Statistical Analysis of Colored Stones by using Random Sampling Naomi Malary
Lab Report 1
Ecology Lab 312 L-1
October 12, 2009
Introduction
Random Sampling, a method often used by ecologist involves an unpredictable component. In this method, all members of the population have an equal chance of being selected as part of the sample. The results involving random sampling can be categorized as descriptive statistics and inferential statistics (Montague 2009).Descriptive statistics includes simplified calculations of a given sample and arrange this information into charts and graphs that are easy to contrast. Trying to reach conclusions that extend beyond the immediate data alone describes inferential statistics. To document the results of sampling, qualitative and quantitative data is used. Quantitative data lack is measured and identified on a numerical scale, whereas Qualitative data approximates data but does not measure characteristics, properties and etc. The purpose of this experiment was to use statistical analysis to evaluate random sampling of colored stones (Montague 2009). While conducting this experiment, we came up with a few null hypotheses. The first null hypothesis is that all the stones that have the same color weigh the same. The second null hypothesis is that there are more blue stones than red or yellow stones. Therefore the Blue stones will be picked the mosr. Our final null hypothesis is that the stones of the same color have the same length and that they will not vary in size. Method

Our team was given a box of one hundred and two red, blue, and yellow stones. Team members A and B took turns choosing stones via random sampling, team member E recorded the color of the chosen stone. Team member C measured the weight of the stone with a scale, and team member D measured the length of the stone using a vernier capiler. Team members A and B placed the stones back into the box, mixed it, and we then repeated the procedure....

...Gender Discrimination: A StatisticalAnalysis
Gender discrimination, or sex discrimination, may be characterized as the unequal treatment of a person based solely on that person's sex. .
It is apparent that gender discrimination is pervasive in the modern workplace, however, its presence and effects are often misrepresented and misunderstood. Statistical testing plays an important role in cases where the existence of discrimination is a disputed issue and has been used extensively to compare expected numbers of members of a protected group, to the actual number of members of that protected group that have been involved in a significant employment action. This paper will use statistical testing and analysis, including a multiple regression model, to estimate the effects that various independent variables have upon the dependent variable, salary level.
This analysis utilized a data sample consisting of 46 employees and variables relating to each of those employees. These variables include: gender, age, level of education, length of employment, job type, and weekly salary. Each of these variables is further broken as follows: gender was divided between males and females; age was listed as the age of the employee; education was broken down to reflect the last level of education obtained by the employee, some high school, high school, college, and graduate school; employment length was...

...Audit SamplingUsingStatistical Methods Presented By: Abhishek Agrawal
AUDIT SAMPLING
• Application of an audit procedure to less than 100% of the items in a population
– Account balance – Class of transactions
• Examination “on a test basis” • Key: Sample is intended to be representative of the population.
APIPA 2009
2
SAMPLING RISK
• Possibility that the sample is NOT representative of the population • As a result, auditor will reach WRONG conclusion • Decision errors
– Type I – Risk of incorrect rejection – Type II – Risk of incorrect acceptance
APIPA 2009
3
TYPE I – RISK OF INCORRECT REJECTION
• Internal control: Risk that sample supports conclusion that control is NOT operating effectively when it really is
– AKA – Risk of underreliance, risk of assessing control risk too high
• Substantive testing: Risk that sample supports conclusion that balance is NOT properly stated when it really is
APIPA 2009 4
TYPE II – RISK OF INCORRECT ACCEPTANCE
• Internal control: Risk that sample supports conclusion that control is operating effectively when it really isn’t
– AKA – Risk of overreliance, risk of assessing control risk too low
• Substantive testing: Risk that sample supports conclusion that balance is properly stated when it really isn’t
APIPA 2009 5
WHICH RISK POSES THE GREATER DANGER TO AN AUDITOR? • Risk of incorrect rejection
– Efficiency
• Risk...

...StatisticalAnalysis
The analysis of the data from the study of Barnes & Noble stores is in two stages, the descriptive study and inferential statistical study. Initially, the Team will distribute and collect the questionnaires. The use of classification will summarize the data and express it in the tabular form for better understanding of the data. For example, if the questionnaires consist of information from males and females, the data is putinto two categories and expressed in a table form. A proper graphical method can display the data summation. As an example, the display of information can be in a pie chart or simple bar chart of different categories like people who prefer to read electronic books and people who prefer to read hard copy books. Finally, a proper statistical hypothesis testing method can answer the research questions in the questionnaire. In the Barnes & Noble case study, the hypothesis test that proportion of people who prefer to read the electronic copy of books is larger than the proportion of people who prefer to read hard copy books. The hypothesis test consists of equality of proportions of two populations. The hypothesis test can assist in determining if the emergence of electronic copy of books is reducing the prices of hard bound and paperback books.
Analyzing the Data
The selection of the analysis is based on two things: the way...

