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Five-step Hypothesis Test Step one of the hypothesis test…

Five-step Hypothesis Test Step one of...
Five-step Hypothesis Test

Step one of the hypothesis test is to state the hypothesis of the research study both verbally and numerically. Verbally, the hypothesis can be described as follows:
The null hypothesis is that the mean annual income for the sample population worker is equal to the national average of $43,460, using a confidence level of 95%.
The alternative hypothesis is that the mean annual income for a local worker is not equal to the national average of $43,460.
Stated numerically:
H0:
H1:
Step 2: Select the test statistic.
Step 3: Find critical value.
Step 4: Compute.
Step 5: Make decision.

Nonparametric Test Selection

Test Results Interpretation and Comparison
Two different studies were used in our research. The first study involved finding the average mean of wages f
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7/5/2010
Stevewh
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Hi,

Can you complete the question ?

Steve
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Customer reply replied 8 years ago

What information do you need? Should I copy the entire exercise. My 5 steps are based on the information before the question. Hold on a minute

 

I need more numbers

Steve
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Customer reply replied 8 years ago

The researchers in this study are interested in using data to evaluate the mean annual wage in a sample population. According to the United State Department of Labor, Bureau of Labor Statistics, the 2009 mean annual income of all workers in the U.S. was $43,460, with a relative standard error of 0.1%. These estimates were calculated with data collected from employers in all industry sectors in metropolitan and nonmetropolitan areas in every State and the District of Columbia (DOL, 2010).

The comparison is to test the differences between the mean annual salaries in the DOL statistics to the mean annual salary of data gathered from a sample population. The researchers will evaluate if the mean annual wages of the sample population are the same as the mean national average. If this is the case, the researchers would fail to reject the null hypothesis stating that the mean annual income for the sample population worker is equal to the national average. Additionally, if the mean annual wages on the sample population are different from the mean national average, the researchers would reject the null hypothesis.

To make this analysis, the researchers used a nonparametric hypothesis test, or a distribution-free test, which "usually focuses on the sign or rank of the data rather than the exact numerical value of the variable, does not specify the shape of the parent population, can often be used in smaller samples, and can be used for ordinal data (when the measurement scale is not interval or ratio)" (Doane and Seward, 2007, p. 699). A more specific specialized nonparametric hypothesis test is the Mann-Whitney Test, named after Henry B. Mann (1905-2000) and D. R. Whitney. This is a nonparametric test that compares two populations. The Mann-Whitney test does not assume normality. Assuming that the populations differ only in centrality (i.e., location) it is a test for equality of medians. It is analogous to the t test for two independent sample means (Doan and Seward, 2007).

Five-step Hypothesis Test

 

Step one of the hypothesis test is to state the hypothesis of the research study both verbally and numerically. Verbally, the hypothesis can be described as follows:

The null hypothesis is that the mean annual income for the sample population worker is equal to the national average of $43,460, using a confidence level of 95%.

The alternative hypothesis is that the mean annual income for a local worker is not equal to the national average of $43,460.

Stated numerically:

H0: 12μ =$43,460'>

H1: 12μ≠$43,460'>

Step 2: Select the test statistic.

Step 3: Find critical value.

Step 4: Compute.

Step 5: Make decision.


Nonparametric Test Selection

Test Results Interpretation and Comparison

Two different studies were used in our research. The first study involved finding the average mean of wages for United States employees and comparing them to a sample of 100 random workers. The second study dealt with gender, in terms of comparing the difference in wage for men and women.

In order to come to a conclusion data must be analyzed from both populations and the wages earned. For the first study the hypothesis was to explore the area of mean annual income on a sample population. The research question is to determine if the mean annual wage of the sample workforce meets the national average. The national average wage is $43,460 taken by the Bureau of Labor Statistics. The sample population was one hundred and was taken randomly. The sample population pulled had a mean average wage of $30,833 which is much lower than the national average. The sample population's standard deviation was 16,947. A 95% confidence interval was used. The sample population was larger than 30 so the z-test was used. The critical value was calculated and concluded at 1.96.

The second study was of more interest to the team; the difference if men still make more money than women. The purpose of this research will determine if there is a significant difference in the annual salary levels of men versus women. When comparing wage differences between men and women, the studies proved that men do make more money than women in the workplace. Despite the age, background, and education, men earn more money than women. We used the z-test because the sample and population was larger than 30. The critical value was the same in this case as 1.96. By using the z-test and computing the critical value, the average income of women was $24,452. The average income for men computed $36,493. The difference of wage between the two is $12,041 favorable for men. The sample pulled from the population is not the actual average for the United States. It is a sample of one hundred individuals; 53 being men and 47 being women. The standard deviation for women was 12446. The standard deviation for men was 18448.

When comparing the two studies most of the information was the same in terms of national average wages. The difference between men and women was a separate study and differed from the original test. The sample population of 100 was pulled from a different source and not from the same sample from the first study.

