Let's analyze the data presented in the table and answer each part of the question step by step.
### Table Data
[tex]\[
\begin{array}{|c|c|c|}
\cline { 2 - 3 } \multicolumn{1}{c|}{} & \text{Vegetarian} & \text{Not vegetarian} \\
\hline \text{Exercise} & 49 & 28 \\
\hline \text{Don't exercise} & 21 & 77 \\
\hline
\end{array}
\][/tex]
### Total Adults
The total number of adults surveyed is 175.
### (a) What percentage of the adults exercise?
To find the percentage of adults who exercise, we need to add the number of vegetarians who exercise and the number of non-vegetarians who exercise, and then divide by the total number of adults surveyed.
Number of adults who exercise = [tex]\(49 + 28 = 77\)[/tex]
[tex]\[
\text{Percentage who exercise} = \left( \frac{77}{175} \right) \times 100 = 44\%
\][/tex]
### (b) What percentage of the adults are vegetarian?
To find the percentage of adults who are vegetarian, we need to add the number of vegetarians who exercise and the number of vegetarians who do not exercise, and then divide by the total number of adults surveyed.
Number of vegetarians = [tex]\(49 + 21 = 70\)[/tex]
[tex]\[
\text{Percentage of vegetarians} = \left( \frac{70}{175} \right) \times 100 = 40\%
\][/tex]
### (c) What percentage of the adults who are vegetarian exercise?
To find the percentage of vegetarians who exercise, we take the number of vegetarians who exercise and divide it by the total number of vegetarians.
[tex]\[
\text{Percentage of vegetarians who exercise} = \left( \frac{49}{70} \right) \times 100 = 70\%
\][/tex]
### (d) Is there evidence that adults who are vegetarian tend to be exercisers more often than average?
To answer this question, we compare the percentage of vegetarians who exercise (from part (c)) with the overall percentage of adults who exercise (from part (a)).
- Percentage of all adults who exercise = 44%
- Percentage of vegetarians who exercise = 70%
Since the percentage of vegetarians who exercise (70%) is much greater than the percentage of all adults who exercise (44%), there is evidence that adults who are vegetarian tend to be exercisers more often than average.
[tex]\[
\text{Conclusion: Yes, because the percentage found in part (c) is much greater than the percentage found in part (a).}
\][/tex]
So the final answers are:
(a) 44%
(b) 40%
(c) 70%
(d) Yes, because the percentage found in part (c) is much greater than the percentage found in part (a).
