Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.
Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena.
A standard statistical procedure involves the collection of data leading to test of the relationship between two statistical data sets, or a data set and synthetic data drawn from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a "false positive") and Type II errors (null hypothesis fails to be rejected and an actual relationship between populations is missed giving a "false negative"). Multiple problems have come to be associated with this framework, ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis. Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also occur. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.
I was doing tech support at a healthcare conference over the weekend in which one of the speakers talked about stats 101 and interpreting research. In discussing it further with my wife this morning, I realized we've missed a piece of the puzzle.
My wife made an spurious example of cars...
Hi Physics Forum, lurked around a bit and need some advice.
I've never particularly liked any branch of my academics, however I excelled in my English classes and I thought the most natural thing to do was declare it my major. I absolutely hate academic reading though, as I see it mostly as a...
Homework Statement
Let X have mean u and variance s^2. Find the mean and the variance of Y=[(X-u)/s]Homework Equations
The Mean is linearThe Attempt at a Solution
I thought to just plug in the mean of X anywhere i saw it in Y so mean of Y would be 0
and then for the variance I was kind of...
I've heard mixed opinions regarding the importance of the PGRE. I heard from some that the PGRE has no relevance at all, as some profs on the admissions committee don't even LOOK at it. However, I've of course heard from others that its very important
I've heard plenty of people with great...
Hi everyone, I have trouble depicting the difference between these two problems. The first problem uses the multiplication rule to solve while the second problem uses the counting rules (combination) to solve. To me, it seems like both problems could be solved using the multiplication rule so I...
I am having a difficult time grasping the multiplication rules - The rules are easy to remember but actually applying it to a problem is so confusing and frustrating as I don't know whether to use Rule #1 (independent events) or Rule #2 (Dependent events).
Here's a problem from my book that I...
Hey guys, this is for an elementary statistics course. When given a problem, I am having trouble determining which is the data set (X) and which is the weight (W).
For example:
Using the weighted mean, find the average number of grams of fat per ounce of meat or fish that a person would...
I really understand most of the question, just having trouble with one part, so I am going to try to sum it up. if you need more info to clarify please let me know...
background...
nielson media research provides two measures of television viewing audience (in this case for the world...
I'm majoring in Physics and minoring in Math at a highly ranked liberal arts school (top 25). I have a 3.9 overall GPA and I'm not sure what my math and Physics GPA is but its higher than 3.9. I have all A's and one A- in math and Physics. I got an 800 on the quantitative section of the GRE...
Homework Statement
A group of 50,000 tax forms has an average gross income of $37,000, with an SD of $20,000. Furthermore, 20% of the forms have a gross income over $50,000. A group of 900 forms is chosen at random for audit. To estimate the chance that between 19% and 21% of the forms...
Homework Statement
Consider X(1)...X(n) IID X~ Poisson(lambda=lnQ), x=0,1,2..., Q >1
Find the Unique MVUE for lnQ?
Homework Equations
The Attempt at a Solution
i let T=sum(x), which is sufficient
and lnQ*=sum(x)/n be an unbiased estimator for lnQ
Not really sure how to...
Homework Statement
Chp 18, Rev Ex 4
A coin is tossed 25 times. Estimate the chance of getting 12 heads and 13 tails.
Chp 16, Rev Ex 8
A gambler will play roulette 50 times, betting a dollar on four joining numbers each. If one of these four numbers comes up, she gets the dollar...
hey guys/gals i have been given this cw question however i spent ages and can't seem to get my head around it can some one give me a hand
" the number N of wrecks in a particular area of sea off the Cornish coast has a poisson distribution with mean \propto . the probability that a wreck is...
Hello all,
I'm a senior Electrical Engineering student at Wright State University in OH and I'll be graduating in March 2011 with my BSEE degree.
I've come to the conclusion that my main area of passion and interest is in power systems and power generation so I'd like to do a masters...
Hello friends,
I am having some trouble with a particular statement an author made in a book.
Despite being a statistics question, it is at its heart, a calculus question. Perhaps someone here with a better understanding of the subject can help, because I'm not convinced the matter has...
