2) Suppose that a random sample X₁, X₂,...,X10 is from a poison distribution with mean 8. It isdesired to test a null hypothesis Ho: 0= 0.1 against alternative H₁:0 = 0.5 at a level ofsignificance.a) Use Neyman Raphson method to show that the best test or uniformly most powerful testrejects H₁ if Σ₁x₁ ≥c where c satisfies the probability equationa = P(2!!! Xi > c |0 = 0.1).b) If c = 3, show that Type I error is 0.0803 for the test in part a).Hint: ΣX, has a poisson distribution with mean 100.

Answered: Image /qna-images/answer/930eb620-c609-415a-b7e2-2baab87176b9.jpg

Answered: 2) Suppose that a random sample X₁,…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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b) Suppose that Y₁, Y₂,..., Y₁0 is a random sample from a bernoulli (P) distribution. It is desired that the null hypothesis Ho: P = 0.5 against the alternative hypothesis H₁: P = 0.1 at a level of significance. If Ho is rejected when Σı Y = 1. i) Determine the level of significance. ii) Find the power of the test.
Suppose that the variable under consideration is normally distributed on each of two populations and that the population standard deviations are equal. Further suppose that you want to perform a hypothesis test to decide whether the populations have different means, that is, whether μ1 = μ2. If independent simple random samples are used, identify two hypothesis-testing procedures that you can use to carry out the hypothesis test.
Our method of calculating a 95 percent confidence interval for the mean µ of a normal population, with known variance o2, is 1.960 1.960 Xn Xn + This method of creating an interval has the property that a single SRS of size n will provide an interval that will containing u with 0.95 probability. If five different individuals select 5 independent samples, each of size their resulting five interval estimates of 4, (i) what is the probability that u will belong to all five of them: (ii) None will contain µ? (iii) What is the probability that at least one of the intervals will contain u? and obtain п, The following``answers" have been proposed. (a) (i) (0.95)5, (ii) (0.95)5, (iii) (0.95)5. (b) (i) (0.05)5, (ii) 1– (0.05)5, (iii) (0.95)5, (c) (i) 1 – (0.05)5, (ii) (0.05)5, (iii) (0.95)5. (d) (i) (0.95)5, (ii) (0.05)5, (iii) 1 – (0.05)5. (e) None of the above. The correct answer is (a) (b) (c) (d) (e) N/A (Select One)
Let µj and µz represent the population means and let "= 2 A test will be made of the hypotheses Ho "a=0 versus 41 "a>0. Can you reject Ho at the a= 0.05 level of significance?
Suppose we have a random sample of size n=100 drawn from a population with a mean of μ=50 and a standard deviation of σ=10. We want to test the null hypothesis H0: μ=48 against the alternative hypothesis H1: μ≠48 using a two-tailed test with a significance level of α=0.05. What is the decision and p-value of this hypothesis test?
You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as µ₁ and process 2 has a mean defined as µ2. The null and alternative hypotheses are Hỏ: µ₁ −µ₂ ≤0 and H₁: ₁-₂ > 0. The process variances are unknown but assumed to be equal. Using random samples of 36 observations from process 1 and 49 observations from process 2, the sample means are 60 and 50 for populations 1 and 2 respectively. Complete parts a through d below. Click the icon to view a table of critical values for the Student's t-distribution. a. Can you reject the null hypothesis, using a probability of Type I error x = 0.05, if the sample standard deviation from process 1 is 28 and from process 2 is 23? The test statistic is t = (Round to three decimal places as needed.)
Let x1, X2, ..., Xn be a random sample from a normal population with unknown mean u and an unknown variance o?. At a given significance level a, derive the generalized likelihood ratio test for Ho : o 5. versus Completely specify the test when a = population: 0.05 and n = 26. Does the power function of the test depend on the mean of the The following `answers" have been proposed. %3B 26 (a) For a = 0.05 and n = 26 the test rejects Ho when E(X; – X„)² > 941.25. The power function of the test indirectly depends on the population mean u via = 7. (b) For a = 0.05 and n = 26 the test rejects Ho when E(X; – Xn)² > 941.25. The power function of the test does not depend on the population mean µ. (c) For a = 26 ,26 0.05 and n = 26 the test rejects Ho when E(X; – Xn)² > 188.25. The power function of the test does not depend on the population mean µ. (d) For a = 0.05 and n = 26 the test rejects Ho when E(X; – X„)² > 188.25. The power function of the test indirectly depends on the population mean…