...Elementary Concepts in Statistics. In this introduction, we will
briefly discuss those elementary statistical concepts that provide the necessary
foundations for more specialized expertise in any area of statistical data analysis. The
selected topics illustrate the basic assumptions of most statistical methods and/or have
been demonstrated in research to be necessary components of one's general
understanding of the "quantitative nature" of reality (Nisbett, et al., 1987). Because of
space limitations, we will focus mostly on the functional aspects of the concepts
discussed and the presentation will be very short. Further information on each of those
concepts can be found in the Introductory Overview and Examples sections of this
manual and in statistical textbooks. Recommended introductory textbooks are:
Kachigan (1986), and Runyon and Haber (1976); for a more advanced discussion of
elementary theory and assumptions of statistics, see the classic books by Hays (1988),
and Kendall and Stuart (1979).
• What are variables?
• Correlational vs.
experimental research
• Dependent vs. independent
variables
• Measurement scales
• Relations between variables
• Why relations between
variables are important
• Two basic features of every
relation between variables
• What is "statistical
significance" (p-value)
• How to determine that a
result is "really" significant
•...

...3
Simple RandomSampling
3.1 INTRODUCTION
Everyone mentions simple randomsampling, but few use this method for population-based surveys. Rapid surveys are no exception, since they too use a more complex sampling scheme. So why should we be concerned with simple randomsampling? The main reason is to learn the theory of sampling. Simple randomsampling is the basic selection process of sampling and is easiest to understand. If everyone in a population could be included in a survey, the analysis featured in this book would be very simple. The average value for equal interval and binomial variables, respectively, could easily be derived using Formulas 2.1 and 2.3 in Chapter 2. Instead of estimating the two forms of average values in the population, they would be measuring directly. Of course, when measuring everyone in a population, the true value is known; thus there is no need for confidence intervals. After all the purpose of the confidence interval is to tell how certain the author is that a presented interval brackets the true value in the population. With everyone measured, the true value would be known, unless of course there were measurement or calculation errors. When the true value in a population is estimated with a sample of persons, things get more complicated. Rather then just...

...key is the use of statistically derived randomsampling procedures. These ensure that survey results can be defended as statistically representative of the population. Surveys that do not follow these procedures can produce results that lead to misguided market research, strategic, or policy decisions. Any so-called "survey" in which no attempt is made to randomly select respondents, such as call-in readers' or viewers' "polls", is likely to produce results that in no way reflect overall public opinion--even if many thousands of individuals participate.
It is true that sampling randomly will eliminate systematic bias
The mathematical theorems which justify most frequentist statistical procedures apply only to random samples.
http://www.ma.utexas.edu/users/mks/statmistakes/RandomSampleImportance.html
no author,
COMMON MISTEAKS MISTAKES IN USING STATISTICS: Spotting and Avoiding Them
4/10/12
Moore and McCabe (2006), Introduction to the Practice of Statistics, Third edition, p 219
Sample Distribution and Sampling Error
Distributions of populations of scores have been discussed. However, a single score does not accurately represent the population. A sample, or subset, of the population is a better estimator of the population. Alternatively, a sample that has received some treatment can be compared to the original population. Just as there is a distribution of scores...

...
StatisticalSamplingStatisticalSampling
1. The authors of the paper make assumptions about the U.S. population on three dimensions. What are the three dimensions? (Hint: The authors refer to these dimensions as "components of change.")
Answer: The three dimensions would be migration, fertility, and mortality.
2. What is the expected population of the U.S. in 2050 given the new series (i.e., based on 1998 data) based on the lowest series? The middle series? And the highest series?
Answer: Lowest - 313,546,000
Middle - 403,687,000
Highest - 552,757,000
3. What do the lowest, middle, and highest series represent?
Answer: Just as one would utilize sampling in an audit context, this document emphasizes how key sampling judgments affect sample results. The lowest, middle, and highest series represent the effects of varying expectations in regards to mortality fertility, and migration. These projections don’t include a systematic measurement of uncertainty regarding these dimensions. By applying variant assumptions for each component in an individual manner, this would result in the range of a population series that would be identified with the maximum variance to this component. In order to produce the lowest and highest series, the authors combined the extreme values of all three major components favored the lowest and highest population growth easily. This...

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