a group of 200 adults were asked whether they exercise and whether they are vegetarian. their responses are…

a group of 200 adults were asked whether they exercise and whether they are vegetarian. their responses are summarized in the following table.\nvegetarian not vegetarian\nexercise 78 20\ndont exercise 26 76\n(a) what percentage of the adults exercise? %\n(b) what percentage of the adults are vegetarian? %\n(c) what percentage of the adults who are vegetarian exercise? %\n(d) is there evidence that adults who are vegetarian tend to be exercisers more often than average?\nyes, because the percentage found in part (c) is much greater than the percentage found in part (a).\nyes, because the percentage found in part (c) is much greater than the percentage found in part (b).\nno, because the percentage found in part (c) is about the same as the percentage found in part (a).\nno, because the percentage found in part (c) is about the same as the percentage found in part (b).

a group of 200 adults were asked whether they exercise and whether they are vegetarian. their responses are summarized in the following table.\nvegetarian not vegetarian\nexercise 78 20\ndont exercise 26 76\n(a) what percentage of the adults exercise? %\n(b) what percentage of the adults are vegetarian? %\n(c) what percentage of the adults who are vegetarian exercise? %\n(d) is there evidence that adults who are vegetarian tend to be exercisers more often than average?\nyes, because the percentage found in part (c) is much greater than the percentage found in part (a).\nyes, because the percentage found in part (c) is much greater than the percentage found in part (b).\nno, because the percentage found in part (c) is about the same as the percentage found in part (a).\nno, because the percentage found in part (c) is about the same as the percentage found in part (b).

Answer

Explanation:

Step1: Calculate number of adults who exercise

The number of adults who exercise is the sum of vegetarians who exercise and non - vegetarians who exercise, $78 + 20=98$.

Step2: Calculate percentage of adults who exercise

The percentage of adults who exercise is $\frac{98}{200}\times100% = 49%$.

Step3: Calculate number of vegetarian adults

The number of vegetarian adults is $78 + 26=104$.

Step4: Calculate percentage of vegetarian adults

The percentage of vegetarian adults is $\frac{104}{200}\times100% = 52%$.

Step5: Calculate number of vegetarian adults who exercise

The number of vegetarian adults who exercise is 78.

Step6: Calculate percentage of vegetarian adults who exercise

The percentage of vegetarian adults who exercise is $\frac{78}{104}\times100%=\frac{7800}{104}% = 75%$.

Step7: Analyze the relationship

Since $75%$ (percentage of vegetarian adults who exercise) is much greater than $49%$ (percentage of all adults who exercise), there is evidence that adults who are vegetarian tend to be exercisers more often than average.

Answer:

(a) 49 (b) 52 (c) 75 (d) Yes, because the percentage found in part (c) is much greater than the percentage found in part (a).