Question

TECHNOLOGY Pew Research Center released a survey that asked whether participants thought technological advancements in the future will make people’s lives better or worse. Of the people interviewed, 423 earned less than $50,000 per year and 328 earned $50,000 or more. Of those earning less than $50,000 per year, 262 thought that people’s lives would get better, and 240 of those who earned $50,000 or more thought the same. Organize the data in a two-way frequency table.

Answer 1

With technology and digital communication, it's

becoming easier to communicate because people

do not have to do that initial face-to-face reaction

when they are behind a keyboard. This can be a

good or a bad thing depending on how one

chooses to communicate.

Answer 2

`\begin{array}c\cline{1-4}\vphantom{\frac12}&\text{Less than \$50,000}&\text{\$50,000 or more}&\text{Total}\\\cline{1-4}\vphantom{\frac12}\text{Lives get better}&262&240&502\\\cline{1-4}\vphantom{\frac12}\text{Lives don't get better}&161&88&249\\\cline{1-4}\vphantom{\frac12}\text{Total}&423&328&751\\\cline{1-4}\end{array}`

Explanation:

From the given information, the two options of the "annual salary" category are:

• Less than $50,000 per year.
• $50,000 or more per year.

From the given information, the two options of the "opinions" category are:

• People's lives would get better.
• People's lives would not get better.

To create a two-way frequency table to visually represent the possible relationships between the two sets of categorical data:

• Create a 4x4 table.
• Label the top row of the table with one category and the left side of the table with the other category.
• Label the right column "Total" and the bottom row "Total".

`\begin{array}c\cline{1-4}\vphantom{\frac12}&\text{Less than \$50,000}&\text{\$50,000 or more}&\text{Total}\\\cline{1-4}\vphantom{\frac12}\text{Lives get better}&&&\\\cline{1-4}\vphantom{\frac12}\text{Lives don't get better}&&&\\\cline{1-4}\vphantom{\frac12}\text{Total}&&&\\\cline{1-4}\end{array}`

Add the given information to the table:

`\begin{array}\cline{1-4}\vphantom{\frac12}&\text{Less than \$50,000}&\text{\$50,000 or more}&\text{Total}\\\cline{1-4}\vphantom{\frac12}\text{Lives get better}&262&240&\\\cline{1-4}\vphantom{\frac12}\text{Lives don't get better}&&&\\\cline{1-4}\vphantom{\frac12}\text{Total}&423&328&\\\cline{1-4}\end{array}`

From the table, we can see that of the 423 of people that earned less than $50,000 per year, 262 thought that people's live would get better.

To calculate the number of people that earned less than $50,000 per year that thought people's lives would not get better, subtract 262 from 423 and place this number in the cell in column 2, row 3.

Continue like this to fill out the rest of the table, remembering to calculate the column and row totals:

`\begin{array}c\cline{1-4}\vphantom{\frac12}&\text{Less than \$50,000}&\text{\$50,000 or more}&\text{Total}\\\cline{1-4}\vphantom{\frac12}\text{Lives get better}&262&240&502\\\cline{1-4}\vphantom{\frac12}\text{Lives don't get better}&161&88&249\\\cline{1-4}\vphantom{\frac12}\text{Total}&423&328&751\\\cline{1-4}\end{array}`