Question

Educational Attainment. The U.S. Census Bureau compiles census data on educational attainment of Americans. From the document Current Population Survey, we obtained the 2010 distribution of educational attainment for U.S. adults 25 years old and older. Here is that distribution.

Highest Level	Percentage
Not HS graduate	12.9
HS graduate	31.2
Some college	16.8
Associate degree	9.1
Bachelor degree	19.5
Advanced degree	10.5

A random sample of 500 U.S. Adults (25 years old and older) taken this year gave the following frequency distribution.

Highest level	Frequency
Not HS graduate	45
HS graduate	163
some collage	76
Associate degree	53
Bachelor degree	102
Advanced degree	61

Decide at the 5% significance level whether this year's distribution of educational attainment differs from the 2010 distribution.

Short answer

The class width is 10

The midpoint of the second class is 20

The lower and upper cut points of the third class is 25 and 35

The third class cut points include the observation $32.4$

Step-by-step solution

Given Information

A quantitative data collection was categorized using cut point grouping with equal-width classes.

a) If the first class's lower and upper cut points are 5 and 15, the common class width is as follows:

The Lower limit of the first class is 5 .

The first class's upper cut point is 15.

$Classwidth=Upperlimit-Lowerlimit$

$$\begin{gathered} =15-5 \\ =10 \end{gathered}$$

Therefore, the class width is $10$.

Definition

b) We find the midpoint of the second class is given below:

The Lower cut point of the first class is 5 .

The Upper cut point of the first class is 15 .

In Cut point grouping the lower cut point of the second class is equal to the upper cut point of the first class.

So the Lower cut point of the second class is 15

The upper cut point of the second class is

= Lower cut point of the second class + Class width

$$\begin{gathered} =15+10 \\ =25 \end{gathered}$$

By definition, the midpoint is given by

$$\begin{gathered} \mathrm{Midpoint}=\frac{\mathrm{Lower}\mathrm{cutpoit}+\mathrm{Upper}\mathrm{cutpoint}}{2} \\ =\frac{15+25}{2} \\ =20 \end{gathered}$$

Therefore, the midpoint of the second class is 20 .

Definition

c) We find the lower and upper cut points for third class is given below:

The Lower cut point of the second class is 15 .

The Upper cut point of the second class is 25 .

In Cut point grouping the lower cut point of the third class is equal to the upper cut point of the second class.

So the lower cut point of the third class is 25

The upper cut point of the third class is

$$\begin{gathered} =\mathrm{Lower}\mathrm{limit}\mathrm{of}\mathrm{the}\mathrm{third}\mathrm{class}+\mathrm{Class}\mathrm{width} \\ =25+10 \\ =35 \end{gathered}$$

Therefore, the lower and upper cut points of the third class is 25 and$35$.

Definition

d) The cut points for the third class are 25 and 35.

Therefore, the third class cut points include the observation $32.4$