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QUESTION6 A Hypothesis relies on a set of hypotheses, a test statistic, the sampling distribution of...
5. (10 points) Let X1,... , Xio be a random sample of size 10 from a Poisson distribution with me...
5. (10 points) Let X1,... , Xio be a random sample of size 10 from a Poisson distribution with mean θ. The rejection region for testing Ho :-0.1 vs. 1.1: θ-0.5 is given by Σ"i z > 4. Determine the significance level α and the power of the test at θ : 05.
5. (10 points) Let X1,... , Xio be a random sample of size 10 from a Poisson distribution with mean θ. The rejection region for testing Ho...
. Suppose a random sample of 25 is taken from a population that follows a normal distribution wit...
. Suppose a random sample of 25 is taken from a population that follows a normal distribution with unknown mean and a known variance of 144. Provide the null and alternative hypotheses necessary to determine if there is evidence that the mean of the population is greater than 100. Using the sample mean, Y, as the test statistic and a rejection region > k}, find the value of k so that α = 0.15. of the form - Using the...
For the given data, (a) find the test statistic, (b) find the standardized test statistic, (c)...
For the given data, (a) find the test statistic, (b) find the standardized test statistic, (c) decide whether the standardized test statistic is in the rejection region, and (d) decide whether you should reject or fail to reject the null hypothesis. The samples are random and independent , a = 0.01. Sample statistics: x = 1235, n 40, x2 = 1195, and n2 = 70. Population statistics: o1 65 and a2 120. Claim: (a) The test statistic for -H2is (b)...
Question 4 (6 marks) Part a) Calculate the statistic, set up the rejection region, interpret the...
Question 4 (6 marks) Part a) Calculate the statistic, set up the rejection region, interpret the result, and draw the sampling distribution. Ho: Hi: μ 10 μ#10 Given that: σ-10, n-100, X-10, α-0.05. Part b) A statistics practitioner is in the process of testing to determine whether is enough evidence to infer that the population mean is different from 180. She calculated the mean and standard deviation of a sample of 200 observations as X -175 and s-22. Calculate the...
Hypotheses Testing
In order to test customer satisfaction with a given service, we conduct a survey and define a random variable Yi as follows:Yi = 1 if customer i is satisfiedYi = 0 if the customer i is not satisfiedGiven the identical and independent Bernoulli distributed samples y1, …, yn withP[Yi = 0] = θP[Yi = 1] = 1 – θwe want to test the hypotheses H0: θ = θ0 = 0:52 et H1 = θ = θ1 = 0:48• Construct the...
For the following information, determine whether a normal sampling distribution can be used, where p is...
For the following information, determine whether a normal sampling distribution can be used, where p is the population proportion, α is the level ofsignificance, p is the sample proportion, and n is the sample size. If it can be used, test the claim.Claim: p≥0.28; α=0.04. Sample statistics: p=0.20, n=140 Let q=1−p and let q=1−p. A normal sampling distribution ▼ cannot can be used here, since ▼ npnp n ModifyingAbove p with caretnp ▼ less than< greater than or equals≥ 5...
Question Help * For the given data, (a) find the test statistic (b) find the standardized...
Question Help * For the given data, (a) find the test statistic (b) find the standardized test statitic, ( should reject or tall to reject the null hypothesis. The samples are random and independent. the rejection region, and (d) decide whether you c) decide whether the standardized test statistic is in nh"P2, α:001 Sample statistics: x.-1225, n.-45, x2-1195. and n2-65 Population stabsics o, so ando, 100 (a) The test statistic for μ1_P2 b) The standardized test statistic ftor p1-P2 (Round...
For the given data, (a) find the test statistic, (b) find the standardized test statistic, (c)...
For the given data, (a) find the test statistic, (b) find the standardized test statistic, (c) decide whether the standardized test statistic is in the rejection region, and (d) decide whether you should reject or fail to reject the null hypothesis. The samples are random and independent Claim: <H2, a=0.01. Sample statistics: x = 1235, n = 30, X2 = 1205, and n = 60. Population statistics: 6 = 70 and 62 = 100. (a) The test statistic for ,...