Conclusion

Customer reply replied 8 years ago

I only need to worry about the 5 steps for the hypothesis statement not any other section

 

Ok, but i need more info

I need sample mean and standard deviation

Steve
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Customer reply replied 8 years ago

Oh, Ok, let me get that the information from Week II

 

Customer reply replied 8 years ago

One Sample Hypothesis Testing Paper

According to the United State Department of Labor, Bureau of Labor Statistics, the 2009 mean annual income of all workers in the U.S. was $43,460, with a relative standard error of 0.1%. These estimates were calculated with data collected from employers in all industry sectors in metropolitan and nonmetropolitan areas in every State and the District of Columbia (2010).

In our investigation we defined the verbal and numerical hypothesis chosen by the team through introducing our statement regarding the research issue, performing the five-step hypothesis testing procedure on the data, and explaining the test chosen to analyze the data. We will then interpret the results of the test. We have also included the raw data tables and results of this test.

Research Question and Hypothesis

To look at income for a comparison against the national mean income, a group of one hundred annual income samples were selected for this study. The purpose of this study is to explore the area of mean annual income on a sample population. The research question is to determine if the mean annual wage of the sample workforce meets the national average.

The data chosen by the team used in this research paper is the same as the data used for the previous sample hypothesis from Research and Evaluation I (RES/341), the Wages and Wage Earners Data Set (Doane & Seward, 2007). The descriptive statistics are shown in Table 1.


Table 1

Descriptive Statistics - Mean Annual Income

Wage

count

100

mean

30,833.46

sample standard deviation

16,947.10

minimum

9,879

maximum

83,601

range

73,722

 

 

confidence interval 95.% lower

27,470.79

confidence interval 95.% upper

34,196.13

half-width

3,362.67

 

Does the mean annual income of the sample population meet the national average? For this example, we have estimated the mean annual income to be $30,883. According to the Department of Labor, the national average is $43,460.

Hypothesis Test

Step 1: State the null and alternative hypothesis

The null hypothesis is that the mean annual income for the sample population worker is equal to the national average of $43,460, using a confidence level of 95%.

The alternative hypothesis is that the mean annual income for a local worker is not equal to the national average of $43,460.

Stated numerically:

H0: 12μ =$43,460'>

H1: 12μ≠$43,460'>

Step 2: Select the test statistic.

Since the sample size is greater than 30, the "z" distribution will be used in this research. The level of significance used in this research assignment will be 5% in order to determine the reliability of the hypothesis testing.

Step 3: Find the critical value.

a/2 = .05/2 = .025, z = 1.96

Step 4: Compute the test value.

X - 12μ'> 43,460 - 30,883

z = s / 12√n'> = 14,947 / 12√100'> = -7.45

The data and results are shown in Table 1.

Table 1

Hypothesis Test: Mean vs. Hypothesized Value

 

43,460.00

hypothesized value

30,833.00

mean Sample

16,947.00

std. dev.

 

1,694.70

std. error

 

100

n

 

 

 

 

 

-7.45

z

 

9.28E-14

p-value (two-tailed)

 

Step 5: Make a decision to reject or not reject the null hypothesis.

Reject null hypothesis since computed z value falls in the rejection region, well outside the acceptance area, as shown below in Figure 1.


Insert bell curve graph here.

 

Figure 1. Two-Sided Hypothesis Test

Findings Explanation

The findings from this hypothesis appear to indicate that the mean of annual wages of the sample population analyzed fell below that of the national average. There are a number of different factors to consider before any definitive conclusion can be drawn. Those factors may include the specific integrity of the data, whether or not the sample is truly random based on the findings, and the geographic congruence of the sample population. According to the data file, 33% of the respondents live in the South, which may have a lower wage base than larger, northern metropolitan areas.

According to the Department of Labor, the specific break down was based on the national salary scale which range into salaries by cities, we also see that median job salaries are fairly diverse across major U.S. cities, ranging from about $60,000 in Atlanta to around $67,000 in New York. This gives us a general view of what people in these cities are earning. In this example, a $7,000 difference in average income between Atlanta and New York exists (United States Department of Labor, 2010).

Conclusion

By looking at income across the United States, and comparing salaries by job title, industry, city and other influential factors, we find significant variation within the national salary range. Texas Teacher Salaries are not the same as New Jersey teacher salaries, pharmacist salaries vary by employment setting, and CEO Salaries may be very different from one industry to the next. From law to nursing, salaries for all professions are influenced by experience, location and many other factors (PayScale, 2009). With so many variables affecting the average job income, reviewing wages across the country only shows part of the picture when it comes to describing a national annual mean income. The analysis by the Department of Labor does provide insight into salary trends across America.

The goal of our research is to determine if the sample data is significant. Based on the current data, we reject the hypothesis as inconclusive at this time. In conclusion more defined testing is necessary to further examine the correlation between the annual wage of US workers and demographic. Further research will give a better understanding of what the data means to a group in a particular area. Expansion of the data set and use of a larger population sample will depict an accurate description of the hypothesis. Our challenge is to find better formulation criteria based on the value of more statistics.
Customer reply replied 8 years ago

Here is something else I found.