Homework Statement
Let A_1, A_2... be any infinite sequence of events, and let B_1, B_2... be another infinite sequence defined as B_1=A_1, B_2=A_1cA_2, B_3=A_1cA_2cA_3 and so on.
Prove that Pr(Union i=1 to n A_i) = Sum i=1 to n Pr(B_i).
(sorry if that notation is hard to understand)...
so I'm somewhat new to statistics proofs, but this one is for the most part a sets proof, which i can do. I'm having trouble connecting them.
(c = complement)(AB = A intersect B)
Let A_1, A_2... be any infinite sequence of events, and let B_1, B_2... be another infinite sequence defined as...
Homework Statement
Suppose that X1,...,Xn form a random sample from a inform distribution on the interval [0,1] and that the random variable Ynmax{X1,...,Xn}.
Determine the smallest value of n such that Pr[Yn≥.99]≥.95
Homework Equations
W=Yn-Y1 where W is the range of the sample...
Homework Statement
for each value of p>1
c(p)= 1/xp
(the n=1 under the sumation symbol should be x=1)
Suppose that the random variable X has a discrete distribution with the following p.f.:
f(x)= 1/[c(p)xp] for x=1,2,...
(a) For each fixed positive integer n, determine the...
I was recently accepted into engineering science 1t4. I am very intrigued by the new finance option being offered but don't have a lot of information about it. I've seen the statement on the u of t website but honestly that doesn't help very much. I would appreciate it greatly if someone with...
I have this residual vs fitted values plot in R, and it should show a scatter of points with constant variance and mean 0. The mean 0 part seems to hold, but there is quite a clear diamond shape for the variance...
I have tried raising the response variable to a power <1 and a log...
Winning the game hinges on owning the more valuable properties and frequently collecting rent on them. Given this, if you could choose to own one color of properties or streets to start the game, what color would you choose? Why?
What is the most the foolish thing a player just sent to jail...
I am have trouble with a question, and how exactly each given part of this question relates to getting the answer.
[b]1. The problemb]
Assume that N,X1, X2...are independent.
Let P(N = k) = qk-1p , k\geq1, p+q = 1
and let X1,X2,X3,...be iid with a common pdf
f(x)...
Well what are your opinions? Would not having a solid grounding in statistics be more useful than a solid knowledge of the applications of econometrics?
Homework Statement
Suppose x = (x1, x2, ..., xn)T ∈ Rn is a random vector drawn from the n-dimensional
standard Gaussian distribution N(0, I), where 0 = (0, 0, ..., 0)^T (0 vector transpose) and I is the identity matrix.
(a) What distribution does ||x||^2 follow? Justify your answer.
(b) On...
Hi
I am doing a research project on how maths can be used to maximise profit and was wondering if anyone knows any examples applications of probability used to maximise profit. E.g. banks insurance etc?
Thanks
Does anyone know any math/stat/operations research grad schools accepting students for PhD in math/stat or MS in financial engr/operations research in the spring semester?
To those familiar with university structure,
mine offers two different statistics courses (besides those that are offered to fields like soc. or bio. which are not open to non majors). One is offered by the statistics department, one by the math department.
Is there a generalized difference...
Homework Statement
Suppose that one year, an insurance company incurred dollar damages,
X, in four different amounts with probabilities, p(x), shown below:
X
0
1000
5000
10000
p(x)
0.7
0.2
0.08
0.02
If the company offers a $500 deductable and wants and wants an...
Homework Statement
Having problems solving some questions for Statistics class
The amount of time spent by North American adults watching TV per day is normally distributed with a mean of 6 hrs and a standard deviation of 1.5hrs.
a. What is the probability that a randomly selected North...
Homework Statement
Let X denote the lifetime of a radio, in years, manufactured by a certain company. The density function of X is given by
f(x)=\left\{\stackrel{\frac{1}{15}e^\frac{-x}{15}\ \ \ \ if\ 0\ \leq\ x\ <\ \infty}{0\\\\elsewhere}
What is the probability that, of eight such...
I have a problem which I can't figure out how to do. Can you please explain how to do it.
