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Sample Hypothesis Testing Paper

Essay by   •  October 9, 2011  •  Case Study  •  2,269 Words (10 Pages)  •  1,670 Views

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One Sample Hypothesis Testing Paper

Sample Hypothesis Testing Paper

Baby boomers are reuniting with the education world. The economy had a major downturn, which cost thousands of Americans to enter a non-working status quo. Many years ago, it was not what an individual knew, to gain a position of employment; it was who the individual knew to obtain a decent paying job. Education was not a major influence on obtaining a position of employment, which would increase his or her income. Unfortunately, unemployment is forcing organizations to seek a high qualifying staff with a higher education. Employers are looking for individuals with higher education to grow with the company and become an asset to the future of the company's organization. This demand proves that education has an influence on individuals' wages. Individuals needing to make an income to prove for his or her living accommodations, is in need of returning to college to further his or her education.

The preliminary data shows that most individuals making over $40,000 per year attended school 12+ years, only a few of the individuals had fewer than seven years of education under his or her belt. The study further shows that the work experience for the individuals who returned to college were in a range from five to 44 years in age. In contrast, individuals who attend school for fewer than 12 years are making less than $40,000 per year, whereas most individuals are not making a large amount of money, his or her experience ranges from 19 years to 54 years.

Purpose of Research

In addition to education, several other factors contributing to individuals earning a higher or lesser wage at the same positions. Those factors include race, age, ethnicity and work experience. Individuals with long history of work experience will be an asset to the company and will in turn make a larger wage than a person newly entering the industry. Our team will try to determine how these factors come into play. The team will also determine how they affect various groups and their ability to attain a high paying job.

Definition of Problem

The ability to earn a higher wage tends to be dependent on the level of education one receives. Our charge will be to determine if the studies are correct in showing that individuals attending school for more than 12 years is more apt to receive a higher wage in the same type of position. The data provided below will assist the team during the research process and will help determine whether or not the team should reject the null hypothesis indicating that those individual attending school for more than 12 years will earn a higher wage.

Hypothesis Statement Formulated

H0 µ ≥ .50 - individuals with a college degree or higher earns 50% more in wages

H1 µ < .50 = individuals with less than a college degree earn 50% less in wages

Five-Step Hypothesis Testing

Our five-step hypothesis test will be formulated as follows and will help us demonstrate the effects a college degree may have on one's ability to earn higher wages:

Step 1

Null hypothesis: H0: ≥ .50

Alternate hypothesis: H1: <.50

Step 2:

Level of Significance:

At α= .05 the critical value is 1.972

Step 3:

Calculate the Test Statistic

v = n1 + n2 - 2 = 100 + 100 - 2 = 198

t = ± 1.972

Step 4:

Make the Decision

Wage Education

Mean: $30,833.46 Mean: 12.73

STDEV: $16,947.10 STDEV: 2.79

Number: 100 Number: 100

Formula:

Number of persons in education = 100

Number of persons in wages = 100

Test Statistic

t = -18.19

Step 5:

Fail to reject the null hypothesis at α = .05 significance level.

The Learning Team concludes that there is significant difference between wages and education (see Appendix B). The test results demonstrate that there is a significant educational influence on individuals' wages. Even though the results listed on the tables may not seem like a large gap in wages it is still a noticeable difference.

The t-test is a more conservative approach for larger samples then would be the z-test. The standard error of difference and hypothesized difference for both the t-test and z-test were relatively small when compared to one another. The information reveals enough evidence of a difference in means when observing the pooled variance. The degree of freedom is typically equal to the sample size minus one (Doane & Seward, 2007, p. 310). In cases where the variances are pooled both variances are added together to calculate their degrees of freedom (Doane & Seward, 2007, p. 407). Review Appendix B for additional information.

T-TEST

Hypothesis Test: Independent Groups (t-test, pooled variance)

Wage Ed

30,833.46 12.73 mean

16,947.10 2.79 std. dev.

100 100 n

198 df

30,820.73 difference (Wage - Ed)

143,602,056.84 pooled variance

11,983.41 pooled std. dev.

1,694.71 standard error of difference

0 hypothesized difference

...

...

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