A poll is conducted to determine who is most likely to win the election for town mayor. Two random samples of 500 residents each are polled. The data is as follows.
Candidate A Candidate B Total
Sample 1
346
154
500
Sample 2
248
252
500
What percentage of the total polled residents would vote for Candidate A as the town mayor?
(1 point)
Sample 1: 346 out of 500 residents would vote for Candidate A, which is 346/500 = 0.692 or 69.2%.
Sample 2: 248 out of 500 residents would vote for Candidate A, which is 248/500 = 0.496 or 49.6%.
Total: 346 + 248 = 594 residents out of 1000 residents would vote for Candidate A, which is 594/1000 = 0.594 or 59.4%.
Therefore, 59.4% of the total polled residents would vote for Candidate A as the town mayor.
To determine the average height of trees in a national forest, 10 trees are randomly selected. Their heights in feet are 85.4, 87.6, 87.1, 85.6, 85.9, 85.3, 84.9, 83.7, 84.0, and 85.2. To ensure the accuracy of the data, another set of
10 trees is randomly selected. Their heights are 87.1, 88.0, 84.2, 85.3, 86.5, 84.2, 83.2, 84.1, 85.2, and 87.3. What is the difference between the mean heights of the trees of these two random samples? (1 point)
Mean height of the first set of trees:
(85.4 + 87.6 + 87.1 + 85.6 + 85.9 + 85.3 + 84.9 + 83.7 + 84.0 + 85.2) / 10 = 854 / 10 = 85.4 feet.
Mean height of the second set of trees:
(87.1 + 88.0 + 84.2 + 85.3 + 86.5 + 84.2 + 83.2 + 84.1 + 85.2 + 87.3) / 10 = 855.1 / 10 = 85.51 feet.
The difference between the mean heights of the two sets of trees is:
85.51 - 85.4 = 0.11 feet.
Therefore, the difference between the mean heights of the trees of these two random samples is 0.11 feet.
Weong
I apologize for the error in the previous response. Let's recalculate the mean height for each set of trees and then find the difference:
First set of trees:
(85.4 + 87.6 + 87.1 + 85.6 + 85.9 + 85.3 + 84.9 + 83.7 + 84.0 + 85.2) / 10 = 865.7 / 10 = 86.57 feet
Second set of trees:
(87.1 + 88.0 + 84.2 + 85.3 + 86.5 + 84.2 + 83.2 + 84.1 + 85.2 + 87.3) / 10 = 869.1 / 10 = 86.91 feet
The difference between the mean heights of the two sets of trees is:
86.91 - 86.57 = 0.34 feet
Therefore, the difference between the mean heights of the two sets of trees is 0.34 feet.