Fifty kids and adults are surveyed about whether they prefer hamburgers or hot dogs. The results are shown in the table.
Category Kids Adults
Hamburgers 8 17
Hot dogs 12 13
Are being a kid and preferring hotdogs independent? Explain how you know.
(3 points)
To determine if being a kid and preferring hotdogs are independent, we need to compare the proportion of kids who prefer hotdogs to the overall proportion of people who prefer hotdogs.
From the table, we can see that out of the 50 surveyed people, 12 kids prefer hotdogs. Therefore, the proportion of kids who prefer hotdogs is 12/50 = 0.24.
Out of the 50 surveyed people, a total of 12 + 13 = 25 people prefer hotdogs.
The proportion of kids in the survey is 50/50 = 1, which means all the surveyed people are kids.
Since the proportion of kids who prefer hotdogs (0.24) is not equal to the proportion of all people who prefer hotdogs (1), we can conclude that being a kid and preferring hotdogs are not independent.