Statistics Essay

666 words - 3 pages


Introduction The Sample Mean The Central Limit Theorem

The Sample Variance Sampling Distribution from The Normal Distribution Sampling from A Finite Population
◦ Distribution of The Sample Mean ◦ Joint Distribution of X and S2

◦ Approximate Distribution of The Sample Mean ◦ How Large A Sample Is Needed




Recall definitions of:
◦ ◦ ◦ ◦ ◦ ◦ ◦ Population Sample Inferential statistics Sampling Random sampling Parameter Statistic


If X1, . . . , Xn are independent random variables having a common distribution F, g , then we say that they constitute a sample (sometimes called a random sample) from the distribution F.




Parametric inference problem: Problems in which the form of the underlying distribution is specified up to a set of unknown parameters, eg: Nonparametric inference problem: problems in hi h i which nothing is assumed about the form thi i d b t th f of ...view middle of the document...

Then for n large, the distribution of
X1 +・ ・ ・+Xn is approximately normal with mean nμ and

variance nσ2. i


The Central Limit Theorem




Problem: An insurance company has 25,000 automobile policy holders If the yearly claim holders. of a policy holder is a random variable with mean 320 and standard deviation 540, approximate the probability that the total yearly claim exceeds 8.3 million.





Since the sample mean has expected value μ and standard deviation σ/√n it then follows √n, that

has approximately a standard normal distribution

The weights of a population of workers have mean 167 and standard deviation 27. (a) If a sample of 36 workers is chosen, approximate the probability that the sample mean of their weights lies between 163 and 171. (b) Repeat part (a) when the sample is of size 144. 144








A general rule of thumb is that one can be confident of the normal approximation whenever the sample size n is at least 30 30. That is, practically speaking, no matter how non normal the underlying population distribution is, the sample mean of a sample of size at least 30 will be approximately normal. normal In most cases, the normal approximation is valid for much smaller sample sizes




Theorem If X1, . . . , Xn is a sample from a normal s sa p e o o a population having mean μ and variance σ2,


◦ X and S2 are independent random variables, with X being normal with mean μ and variance σ2/n and (n − 1)S2/σ2 being chi square with n − 1 degrees of chi-square freedom.


The time it takes a central processing unit to process a certain type of job is p yp j normally distributed with mean 20 seconds and standard deviation 3 seconds. If a sample of 15 such jobs is observed, what is the probability that the sample variance will exceed 12?





A sample of size n from this population is said to be a random sample if it is chosen in such a manner that each of the C(N, n) population subsets of size n is equally likely to be the sample.



Other Papers Like Statistics

Statistics Essay

3466 words - 14 pages descriptive statistics. Students will learn to apply business research and descriptive statistics in making better business decisions. Other topics include examination of the role of statistics in research, statistical terminology, the appropriate use of statistical techniques, and interpretation of statistical findings in business and research. Policies Faculty and students will be held responsible for understanding and adhering to all

Statistics Essay

3604 words - 15 pages Question catalogue: Statistics Self-Study Module Master's programme Media and Communication Science If you are master student of the master programme “Media and Communication Science” and have to fulfill the additional requirement: Self-Study Module Statistics, you have to answer these list of 42 questions. Please answer the following questions concerning statistical methods in social science briefly. Helpful information concerning the


1134 words - 5 pages 1) The main purpose of descriptive statistics is to A. summarize data in a useful and informative manner B. make inferences about a population C. determine if the data adequately represents the population D. gather or collect data 2) The general process of gathering, organizing, summarizing, analyzing, and interpreting data is called A. statistics B. descriptive statistics C. inferential statistics D. levels of measurement 3) The

Statistics - 2264 words

2264 words - 10 pages distributed normally. The Histogram below as well as the Descriptive Statistics (Appendix 1, Table 1b) show that the data distribution is leptokurtic (kurtosis is 2,021) and negatively skewed (skewness -,240). We can determine several outliers (Appendix 1, Table 1c, Table 1d) with extreme ratios. In cases #46 and #178 JSL is more than the highest option provided in the questionnaire. That could be a mistake in data entering or the respondent wanted

