5. Let X ~ N( ,o2) and assume ơ--3. We are to test the null hypothesis Ho: 10 against e) Let a -0...
N(0,02). We wish to use a 1. [18 marks] Suppose X hypothesis single value X = x to test the null Ho : 0 = 1 against the alternative hypothesis H1 0 2 Denote by C aat the critical region of a test at the significance level of : α-0.05. (f [2 marks] Show that the test is also the uniformly most powerful (UMP) test when the alternative hypothesis is replaced with H1 0 > 1 (g) [2 marks Show...
2. A randon sample XI, X. is drawn frotn Normal(μ, σ2), where-oo < μ < oo and 0 < σ2 < x. To test the null hypothesis Ho : σ2-1 against the alternative H1: σ2 > 1, we have designed the following test Reject Ho if S>k where S2 = "LE:-1(x,-X)2, k ís a constant. Noticed that (n-1) distribution with degree of freedom 1 has a (a) Determine k so that the test will have size a. (b) Use k...
suppose you test null hypothesis Ho : μι_Ha versus Ha : μ.μ2 , software gives 12.3 degrees of freedom for your t test. Answer the following questions: a) If test statistics t-2.25 5, use the rejection region to decide if Ho be rejected or not at a .0.05? Include a sketch, clearly label critical value(s) and rejection and nonrejection regions. b) If test statistics was t-1.14, use a 0.05, compute the p-value and decide if Ho b rejected or not...
Compute the test value. Do we reject the null hypothesis? A random sample of second-round golf scores from a major tournament is listed below. At a 0.05, is there sufficient evidence to conclude that the population variance er eeds 9? 73 75 77 79 71 66 68 69 70 Download data Part 1 State the hypotheses and identify the claim with the correct hypothesis. not claim claim This hypothesis test is a one-taled test. Part 2 Find the critical value....
18 marks] Suppose X~N(0,0). We wish to use a single value X hypothesis to test the null against the alternative hypothesis Denote by C aa) the critical region of a test at the significance level of -0.05 (a) 2 marks] What is the sample space S, the parameter space 9 space Θο of the test? and the null parameter (b) 12 marks) Computea (c) 12 marks Compute the power of the test (i.e., at 2) (d) [2 marks] Compute the...
Ignore handwriting (15 pts) Assume that SAT matkematcs scores of studeuts who attend s college are N(μ, σ2-8100). We shall test Ho : μ-530 against HA : μ > 530 Let the critical region be defined by C (x X 2 554.675}, where X is the sample meatu of a random sample of size n = 36 from this distribution. l arts (a) What is the value of the significance level of this test? a o S503 s 6 (b)...
P1 To test the hypothesis Ho: p = 1/2 against H :p < 1/2, we take a random sample of Bernoulli trials, X,X,..., X.,, and use for our test statistic Y = ¿x, which has a binomial distribution b(n, p). Let the critical region be defined by C ={y:y sc}. Find the values of n and c so that (approximately) a = 0.05 and B = 0.10 when p = 1/4. 1=1
10-13.. Consider the hypothesis test H0 : μι Ma against , : μ.< μ2. Suppose that sample sizes n-15 and n-15, that 7.2 and x2-7.9, and that si 4 and s 6.25. Assume that σ-σ and that the data are drawn from normal distribu- tions. Use α 0.05 (a) Test the hypothesis and find the P-value (b) Explain how the test could be conducted with a confidence interval. than μ2? be used to obtain B 0.05 if u, is 2.5...
Suppose that X ~ POI(μ), where μ > 0. You will need to use the following fact: when μ is not too close to 0, VR ape x N(VF,1/4). (a) Suppose that we wish to test Ho : μ-710 against Ha : μ μί are given and 10 < μι. m, where 140 and Using 2 (Vx-VHo) as the test statistic, find a critical region (rejection region) with level approximately a (b) Now suppose that we wish to test Ho...
Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.78. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9...