(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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- Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal. Test Ho : HA HB vs Ha : HA # µB using the fact that Group A has 8 cases with a mean of 125 and a standard deviation of 18 while Group B has 15 cases with a mean of 118 and a standard deviation of 14.Assume we have a sample of size n=16 from independent and identically distributed random variables from a normal distribution with mean u and unknwo standard deviation estimated by the sample standard deviation. We observe x =8 and s=4. We let e denote the length of the confidence interval with confidence level 1-a=95%. Which of the following statements are true? > qnorm(c (0.8,0.9,0.95,0.975,0.99,0.999)) [1] 0.8416212 1.2815516 1.6448536 1.9599640 2.3263479 3.0902323 > qt(c(0.8,0.9,0.95,0.975,0.99,0.999), df=15) [1] 0.866245 1.340606 1.753050 2.131450 2.602480 3.732834 Veuillez choisir au moins une réponse: O a. The confidence interval equals [6.25,9.75]. O b. The confidence interval equals [5.87,10.13]. The confidence interval equals [6.36,9.64]. O c. O d. The confidence interval equals [6.04,9.96].Tests the claim that 1 # p2. Assume the samples are normally distributed, random and independent. of + o S1 =0.77 ; s2 = 0.82 E1 = 48.92 ; z2 = 48.94 n1 = 24; n2 = 31 a. Calculate the Standard Error s-, = (use 3 decimal places) (use 2 decimal places) b. Calculate the t-test statistic using the standard error from part a. t = c. What are the degrees of freedom? df %3! d. At a = 0.02, Use the distribution table to find the critical values for the rejection region t = ± (use 4 decimal places) e. What is your conclusion? O Fail to reject the null hypothesis and do not support the claim O Reject the alternative hypothesis and support the claim O Accept the null hypothesis and support the claim O Reject the null hypothesis and support the claim O Accept the alternative hypothesis and reject the claimA new method has been developed in the treatment of a disease. 12 randomly selected patients were treated with this method and the time until recovery was calculated as in the picture. Establish a confidence interval for the mass mean µ. (α=0.05)Assume that you have a sample of n₁ = 8, with the sample mean X₁ = 42, and a sample standard deviation of S₁ = 7, and you have an independent sample of n₂ = 13 from another population with a sample mean of X₂ = 33, and the sample standard deviation S₂ = 8. Construct a 99% confidence interval estimate of the population mean difference between μ₁ and μ₂. Assume that the two population variances are equal. ≤11-1₂5 (Round to two decimal places as needed.) (...The one-sample t-statistic for a test of Ho: u = 42 versus H1:µ < 42 based on n = 15 observations has the value t = -2.138, where Ho and Hjare the null and alternative hypotheses, respectively. The sample size is denoted by n. Use this t-table to determine which two P-values bracket the P-value of the test. Report your answers in decimal form as listed in the t-table. P-value of the test <Determine if the conditions required for the normal approximation to the binomial are met. If so, calculate the test statistic, determine the critical value(s), and use that to decide whether there is sufficient evidence to reject the null hypothesis or not at the given level of significance. Ho :p = 0.85 H1 :p 0.85 p = 0.782 n= 128 a = 0.2 a. Calculate the test statistic. Round to two decimal places if necessary Enter 0 if normal approximation to the binomial cannot be used b. Determine the critical value(s) for the hypothesis test. Round to two decimal places if necessary Enter 0 if normal approximation to the binomial cannot be usedHow would you find a 95% confidence interval for μX -μY for these distributions?The random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630b) Find the mean and standard deviation of the difference. c) Find the rejection region and state your decision at α = 0.01.SEE MORE QUESTIONS