1) Six 6 trees are randomly selected from an orange grove. Assume the median yield in the entire grove is 2.8 boxes per tree. What is the probability that the yields from 4 of the 6 trees will exceed...
Hello,
I am looking at the stats for a particular academic test:
- In 2007, 11 women out of 50 candidates took the test; there were only 3 women among the 16 successful candidates.
- In 2009, 12 women out of 52 candidates took the test; there was only 1 woman women among the 14 successful...
Homework Statement
i didnt know which forum stats is posted in so i posted it here, but the problem says the q is , Sheilas measure glucose level one hour after a sugary drink varies according to the normal distribution (u= 125 mg/dl) and r=10 mg/dl. What is the level L such that there is a...
Homework Statement
the q is , Sheilas measure glucose level one hour after a sugary drink varies according to the normal distribution (u= 125 mg/dl) and r=10 mg/dl. What is the level L such that there is a probability only 0.05 that the mean glucose level of 4 test results falls above L...
Homework Statement
A function f( x ) had the following form : f ( x) = kx^-(k+1) where 1 < x < infinity
a) for what values of k is f a pdf ?
Homework Equations
See attachments (the theorem is included)
The Attempt at a Solution
started out by using the first equation in the...
Graduate School Advice Needed: Where to Apply with my stats & "backup" schools
As an undergraduate I've studied engineering physics. It seems in general that graduate students in engineering have a lower gpa than those in physics or math. I have since decided I would like to do physics...
I am an incoming sophomore that is majoring in math and having a potential interest in studying physics along side. Right now, I'm trying to take one more class alongside of physics (first year), abstract algebra, and history (for grad requirement). So far, I found these three courses to be...
Homework Statement
Find Z0 such that P(z > z0) = 0.1234
Homework Equations
The Attempt at a Solution
Z is the mean which is 0. So if Z0 is less than the mean it should be a negative number. Looking at the table 0.1234 does not show up but the closest is 0.1217 which is 0.31.
So Z0...
Hi,
Why is -BEi used instead of +BEi as the lagrange multiplier for indistinguishable particles? How is it justified?
I've been reading a book about statistical mechanics and it introduces lagrange multipliers first for distinguishable particles- it has ln(ni) + a + BEi = 0.
(where a is...
Following online programs are freely available for math enthusiasts
1. Graphing Rectangular 2D
2. Graphing Rectangular 3D
3. Graphing Polar
4. Graphing 2D Parametric curves
5. Graphing 3D Parametric curves
6. Graphing 3D Parametric surfaces
7. Finding Area under curve (Rectangular)...
Stats -- Geometric Variance Proof
Hi,
I'm a student in South-East Indiana, enrolled in a AP Stats class.
Our teacher has asked us to prove the geometric variance equation (the first equation pictured) USING ALGEBRA ONLY.
I've gotten it all the way down to the 2nd equation and now I'm stuck...
Very urgent probability and stats question.
Homework Statement
Hi
I have the following problems.
During an investigation of polution in a river scientistists have taken 60 water samples in the river
and measured the concentration c of bacteria. They have taken 20 samples in a...
-I have no clue where to start-
--------------------------------------------------------------------------------------
A roadway construction process uses a machine that pours concrete onto the roadway and measures the thinckness of the concrete so the roadway will measure up to the...
Homework Statement
The question is
Let Y be a continuous random variable with pdf f_Y(y) = 3(1-y)^2
and I have to find P(|Y - 1/2| > 1/4)
Homework Equations
Is there a formula involved here or something that can help me?
The Attempt at a Solution
I'm not even sure how...
Homework Statement
When constructing a stem and leaf graph I'm confused on how to label the stem and leaf still.
For example:
On page 20, number 12 in section 1.2:
The observations look like this:
.31 .35 .36 .36 .37 .38 .40 .40 .40
.41 .41 .42 ...
We were told to use repeating...
Hi everyone, I just started stats and had a question.
Question:
The accompanying specific gravity values for various wood types used in construction appeared in the article "Bolted Connection Design values based on Eurpoean yeidl Model"
.31 .35 .36 .36 .37 .38 .40 .40 .40
.41 .41 .42 .42 .42...