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    Statistical Theory

    ADD Test: Sensitivity, Specificity, Positive/Negative Prediction

    A diagnostic test for attention deficit disorder (ADD), determines that 83 children have the disorder and that 1,325 do not. However, 4 of the children that were diagnosed as having ADD, do not actually have it. Furthermore, 15 children that were diagnosed as not having ADD, actually do have ADD. What is the sensitivity, specifi

    Statistics: Maximizing farmer profits of growing fodder

    A farmer, in the business of growing fodder for livestock, has 90 acres for planting alfalfa and corn. The cost of seed per acre is $4 for alfalfa and $6 for corn. The total cost of labor will amount to $20 per acre for alfalfa and $10 per acre for corn. The expected income is $110 per acre from alfalfa and $150 per acre from

    Brief descriptions and examples - statistical terms

    Describe, in your own words, the following terms and give an example of each. a. F distribution: b. F statistic: c. Chi-square distribution : d. T distribution e. Dependent samples f. Independent samples g. Degrees of freedom h. T statistic i. Paired difference

    Mean Square Error of Exponential

    Given "X[1, ]X[2,]..... X[n]" form a random sample from an exponential λ distribution, find the estimator of the form "T[a]= a/(sum( X[i])" with the smallest mean square error as an estimator of λ. PDF attached for easier reading.

    Sensitivity, Specificity Calculations

    Xray No TB Yes TB Total Negative 1739 8 1747 Positive 51 22 73 Total 1790 30 1820 Calculate the sensitivity and specificity of an X-ray as a screen for TB and write a brief conclusion statement.

    Sampling Methods - Mid-Motors Ford

    There are five sales associates at Mid-Motors Ford. The five representatives and the number of cars they sold last week are: Sales Representative Cars Sold Peter Hankish 8 Connie Stallter 6 Juan Lopez 4 Ted Barnes 10 Peggy Chu 6 a. How many different samples of size 2 are pos

    Express the Confidence Interval

    Express the confidence interval 0.24 < p < 0.36 in the form of p-hat /plus sign with a line under it/ E What is the value of p-hat (round to nearest hundredth) What is the value of E (round to the nearest hundredth).

    Inferential Statistics and Point Estimate

    Suppose a confidence level is 0.44 < p < 0.60 What is the value of the point estimate p-hat (round to nearest hundredth) What is the margin of error E= (round to the nearest hundredth)

    Samples & Populations Mean

    See attached file for full problem description. Five bundles of pencils contain the quantities shown at the right. How many different samples of 2 bundles each are there? List all possible samples of size 2 and compute the mean of each sample. Calculate the population mean and compare it to the mean of the sampling distr

    Mixed Data and Statistics Questions

    1. What is the differences between statistics as numerical facts and statistics as a discipline or field of study. 5. Consider the data set for the sample of 10 minisystems in Table 1.7 a. how many variables are in the data set? b. Which of the variables are quantitative and which are qualitative? c. Which is the average C

    Conditional Expectation Function

    P(x1,x2)= (x1 choose x2) (1/2)^x1 (x1/15), x2= 0,1,2, ...., x1 x1= 1, 2, 3, 4 ,5 0 elsewhere is the joint pmf of X1 and X2. Determine E(X2|x1)

    Finding CDF, PMF and Order of Integers

    Let f(x) =1/6, x=1,2,3,4,5,6, zero elsewhere be the pmf of a distribution of the discrete type. Show that the pmf of the smallest observation of a random sample of size 5 from this distribution is: g1(y1)= [(7-y1)/6]^5 - [(6-y1)/6]^5, y1=1,2,3,4,5,6 What is the cdf of y1? For some reason, I just can't seem to understand

    Indicator function and ancillary stats

    7.9.1 Let Y1<Y2<Y3<Y4 denote the order statistics of a random sample of size n=4 from a distribution having pdf f(x;&#952;)= 1/&#952;, 0<x<&#952;, zero elsewhere, where 0<&#952;<infinity. Show that the pdf is of the form 1/&#952; f(x/&#952;), where f(w)=1, 0<w<1, zero elsewhere. Please see attached for full question.

    Sufficiency and Order Statistics

    Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the uniform distribution over the closed interval [-theta, theta ] having pdf f(x; theta ) = (1/2(theta))I[-theta , theta ](x). Argue that the mle of theta; equals theta;hat= max(-Y1, Yn). Demonstrate that the mle theta;hat is a sufficient statisti

    Sufficiency

    7.2.6 Let X1, X2,...,Xn be a random sample of size n from a beta distribution with parameters alpha= &#952; and beta= 2. Show that the product X1,X2...Xn is a sufficient statistic for &#952;. Use Neyman's Factorization Theorem.

    Distribution of Y in a Random Sample

    Let X1, X2,...,Xn denote a random sample from a distribution that is N(&#956;, &#952;), 0<&#952;<infinity, where &#956; is unknown. Let Y = the sum from 1 to n of (Xi-Xbar)^2/n=V. What are the E[Y] and Var[Y].>0. Please see attachment.

    Likelihood Tests

    Let X1, X2, ...., Xn be a random sample from a N(µ0, σ ^2= Ө) distribution, where 0 < Ө < Infinity and µ0 is known. Show that the likelihood ratio test of H0: Ө = Ө0 versus H1: Ө Not = Ө0 can be based upon the statistic W= the sum from i=1 to n (Xi - µ0)^2/ &#1257;0. Determine the null distribution of W and give, ex

    Order Statistics-Determine the E(Yn) and V(Yn)

    Let Y1<Y2<.....<Yn denote the order statistics of a random sample of size n from a uniform distribution on [0, theta] ie) f(x)=1/theta if 0<x<theta, 0 otherwise, where theta>0. Determine the E(Yn) and V(Yn).

    Estimation is examined.

    "Hockey-r-us," a store specializing in sales of hockey equipment, wants to find out the average age of all its customers. A random sample of 25 customers reveals an average age of 38 years with a standard deviation of six years. It determines a 95% confidence interval of the average age of all customers.

    Distribution function samples

    Let X1 and X2 denote a random sample of size 2 from a distribution with pdf f(x) = 1/2, 0 < x < 1, zero elsewhere. Find the distribution function and the pdf of Y = X1/X2.

    Statistics - Data Models Topic

    10) Clearly define the decision variables, the objective function and each constraint. From the Solver Solution, include the value of objective function and each of the decision variables.

    Binary integer programming model (capital budgeting)

    A. Define the decision variables for this formulation. b. Show the binary integer programming formulation including the objective function and all relevant constraints. c. Solve the problem as a binary integer programming model on a spreadsheet, or in LINDO. d. Interpret this solution to management in its language.