8.4.2. Let X have a Poisson distribution with mean . Find the sequential proba-bility ratio test for testing Ho: 0= 0.02 against H₁ : 0 = 0.07. Show that this testcan be based upon the statistic Σ X₁. If aa = 0.20 and 3a = 0.10, find co(n) andc₁(n).

X have Poisson distribution with mean θ. H0:θ=0.02, H1:θ=0.07. αa=0.20, βa=0.10.

Answered: 8.4.2. Let X have a Poisson…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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A random sample of n1 = 20 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that σ1 = 11. For Englewood (a suburb of Denver), a random sample of n2 = 15 winter days gave a sample mean pollution index of x2 = 49. Previous studies show that σ2 = 16. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) What is the level of significance? What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
3.6.1. Let T have a t-distribution with 10 degrees of freedom. Find P(|T| > 2.228) from either Table III or by using R. 1: 1
2.6 Given that the moment-generating function for the chi-square random variable is derived by m(t) = (1 – 2t) 2. Differentiate this mgf to find the mean and variance of the chi-square distribution.
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[4.2.14. Let X denote the mean of a random sample of size 25 from a gamma-type distribution with a = 4 and B > 0. Use the Central Limit Theorem to find an approximate 0.954 confidence interval for u, the mean of the gamma distribution. Hint: Use the random variable (X- 43)/(432/25)/2 = 5X/23- 10. %3D
9.3 Let Y₁, Y₂,..., Y, denote a random sample from the uniform distribution on the interval (0, 0+1). Let 0 =Y-; and O=Y). a Show that both ₁ and ₂ are unbiased estimators of 0. b Find the efficiency of 8₁ relative to ₂. n n+1
A random sample of n1 = 18 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that σ1 = 17. For Englewood (a suburb of Denver), a random sample of n2 = 20 winter days gave a sample mean pollution index of x2 = 52. Previous studies show that σ2 = 16. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) What is the level of significance? What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
Let X~Geo(0.3). Find the following a. P(X = k). b. P(1 ≤ X 3) and describe its interpretation. d. The mean μ = E(X) and the Variance σ2 = Var (X) of the random variable X.
A random sample of n1 = 20 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that σ1 = 11. For Englewood (a suburb of Denver), a random sample of n2 = 10 winter days gave a sample mean pollution index of x2 = 31. Previous studies show that σ2 = 18. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. H0: μ1 < μ2; H1: μ1 = μ2H0: μ1 = μ2; H1: μ1 > μ2 H0: μ1 = μ2; H1: μ1 ≠ μ2H0: μ1 = μ2; H1: μ1 < μ2 (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.The Student's t. We assume that both population…

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8.4.2. Let X have a Poisson distribution with mean . Find the sequential proba- bility ratio test for testing Ho: 0= 0.02 against H₁ : 0 = 0.07. Show that this test can be based upon the statistic Σ X₁. If aa = 0.20 and 3a = 0.10, find co(n) and c₁(n).