Question

b.e.s.t. mathematics sample items

1. in a survey of 3,260 people, 57% of people said they spend more than 2 hours a day on their smartphones. the margin of error is ±2.2%. the survey is used to estimate the number of people in a town of 17,247 who spend more than 2 hours a day on their smartphones.

based on the survey, what are the estimated minimum and maximum numbers of people in the town who spend more than 2 hours a day on their smartphones? round your answers to the nearest whole numbers.
write your responses in the shaded boxes below.
minimum:
maximum:

Explanation:

Step1: Calculate the lower - bound percentage

The lower - bound percentage of people who spend more than 2 hours a day on smartphones is $57\% - 2.2\%=54.8\% = 0.548$.

Step2: Calculate the minimum number of people in the town

Multiply the lower - bound percentage by the total number of people in the town. So the minimum number is $0.548\times17247\approx9441$.

Step3: Calculate the upper - bound percentage

The upper - bound percentage of people who spend more than 2 hours a day on smartphones is $57\%+ 2.2\% = 59.2\%=0.592$.

Step4: Calculate the maximum number of people in the town

Multiply the upper - bound percentage by the total number of people in the town. So the maximum number is $0.592\times17247\approx10200$.

Answer:

Minimum: 9441
Maximum: 10200