when the computed F-statistic exceeds the critical value fa(1, n 2) the null hypothesis is non-rejected, ulgn O hi O
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- Let ZZ be a discrete random variable taking one of the four distributions covered in Chapter 10. Suppose you know that Var(Z)=(k+1)E(Z)Var(Z)=(k+1)E(Z) where kk is the last non-zero digit of your student ID number. Determine the distribution of ZZ and find its parameter(s), explaining your argument carefully.In a Right Tailed Hypothesis test, the test statistic was found to be Z=2.74The rejection region included values greater than the critical value Zc=2.02 The conclusion would be to... Reject the null hypothesis because the test statistic is NOT in the rejection region Fail to reject the null hypothesis because the test statistic is in the rejection region Fail to reject the null hypothesis because the test statistic is NOT in the rejection region Reject the null hypothesis because the test statistic is in the rejection region Accept the null hypothesis because the test statistic is NOT in the rejection regionState The null or alternative hypothesis. Determine the critical Value(S) Find the Z- test
- A hypothesis test is to be performed for a population mean with null hypothesis of H0: u=u0 . The test statistic used will be z= x - u0 / o / square root of n..Find the critical value(s) for a two-tailed test with α = 0.02 and draw a graph that illustrates your answer.Two random variables X and Y have joint char- acteristic function l@,,m)=exp(-20,?-80;) (i) Show that X and Y are zero mean ran- dom variables.ts) Let X₁, X₂, ..., X, be a random sample from the Normal distribution N(μ, o²) (a) Using simple statistics to estimate the parameters μ and o² (b) Using maximum likelihood estimation to estimate the parameters μ and ² (c) Are those estimators from the above methods for parameter μ the same? Which one is unbiased? How about the estimators for parameter o²?
- 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?State which test (z-test, t-test, ANOVA, χ 2 test) is most suitable for each of the following cases: (i) In an election, voters may support the Democrat candidate, Republican candidate, or Independent candidate. A researcher would like to conduct a poll to test if this year the supportive rates of the three candidates follow the same supportive rates as in the last election, which was 60% : 25% : 15%. (ii) A vaccine is developed for preventing the infection of a disease. An experiment is developed to test its effectiveness. 300 volunteers are divided into two groups randomly. One group of participants will take the vaccine and the other group of participants will not take the vaccine but only vitamin. The proportion of participants in the two groups being infected by the disease will be compared. (iii) A researcher wants to conduct a test to verify if children’s outside school learning experiences would be affected by the families’ income level. Family income will be classified as high…the maximum likelihood estimator of a random variable x with uniform distribution U(0, 0), 0 = max(x₁.x). Is the estimator biased?
- Suppose X~ Binom(6, p) and define an estimator T ==to estimate p. Then, variance 6. of T is, p(1–p) a) Var (T)= 6. b) Var (T) = 6 p(1 – p) c) Var (T)~ p(1-p) d) Var (T) - 36рHow do we find the gamma and the p-value to evaluate the hypothesis that people who are more satisfied with their jobs are more likely to be happily married than those who are less satisfied with their jobs? The table is attatched.a) Let X₁, X₂, X3,..., X, be a random sample of size n from population X. Suppose that X~N(0, 1) you and Y = -√n. VR i) Show that the standard score of the sample mean X, is equal to Y. ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively. iii) Show using the moment generating function technique that Y is a standard normal rando... variable. iv) What is the probability that Y² is between 0.02 and 5.02? b) Let X₁, X₂, X, and Y₁, Y₂.... Y be random samples from populations with moment generating functions Mx, (t) = eat+t² and My (t) = (-), respectively. 25 i) Find the sampling distribution of the statistic W = X₁ + 2X₂ X3 + X₁ + X5. ii) What is the value of the sample size n, if PIX(X-X)2> 68.3392] = 0.025? iii) What is the value of the sample size m, if P(|Y-Hy ≥10) <0.04? QUESTION A
