Step 3: Fill in the blanks

Based on the calculations:

  • The administrators sampled \( 25 \% \) of the students from the school.
  • The 10% condition is not met because 50 is greater than 10% of all students at the small school.

Final Answer

The administrators sampled \( \boxed{25\%} \) of the students from the school. The 10% condition is not met because 50 is greater than 10% of all students at the small school.

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