Income Difference in Alabama, Arizona and Alaska

Abstract:

Income is an important economic indicator that influences decision making. This paper highlights the differences in income across regions and also shows that past changes in income will influence *future* income levels. An estimated model shows that comparing 1989 and 1979 income levels in the UK the 1979 income level explains 1989 income level changes in the selected sample.

Introduction:

This paper focuses on the income differences in three states namely Arizona, Alabama and Alaska in the year 1989, a random sample of 38 counties were selected from data collected from the US Census website, this analysis is important given that the level of income will influence both investment and consumer spending, higher __income__ means *that* consumer spending is higher, this means that companies will opt to invest in area with high income consumers due to the higher demand in these areas. The following is a discussion of major finings in the data:

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Income *Difference* in Alabama, Arizona and Alaska

Income differences:

The mean income in Alabama for the selected sample was 20766 with a standard deviation value of 5705.7, mean income in Alaska was 36051 with a standard deviation of 8915.5 and in Arizona the mean income was 21652 and the standard deviation value was 3442.6. The chart below summarizes the results:

The chart shows that Alaska had the highest mean income while Alabama had the lowest mean income value, this shows that in the year 1989 there were income differences across the three states.

The sample contained 38 counties whereby 26.32% are Arizona counties, 42.11% are Alabama counties and 31.58% are Alaska counties, the following pie chart shows the percentage number of counties in each state:

The above chart shows that 42.11% counties included in the sample were Alabama counties and only 26.32% were Arizona counties.

Further analysis of the data shows that majority of income levels ranged between 20,001 and 30,000; the following chart summarizes the results:

The chart above summarizes the income distribution across the 4 classes, the percentage frequency of the categories show that 50% of the income data ranged between 20,001 and 30,000, also that 13.16% of the income data range between 40,000 and 50,000.

Hypothesis testing:

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Income Difference in Alabama, Arizona and Alaska

The mean income level in Alaska is higher than the other states; this section tests the hypothesis that the mean income in Alaska is higher than the mean income in Arizona.

Null hypothesis:

H0: u1 = u2

Alternative:

HA: u1≠u2

Where u1 represents the mean income in Alaska and u2 represents the mean income in Arizona.

Assumptions:

In this case the T test is used to test this hypothesis and for this reason make the sample to be less than 30 units of data; the assumption made when testing is that income data across the counties is normally distributed.

Results:

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Income Difference in Alabama, Arizona and Alaska

The table below shows the results of the test:

Independent Samples Test

Levene’s Test for Equality of Variances

t-test for Equality of Means

F

Sig.

t

df

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Income Difference in Alabama, Arizona and Alaska

Sig. (2-tailed)

Mean Difference

Std. Error Difference

95% Confidence Interval of the Difference

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Income Difference in Alabama, Arizona and Alaska

Lower

Upper

Equal variances assumed

11.332

.003

-4.802

20

.000

-14398.683

2998.773

-20654.014

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Income Difference in Alabama, Arizona and Alaska

-8143.353

Equal variances not assumed

-5.153

14.713

.000

-14398.683

2794.464

-20365.086

-8432.280

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Income Difference in Alabama, Arizona and *Alaska*

From the table above the T calculated value is -5.153 and given that the T critical value at the 0.05 level of test is 2.23 then the null hypothesis is rejected, this means that the null hypothesis that the two means are equal is rejected.

Interpretation of results:

From the above results the null hypothesis is rejected, this means that the mean income value in Alaska is greater than the mean income value in Arizona. For this reason at the 0.05 level of test it is statistically significant to state that the mean income in Alaska is higher than the mean income level in Arizona.

Hypothesis two:

The mean income for all the states is 25825.82, given this value the next step is to determine whether the mean income for all the three states is less than the Alaska mean income 25825.82, for this the null hypothesis is stated as follows:

Null hypothesis:

H0: u1 = u2

Alternative:

HA: u1≠u2

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Income Difference in Alabama, Arizona and Alaska

Where u2 is the overall mean and u1 is Alaska mean income.

Z = 0.000705

Z critical = 1.9

Given that the Z critical value is greater then the Z score calculated, this means that the null hypothesis is accepted, the conclusion is that the mean *income* for Alaska is not greater than the mean value for all the states combined.

Correlation and regression:

This section analyses the relationship between the income levels in 1979 and income levels in 1989, the following table shows the results:

Correlations

income1989

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Income Difference in Alabama, Arizona and Alaska

income1979

income1989

Pearson Correlation

1

.958(**)

Sig. (2-tailed)

.

.000

N

37

37

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Income Difference in Alabama, Arizona and Alaska

income1979

Pearson Correlation

.958(**)

1

Sig. (2-tailed)

.000

.

N

37

37

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Income Difference in Alabama, Arizona and Alaska

From the table the correlation coefficient value is 0.958 which depicts a strong correlation between 1979 and 1989 income levels, this means that future income levels *will* depend on past income levels.

Regression analysis:

Having determined the strong correlation between the two variables the next step is to estimate a model as follows:

It = C + bIt-1

The table below shows the results:

Coefficients (a)

Model

Unstandardized Coefficients

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Income Difference in Alabama, Arizona and Alaska

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

440.922

1341.529

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Income Difference in Alabama, Arizona and Alaska

.329

.744

income1979

1.643

.083

.958

19.678

.000

The estimated model is as follows:

It = 440.922 +1.643 It-1

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Income Difference in Alabama, Arizona and Alaska

The model states that an increase in past income levels by one unit will increase income by 1.643 units; the R squared for this model is 0.917 showing that 91.7% deviations in 1989 income are explained by the changes in 1979 income.

Conclusion:

Some regions have higher income levels than others and from the above discussion the sample shows that Alaska had a higher mean income compared to the other two states. Another finding is that past income levels will influence future income levels and this is evident from the results of the regression model and the high R squared value.

REFERENCE:

William Mendenhall (*2003*) Introduction to statistics, Prentice Hall press, New Jersey

Census (2009) Income data, retrieved on 3rd December, from

http://www.census.gov/hhes/www/income/histinc/county/county1.html

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