Question

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. minimum: maximum:

Explanation:

Step1: Calculate minimum percentage

First, find the minimum percentage by subtracting the margin of error from the given percentage. The given percentage is 57% and the margin of error is 2.2%, so the minimum percentage is \( 57\% - 2.2\% = 54.8\% \). Convert this percentage to a decimal: \( 54.8\% = 0.548 \).

Step2: Calculate minimum number of people

Multiply the total number of people in the town (17,247) by the minimum decimal percentage to find the minimum number of people. So, \( 17247\times0.548 \approx 17247\times0.548 \). Let's calculate that: \( 17247\times0.5 = 8623.5 \), \( 17247\times0.04 = 689.88 \), \( 17247\times0.008 = 137.976 \). Adding these together: \( 8623.5 + 689.88 = 9313.38 + 137.976 = 9451.356 \approx 9451 \).

Step3: Calculate maximum percentage

Next, find the maximum percentage by adding the margin of error to the given percentage. So, \( 57\% + 2.2\% = 59.2\% \). Convert this to a decimal: \( 59.2\% = 0.592 \).

Step4: Calculate maximum number of people

Multiply the total number of people in the town (17,247) by the maximum decimal percentage to find the maximum number of people. So, \( 17247\times0.592 \approx 17247\times0.592 \). Let's calculate that: \( 17247\times0.5 = 8623.5 \), \( 17247\times0.09 = 1552.23 \), \( 17247\times0.002 = 34.494 \). Adding these together: \( 8623.5 + 1552.23 = 10175.73 + 34.494 = 10210.224 \approx 10210 \).

Answer:

Minimum: 9451
Maximum: 10210