5. Let X₁, X2, X3, X4, X5 be a random sample of size 5 from the pdff(x; 0): = 0 < x < 0.2.x0²where > 0. Suppose we want to test Ho: 0 = 1 vs. H₁ : 0 < 1.(a) Find the MLE of 0.(b) Using your result in (a), define a decision rule for rejecting Ho at a level of signif-icance a.(c) Determine the power function for this testing procedure. (Note: A power functionK(0) is a function that gives the power of the test when the specific value of thealternative hypothesis is 0 = 0 a.)

It is given that X1, X2, …X5 be a random sample that follows the pdf fx;θ=2xθ2, 0<x<θ The…

Answered: 5. Let X₁, X2, X3, X4, X5 be a random…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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1) Below are data of foam indexes for three different espresso makers. Test the hypothesis that foam indexes differ between the three. (Note: these data are highly kurtotic, so normality cannot be assumed.) Set a at 0.05. Which test should you use and why? State the hypothesis, provide the critical value and test statistic and state your conclusions. Hyper-Espresso Method (HIP) I-Espresso System (IT) 56.19 Bar Machine (BM) 36.64 70.84 39.65 46.68 36.67 35.35 40.11 37.74 73.19 35.96 57.78 38.52 48.61 33.52 37.12 37.33 72.77 21.02 24.81 65.04 32.68 48.33 34.18 62.53 23.08 54.26
a) & b)
5
6
Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.
(b) A rescarcher supccts that the fish in a particular elevated wetland have elevated mercury level. To confirm that, five striped bass in that wetland were caught and their tissues were tested for mercury. Then four striped bass in an unpolluted wetland were also caught and tested for the purpose of comparison. Table QI shows the fish mercury levels in mg/kg. Table QI shows the fish mercury levels in mg/kg. Sample from polluted wetland Sample from unpolluted wetland 0.580 0.382 0.711 0.276 0.571 0.570 0.666 0.366 0.598 Construct the 95% confidence interval for the difference in the population means. Then, test at the 5% level of significance, whether the researcher's suspicion is valid. Assume that the population variances are equal.
Obtain 100 (1 x)% confidence limits (for large samples) for the parameter 2 of the f(x, 2) = e-^.^* ; x ; x = 0, 1, 2,... x! Poisson distribution:
The quality characteristic of a product Y consists of three components X1, X2, and X3. The distributions of these components are normal with means 100, 2, 1 and variances 1, 1, 1 respectively. The specifications of the product are 90 ± 8. If Y= X1 + -7X2 + -9X3. Products that are below the lower specification limit are scrapped. Find the proportion of scrapped products = Ф(z).
We calculate the correlation between the percent of adult population fully vaccinated for COVID-19 and the COVID-19 death rate per 100,000 in 2021 for the states and territories of the United States (55 observations). We observe a correlation r=-0.3558 Test the hypothesis H_0: ρ=0 against H_a: ρ≠0 at the 99% level (α=.01)
12. Let (*1, 12, ., r„) be independent samples from the uniform distribution on [0,0]. Let X(n) and X(1) be the maximum and minimum order statistics respectively, (a) Find the distribution of X(m) and X(a) and hence, their means and variances. X{n) (b) Show that 2nY x where Y = – In %3D (c) Show that 2) In - Xản: Hence write a function of the geometric mean, i=1 (II GM(r) = which is Xn 1
Suppose X1, ..., Xn have been randomly sampled from a normal distribution with mean 0 and unknown variance sigma^2, and let U = c * i=1 -> n summation (X_ i)^2 , where c is a constant. Find the value of c that minimises the Mean Squared Error (MSE)
DEx2)-Ex)(Exy) |t= (X- X)// Examus - cdn.student.uae.examus.net/?rldbqn=1&sessi... STAT-101 FEX_2021_2_Male State whether the question is true or false 4 - 30 -> 118:50 362 The degree of freedom of t-test for independent samples (where of & o are unknown and not assumed to be equal) with sample sizes n1=37 and n 43 is equal to 79. ce362d6 2dcf91 F-E <µ < i+E where E = Za/2• e362d ef917 Formulae Sheet STAT-101-2 d.f. = min (n– 1,n2 – 1) p – E

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