You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as µ₁ and process 2 has a mean defined as µ₂. The null and alternative hypotheses are Ho: H₁ H₂ ≤0 and H₁: μ₁ −μ₂ > 0. The process variances are unknown but assumed to be equal. Using random samples of 36 observations from process 1 and 49 observations from process 2, the sample means are 60 and 50 for populations 1 and 2 respectively. Complete parts a through d below. Click the icon to view a table of critical values for the Student's t-distribution. The test statistic is t = 1.806. (Round to three decimal places as needed.) The critical value(s) is(are) 1.663. (Round to three decimal places as needed. Use a comma to separate answers as needed.) reject Ho. Since the test statistic is greater than The test statistic is t = tnx + My- -2,α¹ b. Can you reject the null hypothesis, using a probability of Type I error x = 0.05, if the…
Suppose that xi and x2 are random samples of observations from a population with mean m and variance s2. Consider the following three point estimators, A.B.C, of m: *1 + x2 *1 + 3r2 *1 + 2x2 C = A = B = 2 3 a) Which of these estimators yields an unbiased estimator of m? Justify your answer. b) Of those that are unbiased, which is the most efficient? Justify your answer.
The farmers' association of the Amatole region in the Eastern Cape wants to report on the average milk production in this region. It has been shown that the milk production in this region is normally distributed with mean u and variance o?. Suppose a random sample of farms,Y1,Y2, Y3, Y4 is taken from the region. Consider the following estimators of 0: Ô, = Ÿ and Ôô, = 2Y2+2Y4 _ 1. Identify the parameter of interest. 2. You have been presented with two estimators of the parameter of interest. (a) Find the expected value of each of the estimators. (b) Find the variance of each of the estimators. (c) Based on your calculations in (a) and (b), which estimator would you choose and why?
An automobile owner found that 20 years ago, 70% of Americans said that they would prefer to purchase an American automobile. He believes that the number is much less than 70% today. He selected a random sample of 50 Americans and found that 32 said that they would prefer an American automobile. Can it be concluded that the percentage today is less than 70%? At α=0.01α=0.01 , is he correct? 1) State the null and alternative hypotheses. A) p=0.70p=0.70 B) p<0.70p<0.70 C) p≠0.70p≠0.70 D) p>0.70p>0.70 Answer A, B, C, or D in the box Ho: H1: 2) Compute test statistics. Round the answer to two decimal place. Test statistics = 3) Compute the P value. Round your answer to four decimal places. P value = 4) Compute the critical value. Round your answer to two decimal places. Critical Value = 5) Decision E) Reject the Ho F) Do not reject the Ho Type E or F in the box 6) Conclusion G) There is enough evidence to support the claim that the percentage…
Reynir examines the difference in the amount of carbon dioxide in two types of mineral water. He performs a two-group t-test to compare the average carbon dioxide levels in the two groups. His hypotheses are H0 : μ1 - μ2 = 0 og H1 : μ1 - μ2 ≠ 0. Reynir also calculated a confidence interval for the difference between the means of the two groups α and in the hypothesis test). Reynir rejected the null hypothesis. Which of the following applies to the safety margin calculated by Reynir?a) It contains the value zero.b) It contains 95% of the values that can occur when the experiment is performed.c) It does not contain the value zero.d) It contains both values greater than zero and values less than zero.

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