(a) Show that the likelihood ratio test of Ho: 0 = 0o versus H₁ : 000 is based upon the statistic Y = 1 X₁. Obtain the null distribution of Y. (b) For n = 100 and 0o = 1/2, find c₁ so that the test rejects Ho when Y ≤ c₁ or Y Z C₂ = 100 - c₁ has the approximate significance level of a = Use the Central Limit Theorem. 0.05. Hint:
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- You wish to test the following claim (HaHa) at a significance level of α=0.002. Ho:p1=p2 Ha:p1≠p2 You obtain 383 successes in a sample of size n1=498 from the first population. You obtain 318 successes in a sample of size n2=443 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the first population proportion is not equal to the second population proprtion. There is…Let x1, X2, ... , X, be a random sample from a normal population with unknown mean µ and an unknown variance o2. Construct the generalized likelihood ratio test for Ho : µ 2 µo = 10 versus H1 : 4 C, (b) The test rejects Ho if > c, where c is the value so that to the right of c lies the area of a under the i density with n – 1 degrees of freedom. (c) The test rejects Ho if normal density. C, where c is the value so that to the left of c lies the area of a under the the standard (d) The test rejects Ho if where c is the value so that to the left of c lies the area of a under the i density withYou wish to test the following claim (Ha) at a significance level of α=0.02. Ho:p1=p2 Ha:p1<p2You obtain 16.4% successes in a sample of size n1=427 from the first population. You obtain 25.5% successes in a sample of size n2=330 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the test statistic for this sample? (Report answer accurate to two decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion. There is not…can you find two tailed test p value for given data sample size 14 test statistics -2.23please helpYou wish to test the following claim (Ha) at a significance level of α=0.01. Ho:p1=p2 Ha:p1>p2You obtain 54.3% successes in a sample of size n1=529 from the first population. You obtain 47.9% successes in a sample of size n2=555 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) α greater than αYou wish to test the following claim (HaHa) at a significance level of α=0.001 Ho:p1=p2 Ha:p1<p2You obtain 4.7% successes in a sample of size n1=299 from the first population. You obtain 7.8% successes in a sample of size n2=602 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null hypothesis accept the null hypothesis fail to reject the null hypothesis As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second…I need help with this question. Can you please go step by step because I am very confused?please and thank youYou wish to test the following claim (Ha) at a significance level of α=0.005 Ho:p1=p2 Ha:p1>p2You obtain 88.3% successes in a sample of size n1=642 from the first population. You obtain 82% successes in a sample of size n2=748 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the test statistic for this sample? (Report answer accurate to two decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the first population proportion is greater than the second population proportion. There is not…You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001. Ho:p=0.71Ho:p=0.71 Ha:p>0.71Ha:p>0.71You obtain a sample of size n=234n=234 in which there are 171 successful observations. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the critical value for this test? (Report answer accurate to three decimal places.)critical value = What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic =A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1,300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with o = 69. Let u denote the true average compressive strength. (a) What are the appropriate null and alternative hypotheses? O Ho: H > 1,300 H: u = 1,300 Ο H,: μ= 1,300 H: u 1,300 (b) Let X denote the sample average compressive strength for n = 15 randomly selected specimens. Consider the test procedure with test statistic X itself (not standardized). What is the probability distribution of the test statistic when Ho is true? O The test statistic has a binomial distribution. O The test statistic has a gamma distribution. The test statistic has a normal distribution. O The test statistic has an exponential distribution. If X = 1,340, find the…
