Question

use the situation below to answer questions 1-2.
the local community college has 2,500 students enrolled. a random survey was conducted in which 600 students were asked to check the \screen time\ data on their smartphones and report their average daily \screen time.\ the results are shown in the table below.
screen time
0-2 hours 5
2-4 hours 12
4-6 hours 150
6-8 hours 305
8-10 hours 102
10-12 hours 18
12-14 hours 8
① approximately what percentage of the population of the college can it be assumed spends a daily average of 8 - 10 hours of screen time on their phones?
a) 33%
b) 21%
c) 4%
d) 17%
② about how many students enrolled at the college will be expected to spend between 6 - 8 hours on their phones per day?
a) 305
b) 610
c) 1,271
d) 1,220
use the situation below to answer questions 3-4.
there are 5,000 college seniors enrolled at state college. a randomized list of 1,000 seniors was generated and those 1,000 seniors answered a brief survey about their preferred spring break vacation destination. the results are shown in the table below.
spring break
mountains/lakes 115
beach 650
theme parks 95
home 140
③ about how many seniors total would be likely to choose \beach\ as their preferred spring break destination?
a) 650
b) 1,300
c) 2,600
d) 3,250
④ the surveyors predicted that 80% of seniors would prefer to go to the beach for spring break. by how many percentage points was this prediction off?
a) 15%
b) 20%
c) 10%
d) 13%

Explanation:

Step1: Calculate sample percentage (Q1)

$\text{Percentage} = \frac{102}{600} \times 100\% = 17\%$

Step2: Scale sample to population (Q2)

$\text{Expected students} = 2500 \times \frac{305}{600} \approx 1271$

Step3: Scale sample to population (Q3)

$\text{Expected seniors} = 5000 \times \frac{650}{1000} = 3250$

Step4: Find prediction error (Q4)

$\text{Actual percentage} = \frac{650}{1000} \times 100\% = 65\%$
$\text{Difference} = 80\% - 65\% = 15\%$

Answer:

1. D) 17%
2. C) 1,271
3. D) 3,250
4. A) 15%