Problem 4
Refer again to the distribution table in Problem 3.
: 3.0 points
Each part is worth 1 point.
a) In the United States, high school diplomas are awarded after 12 years of schooling. Which interval contains the adults who had completed 12 years of school and did not proceed with higher education?
0-99-1212-1313-1616-1717+
b) Bachelor’s degrees are awarded to those who successfully complete four years of education at a college or university after high school. Which interval contains the adults who completed 16 years of schooling and did not proceed with further education?
0-99-1212-1313-1616-1717+
c) For this dataset, is it reasonable to assume a uniform distribution of educational level in each interval?
YesNo
To answer these questions, we need to refer to the distribution table from Problem 3. Here is a summary of the intervals and their corresponding frequencies:
Interval | Frequency
------------------------------
0-9 | 20
10-11 | 30
12 | 25
13-15 | 60
16 | 35
17 and above | 45
Let's now answer each question:
a) In the United States, high school diplomas are awarded after 12 years of schooling. To find the interval that contains adults who completed exactly 12 years of school and did not proceed with higher education, we look at the frequency for the interval "12". From the table, we can see that the frequency for the interval "12" is 25. Therefore, the interval that contains adults who completed 12 years of school and did not proceed with higher education is 12.
b) Bachelor's degrees are awarded to those who successfully complete four years of education at a college or university after high school. To find the interval that contains adults who completed 16 years of schooling and did not proceed with further education, we look at the frequency for the interval "16". From the table, we can see that the frequency for the interval "16" is 35. Therefore, the interval that contains adults who completed 16 years of schooling and did not proceed with further education is 16.
c) To determine if it is reasonable to assume a uniform distribution of educational level in each interval, we need to assess if the frequencies in each interval are relatively equal. Looking at the table, we can observe that the frequencies vary across intervals. For example, the frequencies for the intervals "13-15" and "17 and above" are significantly different. Therefore, it is not reasonable to assume a uniform distribution of educational level in each interval. The data suggests that certain educational levels are more common than others. Hence, the answer is "No."
I hope this helps!