Statistics - 1168 words

1168 words - 5 pages 3 ( HA: μ< 3 ) Challenges the status quo Never contains the “=”, “≤” or “≥” sign May or may not be accepted Is generally the hypothesis that is believed (or needs to be supported) by the researcher –a research hypothesis. • Test Statistics: Sample used to determine whether a hypothesis will be accepted or rejected. If

Statistics - 1105 words

1105 words - 5 pages relied on the collection of data to make decisions that propel the human race into the next era of technical development and business growth. The type of data varies as it can either be quantified or qualitative to meet the needs and purpose of the research. The age old question has always been which of the two is the most preferred methodology, but the real question should be how both mirror the theme of statistics to provide the closest range to

Statistics - 1921 words

1921 words - 8 pages one has tertiary or professional qualifications) P(A)=8C1*12C2/20C3+8C2*12C1/20C3+ 8C3*12C0/20C3 =8*66/1140+28*12/1140+56/1140 =0.807 3. Explain in detail the following key statistical concepts. Where possible illustrate your explanation with a graph or drawing. a) Descriptive Statistics Descriptive statistics means basic features of the raw data. A set of descriptive is used to describe the concerned samples. Arithmetic mean

Statistics - 1894 words

1894 words - 8 pages BUSINESS STATISTICS ASSIGNMENT Project Title: Employee retention at D&Y consulting firm Section E: Group 2:Anshul Garg (11FN-015)-Finance Gokul Sudhakaran(11DM-039)-Marketing Kaviya .A. (11DM-057)- Marketing Nikhil Gagrani(11DM-089)- Marketing Sheth Dharmil Nirupam(11DM-147)-Marketing Taru(11IB-061)-International Business Submission Date:- 9th September,2011

Statistics - 1794 words

1794 words - 8 pages adolescents’ reported incidence of being victims or perpetrators or traditional and electronic bullying. a. Using this table as an example, explain the idea of a frequency table to a person who has never had a course in statistics. Frequency is how many times something has happened and of all of the possible results that can occur, and each result's respective chance of happening. So the frequency of the table would be how many times the

Statistics - 1778 words

1778 words - 8 pages ) c) Copy and paste your regression result below. SUMMARY OUTPUT | | | | | | | | | | | | | | | | | Regression Statistics | | | | | | | | Multiple R | 0,66669338 | | | | | | | | R Square | 0,444480063 | | | | | | | | Adjusted R Square | 0,428141241 | | | | | | | | Standard Error | 0,050770391 | | | | | | | | Observations | 36

Statistics - 2018 words

2018 words - 9 pages Statistics Name Institution Question 1 of 20 | 5.0 Points | When comparing two population means with an unknown standard deviation you use a t test and you use N-2 degrees of freedom.  A. True |  B. False | | Reset Selection Question 2 of 20 | 5.0 Points | Pretend you want to determine whether the mean weekly sales of soup are the same when the soup is the featured item and when it is a normal item on the menu. When it is the

Related Essays

Statistics Essay 578 Words

578 words - 3 pages This paper will explain what statistics are. Statistics are used in so many ways, including business. This paper will thoroughly defining statistics, the types and levels of statistics, the role of statistics in a business and examples of how statistics may be used. The most common definition for statistics would be the collection of numerical data. Examples of numerical data could be the percentage of how many African-Americans passed

Statistics Essay 593 Words

593 words - 3 pages In a world ridden with endless problems and possibilities, it is statistics that is relied upon to find solutions to the problems and help determine what possibilities are truly feasible. Statistics may be best defined as the means by which data is gathered, analyzed, and interpreted to better understand a problem or situation. There are two types of data that can be analyzed in statistics. These are quantitative and qualitative data

Statistics Essay 2717 Words

2717 words - 11 pages Descriptive and Inferential Statistics ________________________________________ Statistics can be broken into two basic types. The first is known as descriptive statistics. This is a set of methods to describe data that we have collected. Ex. Of 350 randomly selected people in the town of Luserna, Italy, 280 people had the last name Nicolussi. An example of descriptive statistics is the following statement : "80% of these people have the

Statistics Essay 1100 Words

1100 words - 5 pages , observe and interpret information regarding this population. The purpose of this paper is to determine which methods of statistics are used as a measuring tool and what levels of measurements are used or could be used to improve the decision-making process for this organization. Statistics in the Workplace Many areas of the hospital facility use statistics in measurement. How do statistics affect this hospital healthcare facility in women