Suppose that the null hypothesis is true, that the distribution of the test statistic, say T,...
Suppose that the null hypothesis is true, that the distribution of the test statistic, say T, is continuous with cumulative distribution function F and that the test rejects the null hypothesis for large values of T. Let V denote the p-value of the test. a. Show that V = 1 − F(T). b. Conclude that the null distribution of V is uniform. c. If the null hypothesis is true, what is the probability that the p-value is greater than 0.1?
3. Let X,,X,,..., X, be a random sample from a Gamma 40distribution, where 6>0. we wish to test H0 : θ-1 vs. Hi : θ #1. Show that the likelihood ratio test statistic, A , can be written as A(V) wh...
3. Let X,,X,,..., X, be a random sample from a Gamma 40distribution, where 6>0. we wish to test H0 : θ-1 vs. Hi : θ #1. Show that the likelihood ratio test statistic, A , can be written as A(V) where a. What is the distribution of V? what is the null distribution of what will be the rejection region for an α level test? b. 20 d.
3. Let X,,X,,..., X, be a random sample from a Gamma 40distribution,...
5. (10 points) Let X1,... , Xio be a random sample of size 10 from a Poisson distribution with mean θ. The rejection region for testing Ho :-0.1 vs. 1.1: θ-0.5 is given by Σ"i z > 4. Determine the significance level α and the power of the test at θ : 05.
5. (10 points) Let X1,... , Xio be a random sample of size 10 from a Poisson distribution with mean θ. The rejection region for testing Ho...
. Suppose a random sample of 25 is taken from a population that follows a normal distribution with unknown mean and a known variance of 144. Provide the null and alternative hypotheses necessary to determine if there is evidence that the mean of the population is greater than 100. Using the sample mean, Y, as the test statistic and a rejection region > k}, find the value of k so that α = 0.15. of the form - Using the...
For the given data, (a) find the test statistic, (b) find the standardized test statistic, (c) decide whether the standardized test statistic is in the rejection region, and (d) decide whether you should reject or fail to reject the null hypothesis. The samples are random and independent , a = 0.01. Sample statistics: x = 1235, n 40, x2 = 1195, and n2 = 70. Population statistics: o1 65 and a2 120. Claim: (a) The test statistic for -H2is (b)...
Question 4 (6 marks) Part a) Calculate the statistic, set up the rejection region, interpret the result, and draw the sampling distribution. Ho: Hi: μ 10 μ#10 Given that: σ-10, n-100, X-10, α-0.05. Part b) A statistics practitioner is in the process of testing to determine whether is enough evidence to infer that the population mean is different from 180. She calculated the mean and standard deviation of a sample of 200 observations as X -175 and s-22. Calculate the...
Question Help * For the given data, (a) find the test statistic (b) find the standardized test statitic, ( should reject or tall to reject the null hypothesis. The samples are random and independent. the rejection region, and (d) decide whether you c) decide whether the standardized test statistic is in nh"P2, α:001 Sample statistics: x.-1225, n.-45, x2-1195. and n2-65 Population stabsics o, so ando, 100 (a) The test statistic for μ1_P2 b) The standardized test statistic ftor p1-P2 (Round...
For the given data, (a) find the test statistic, (b) find the standardized test statistic, (c) decide whether the standardized test statistic is in the rejection region, and (d) decide whether you should reject or fail to reject the null hypothesis. The samples are random and independent Claim: <H2, a=0.01. Sample statistics: x = 1235, n = 30, X2 = 1205, and n = 60. Population statistics: 6 = 70 and 62 = 100. (a) The test statistic for ,...
3. Let X,,X,,..., X, be a random sample from a Gamma 40distribution, where 6>0. we wish to test H0 : θ-1 vs. Hi : θ #1. Show that the likelihood ratio test statistic, A , can be written as A(V) where a. What is the distribution of V? what is the null distribution of what will be the rejection region for an α level test? b. 20 d.
3. Let X,,X,,..., X, be a random sample from a Gamma 40distribution,...
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