Question

Eastern vs. Western States’ Spending on K-12 Education in 2014

Using the data below, compare how much the states East of the Mississippi spend on their K-12 students with how much states West of the Mississippi spend on their K-12 students. Make sure to create a numerical display (make a picture!), describe each distribution (in terms of shape, center and spread) and answer the question: who spends more?

Data in Desmos (Links to an external site.).

Eastern State	$ per Student		Western State	$ per Student
Alabama	9,028		Alaska	18,416
Connecticut	17,745		Arizona	7,528
Delaware	13,938		Arkansas	9,616
D.C.	18,485		California	9,595
Florida	8,755		Colorado	8,985
Georgia	9,202		Hawaii	12,485
Illinois	13,077		Idaho	6,621
Indiana	9,548		Iowa	10,688
Kentucky	9,312		Kansas	9,972
Maine	12,707		Louisiana	10,749
Maryland	14,003		Minnesota	11,464
Massachusetts	15,087		Missouri	9,875
Michigan	11,110		Montana	11,017
Mississippi	8,263		Nebraska	11,726
New Hampshire	14,335		Nevada	8,414
New Jersey	17,907		New Mexico	9,734
New York	20,610		North Dakota	12,358
North Carolina	8,512		Oklahoma	7,829
Ohio	11,354		Oregon	9,945
Pennsylvania	13,961		South Dakota	8,881
Rhode Island	14,767		Texas	8,593
South Carolina	9,732		Utah	6,500
Tennessee	8,630		Washington	10,202
Vermont	16,988		Wyoming	15,797
Virginia	10,973
West Virginia	11,260
Wisconsin	11,186

If you would like the data in a Google sheet, click here to find it. (Links to an external site.)

Data based on US Census Bureau. Source: http://www.governing.com/gov-data/education-data/state-education-spending-per-pupil-data.html (Links to an external site.)

(Links to an external site.) (Links to an external site.)

Think It Through:

(1) Develop a thesis statement: You can complete the statement below or develop one of your own. You can also change your thesis statement later if your observations about the data warrant it.

Example: The Eastern States spend more on K-12 students than the Western States.

(2) Make observations about shape, center, spread and outliers (if there are any).

	Eastern	Western
Shape (any outliers?)
Center (a representative or typical measurement)
Spread (overall range, along with an interval of typical measurements).
Other observations that will be useful in supporting your thesis.

(3) Write the analysis:

Write one or more paragraphs that use your observations to support the thesis.

Answer 1

Solution:

1)

Thesis: (Eastern State Colleges spend more on Students than Western State Colleges)

Null and Alternate Hypothesis

H₀: Mean Per Student Spends for Eastern State is Same as Western State

H_a: Mean Per Student Spends for Eastern State is greater than Western State.

2)

Eastern State

Since the mean is greater than Median, the data is skewed to the right. Also, the large Standard Deviation suggests that the data is spread out (more than Western State)

From the boxplot, we conclude that there are no outliers.

Western State

Since the mean is greater than Median, the data is skewed to the right. Also, the large Standard Deviation suggests that the data is spread out.

From the boxplot, we conclude that there are two outliers.

3)

We will be using Hypothesis testing to conclude if our earlier thesis is correct.

Alpha = 0.05

Test Statistic

t = (x1-x2)/(s₁²/n₁ + s₂²/n₂)^1/2 = 2.67

P-value = TDIST(2.67,27+24-2,1) = 0.005103

Result

Since the p-value is less than 0.05, we reject the null hypothesis in favour of alternate hypothesis ie Mean Per Student Spends for Eastern State is greater than Western State.