One Sample Hypothesis 4
Running head: ONE SAMPLE HYPOTHESIS TESTING
One Sample Hypothesis Testing
Sean E. Snook
Jessica Awe
University of Phoenix
Research and Development II
RES 342
Carrae Echols
Nov 21, 2008
One Sample Hypothesis 4
One Sample Hypothesis 4
One Sample Hypothesis Testing
Popular opinion tells us that the better educated one is, the more he or she can expect to earn. In other words, a person with a high school education will earn more than a high school drop-out, a person with an Associates Degree will earn more than a high school graduate, a person with a Bachelors Degree will earn more than someone with less education, and so on. Team A will attempt to prove this assumption by evaluating the data that we have at our disposal in the form of a one sample hypothesis test.
According to the 2007 Census, the mean earnings of 80% of men over twenty-five years of age, with fifteen to seventeen years of education, was $73,398 (U.S. Census Bureau, 2008). Of the population sampled in our hypothesis test, does this fact hold true?
Hypothesis Statement: The mean income of 80% of men over 25 years of age, with between 15 and 17 years of education is $73,398.
1. State the hypothesis.
Hypothesis Test
Hypotheses: H0: On average, the wages earned by 80% of men over twenty-five years of age with fifteen to seventeen years of education is $73,398. If given a random sample of 100 men the result it is found that 32 men who are over twenty-five years of age with fifteen to seventeen years of education who do not earn $73,398, we can reject the claim at the 0.05 significance level.
In numerical form,
H0: m1 = m2
Vs.
H1: m1 < m2
2. Select a level of confidence.
The second phase in testing a hypothesis is to select a level of confidence. By using a 95% confidence level, Team A can determine if the null can be accepted or rejected.
Level of Significance: a = 5%
3. Identify the test statistic
The third step is conducted in order to identify the test. We have chosen to use a z- test because this type of test is used to test hypothesis about μ when the population standard deviation is known.
Decision Rule:
Team A will make the decision to reject or accept the null hypothesis if p-value < 0.05
4. Analyze the sample data.
σ = sqrt P * (1 - P) = sqrt (0.80 x 0.20) = sqrt (0.0016) = 0.04
n 100
Z= (p – P) = (.32 - .80) = -12
0.04 0.04
P is the sample proportion, and n is the sample size.
Since a one-tailed test was conducted, Using Normal Distribution to find P (z < -12) = 0.04, consequently the P-value = 0.04.
5. Interpret results.
Since the significance level 0.05 the P-value 0.04, the null hypothesis cannot be accepted.
From our research we can determine that the null hypothesis be rejected. Since the null hypothesis is rejected we then find that we must go with the alternative hypothesis, which is that the mean income of 80% of men over 25 years of age, with between 15 and 17 years of education is not equal to $73,398. Although our hypothesis has led us to this assumption, it does not necessarily mean that more education does not equal more money, but it does lead us to the conclusion that this is not true in all cases. Some career choices require more education than others to make more money; however, some do not. It depends on the career, the location, and what type of degree you have.
For our hypothesis we wanted to prove a point and that is the more education, the more money you can make. With our test and hypothesis we did not prove this hypothesis completely because there are many factors that can change the outcome. The different careers and locations play a big role on the amount of income a person is going to make. For example there can be a doctor that works for a clinic and a doctor that has a private practice, the doctor working the private practice can make more money than the person working for the clinic. This type of scenario holds to be true for many different jobs. The null hypothesis was to see if the level of education affects the income that a person generates in his or her job. The alternative hypothesis was to prove that the population that was sampled could show that the men that have more education make a fairly good amount of income. This research can be developed over a period of time to show that more education is better.
Reference
U.S. Census Bureau (2008). Current population survey. Retrieved November 21, 2008, from http://www.census.gov/hhes/www/income.html