Question

the local high school has 250 seniors in this years graduating class. a random name generator produced the names of 50 seniors from the full-class roster. these 50 students were surveyed and asked if they participated in any after-school activities. the results are shown in the table below. answer the questions based on the data given.

after school activities
dance 8
sports 20
drama/music 5
part-time job 10
none 7

2 approximately what percent of the population participates in sports after school?
percent: $\frac{survey part}{survey total} \times 100 = \\%$

3 about how many total seniors have a part time job after school?
population: set up a key! $\frac{survey part}{survey total} = \frac{x}{population}$

4 before the survey was conducted, it was estimated that about 20% of seniors did not participate in any after-school activity. according to the data, how many percentage points was this estimate off?

cherry tree middle school has 300 seventh graders. a survey was conducted with 90 randomly selected 7th graders asking about their favorite hobby to engage in during their free time. the results are shown in the table below. answer the questions based on the data given.

favorite hobbies
video games 36
social media 18
creating internet videos 9
movies/tv 20
other 7

5 about how many 7th graders prefer to play video games in their free time?

6 approximately what percent of the population chooses to create internet videos?

7 if those conducting the survey originally predicted that 25% of students would choose movies/tv as their favorite hobby, about how many percentage points off was their prediction? round to the nearest 10th.

Explanation:

Step1: Calculate sports participation percent

$\frac{20}{50} \times 100 = 40\%$

Step2: Estimate total part-time job seniors

$\frac{10}{50} = \frac{x}{250} \implies x = \frac{10 \times 250}{50} = 50$

Step3: Calculate non-participation error

Survey non-participation: $\frac{7}{50} \times 100 = 14\%$
Error: $|20\% - 14\%| = 6$ percentage points

Step4: Estimate video game preferring students

$\frac{36}{90} = \frac{x}{300} \implies x = \frac{36 \times 300}{90} = 120$

Step5: Calculate internet video creator percent

$\frac{9}{90} \times 100 = 10\%$

Step6: Calculate hobby prediction error

Survey Movies/TV percent: $\frac{20}{90} \times 100 \approx 22.22\%$
Error: $|25\% - 22.22\%| \approx 3$ percentage points (rounded to nearest 10th)

Answer:

1. $40\%$
2. 50
3. 6 percentage points
4. 120
5. $10\%$
6. 3 percentage points