TESTING OF HYPOTHESIS — DU B.Sc (hons) Statistics Previous Year Question Papers

Testing of Hypothesis (NEP-UGCF) Use of statistical tables is permitted. (a) Define the power function of a statistical test. What are the relationships of the power function with Type I and Type 11 errors? (b) A new teaching pedagogy claims that the success rate of this pedagogy in cracking entrance exams is 90%. A competitor claims that the recovery rate is just 70%. In order to reach at a decision, the pedagogy is tested on a group of 30 students and the number of successes is observed. The claim of the pedagogy will be accepted if the number of successes is at least 2] . Set the null and the.altemate hypotheses and calculate ex and P. (c) If there are 77, =5 letters of one kind and 772 =5 letters of another kindg what is the probability of (a) 6 runs; (b) 7 runs? (d) Hypertension can be controlled by diet. In order to test this claim, a diet plan was administered on 11 people, with a history of high blood pressure for three months. Their blood pressures were measured repeatedly before the plan, during the plan and after its completion. The following are the average upper blood pressures before and after the plan: Is there any evidence of the effectiveness of the plan at 5% level of significance? Use a Paired sign test to verify the claim. (e) Differentiate between the ratio and ordinal scales of measurement giving suitable A coin is tossed 14 times. The following sequence of IIeads (H) and Tails (T) has been obtained: Test whether the heads and tails occur in random order at 5% level of significance. (Critical Interval = (3,12)) Define the most powerful test. Prove that a cril:ical region determined by the Neymann- Pearson lemma is the most powerful critical region for testing a simple null hypothesis against a simple alternative hypothesis. (b) Let JY,,.Y2 be arandom sample from /(#,G)=OxG-i; 0<;¥<1, G>0. It is given that for testing Ho : G = I against ff, : G = 2 is C = I and Type 11 errors for the test. i(a) Show that the LRT for testing based on a random sample of size n from a population with density /(x;a;4)=±; c¥-4s:a:<c¥+A is (£)"where jt=X(„)-X„ and (b) Two independent observations x„ x2are made on a random variable X having the density function /(.I;G)=;e-5;-co<x<co; G>0. In order to test the hypothesis Ho :G=2 against ff,:G=4,therejectionregionisx,+A-2>9.5.Findthelevelofsignificanceandthe power of the test. (8,7) 4(a) For the distribution dE = (Bexp(-B(x-y)} dx, ==Y 1, Y = Y1, the best critical region is given b how that for testing the hypothesis Ho : B = Bo, y = Yo against the alternative H2 : B = provided that the admissible hypothesis is restricted by the condition y1 ≤ Yo, B1 ≥ Bo. (b) Define Monotone Likelihood Ratio (MLR). Show that for the family of distributions IN E ER}, there exists an MLR. (8,7) 5(a) Define ASN function of SPRT. Let X1, X2 ...,Xn be a random sample of size n from a normal distribution with mean j and variance 100. SPRT was done to test the hypothesis