Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [statistics]

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.

Statistics is the science of the collection, organization, and interpretation of data. It deals with many aspects of data, which includes the planning of data collection in terms of the design of surveys and experiments. (From Wikipedia)

More specifically, mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and mathematical analysis. (From Wikipedia)

For questions which are more generally about collecting and treating data, it is advised that you post your question on Cross Validated and DSSE.

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avoiding type 1 error

Please help me with this Suppose that a labor union claims that a given procedure requires 20 minutes to perform. To evaluate this, suppose that we measured the amount of time required to complete the procedure on each of 36 occasions. 12, 15, 18,…
hani
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Dice rolling question (multinomial)

Three $6$-sided fair dice are rolled. In $10$ independent throws, Let $A$ be the number of times all the sides are the same and let $B$ be the number of times only two sides are the same. Find $E(6AB)$: Here is how I approached this: I know that…
icobes
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Use the data to calculate a 95% confidence interval for the standard deviation of the weights.

A cannery prints “weight 175 grams” on its label. The quality control supervisor selects 64 cans at random and weighs them. He finds the sample mean to be 173 grams, and the sample standard deviation to be 6 grams. I do not understand how to…
user1919987
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plots and probabilities

Assume that the aggressive invasive tree known as European Buckthorn is randomly distributed in a degraded forest preserve with λ =40 trees/seedlings per 100m^2. If two 100 m^2 plots are randomly chosen then what is the probability that one of the…
kingjames
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Auction with reserve price $X$ chosen from distribution $G$

"Consider an auction, with reserve price $X$ chosen from distribution $G$ where the item is allocated to a uniformly chosen random bidder among those who bid above the reserve price. The winner pays $X$, the reserve. Show that this auction is…
Alex
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What is a chi-square distribution?

I am studying statistics for a political science course (the second semester of statistics under that department) and I have no idea what this formula even means: $ \frac{(n-1)s^2}{\sigma^2}$ and this language being used "If a simple random sample…
poli-sci
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Negative Bionomial Distribution?

Assume City A has three parties, Party B, Party C, and Party D, with n1, n2, n2 citizens in them, respectively. Assume, for people in B, they will always support the motion by the government, while, for people in C, they will always be against the…
Takumi
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Probability of combinations in bingo games

Consider a grid of $n$ rows and $m$ columns (in the figures that I attach, is $n = 3$ and $m = 5$, but it might be arbitrary). The grid is populated with integer numbers in the range of [1...90]. How to calculate the probability that one particular…
Luca Fagioli
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If a measure is Valid (but not necesarily reliable), can it be consistently replicated?

I had this question on an exam, and I was positive that the answer was A. The Beck Depression Inventory is a scale intended to measure depression levels, with higher scores indicative of higher levels of depression. If this were a valid measure…
user125334
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Relationships between mean and standard deviation when one variable is linear function of another

Let $a$ and $b$ be constants and let $y_j = ax_j + b$ for $j=1,2,\ldots,n$. What are the relationships between the means of $ya$ and $x$, and the standard deviations of $y$ and $x$? I'm slightly confused with how to approach a theoretical question…
Valrok
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Calculating Average Percent Change

I'm trying to calculate the average percent change of 3 points in time that I have. The time periods are from 2011 to 2013 I calculated the percent change for 2011 to 2012 (2012-2011)/(2011) 2012 to 2013 (2013-2012)/(2012) and 2011 to 2013 (This is…
user3253967
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Application of the Normal Distribution

Test scores on a university admissions test are normally distributed, with a mean of 500 and a standard deviation of 100 (a) What is the probability that a randomly selected applicant scores 625 or more? (b)What is the probability that a randomly…
syndy
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Proving that the estimate of a mean is a least squares estimator

I think this is a really simple question so please bear with me -- I just had my first class in regression and I'm a little confused about nomenclature/labeling. Does anyone recommend some good weblinks that explain beginning linear regression…
Jessie Bullock
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Using the negative binomial distr.

Tom "makes"(scores) a basketball shot with the probability $0.8$. He stops when he has made 10 scores. (A) what is the probability that he makes it in $13$ attempts so here i used the negative binomial distribution: $\binom{k-1}{r-1}p^rq^{k-r}$…
Danny
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What is Russell Wilson's QB Rating?

Suppose it is known that QB Ratings in the NFL are normally distributed with mean 87.2 and standard deviation 8. Suppose it is known that Russell Wilson, a second year quarterback for the Seattle Seahawks,is ranked in the 87th percentile among all…
EhBabay
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