 

 

Nonparametric Hypothesis Testing Paper

Introduction

The researchers in this study are interested in using data to evaluate the mean annual wage in a sample population. According to the United State Department of Labor, Bureau of Labor Statistics, the 2009 mean annual income of all workers in the U.S. was $43,460, with a relative standard error of 0.1%. These estimates were calculated with data collected from employers in all industry sectors in metropolitan and nonmetropolitan areas in every State and the District of Columbia (DOL, 2010).

The comparison is to test the differences between the mean annual salaries in the DOL statistics to the mean annual salary of data gathered from a sample population. The researchers will evaluate if the mean annual wages of the sample population are the same as the mean national average. If this is the case, the researchers would fail to reject the null hypothesis stating that the mean annual income for the sample population worker is equal to the national average. Additionally, if the mean annual wages on the sample population are different from the mean national average, the researchers would reject the null hypothesis.

To make this analysis, the researchers used a nonparametric hypothesis test, or a distribution-free test, which "usually focuses on the sign or rank of the data rather than the exact numerical value of the variable, does not specify the shape of the parent population, can often be used in smaller samples, and can be used for ordinal data (when the measurement scale is not interval or ratio)" (Doane and Seward, 2007, p. 699). A more specific specialized nonparametric hypothesis test is the Mann-Whitney Test, named after Henry B. Mann (1905-2000) and D. R. Whitney. This is a nonparametric test that compares two populations. The Mann-Whitney test does not assume normality. Assuming that the populations differ only in centrality (i.e., location) it is a test for equality of medians. It is analogous to the t test for two independent sample means (Doan and Seward, 2007).

Five-step Hypothesis Test

 

Step one of the hypothesis test is to state the hypothesis of the research study both verbally and numerically. Verbally, the hypothesis can be described as follows:

The null hypothesis is that the mean annual income for the sample population worker is equal to the national average of $43,460, using a confidence level of 95%.

The alternative hypothesis is that the mean annual income for a local worker is not equal to the national average of $43,460.

Stated numerically:

H0:

H1:

Step 2: Select the test statistic.

Step 3: Find critical value.

Step 4: Compute.

Step 5: Make decision.


Nonparametric Test Selection

Test Results Interpretation and Comparison

Conclusion

 

References

Doane, D.P., & Seward, L.E. (2007). Applied statistics in business and economics. Boston, MA: McGraw-Hill/Irwin.

United States Department of Labor (2010). Bureau of labor statistics: occupational employment statistics. Retrieved July 3, 2010 from http://www.bls.gov/oes/current/oes_nat.htm

But i see that the results are done ?

What do you need exactly ?

Steve
Ask Your Own Math Homework Question
Customer reply replied 8 years ago
If you look at the 1st posting, there is a section that is titled "5 step hypothesis testing" The steps are numbered. The hypothesis is stated. There are five steps that have to be completed in order to accept or reject the null hypothesis. That is all.
Customer reply replied 8 years ago

Five-step Hypothesis Test

 

Step one of the hypothesis test is to state the hypothesis of the research study both verbally and numerically. Verbally, the hypothesis can be described as follows:

The null hypothesis is that the mean annual income for the sample population worker is equal to the national average of $43,460, using a confidence level of 95%.

The alternative hypothesis is that the mean annual income for a local worker is not equal to the national average of $43,460.

Stated numerically:

H0: 12μ =$43,460'>

H1: 12μ≠$43,460'>

Step 2: Select the test statistic.

Step 3: Find critical value.

Step 4: Compute.

Step 5: Make decision.

Customer reply replied 8 years ago
I need them done again for this week. And to accept or reject the hypothesis and why using a non-parametric test
Customer reply replied 8 years ago

Step 2. Select the test statistic (non parametric test) Which one and why?

 

Step 3. Find the critical Value

 

Step 4. Compute

 

Step 5. Accept or Reject Null hypothesis and why

Ok, but i see the results in your second post:

Anyway here are the steps:

Step 1)

H0:μ=43,460
H1:μ≠43,460


Step 2)

Test statistic = z


Step 3) Critical values are : -z(0.025)=-1.96 and z(0.025)=1.96

We reject H0 if z<-1.96 or z>1.96

Step 4) Statistic value = z=(43,460-30,883)/(16,497/√100)=7.624

Step 5) Decision:

Since z=7.624>1.96 we reject H0

Bonus is appreciated

Thanks

Steve
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Customer reply replied 8 years ago

Why is Z test chosen and Why do we reject?

If you look the exlpanation above:

"Since the sample size is greater than 30, the "z" distribution will be used in this research"

We reject z is in {z/ z<-1.96 or z>1.96}

Since z=7.624 (computed before) and 7.624>1.96 we reject H0

Steve

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