B4 Observations are available sequentially from a distribution with unknown parameter The null hypothesis H:0=0, is...

 

Transcribed Image Text:

B4 Observations are available sequentially from a distribution with unknown parameter The null hypothesis H₁:0=0, is to be tested against the alternative H₁:0=0 with Type I and Type II error probabilities of approximately a and ß respectively. (i) Give instructions, in terms of a and, as to how to perform the sequential probability ratio test (SPRT), and state, without proof, Wald's formulae for the (approximate) mean sample sizes needed, under each hypothesis. (8 Marks) Without doing any calculations, discuss briefly the sample sizes needed for the above SPRT compared to the sample size of the corresponding most powerful fixed sample size test when the true value of lies strictly between 0 and ₁. (5 Marks) Now suppose that the observations come from a Normal N(0,0²) population and we wish (ii) to test H₁:0=1 against the alternative Ho=2 with the Type I and Type II error probabilities approximately being equal to 0.05 and 0.10 respectively. (iii) Obtain the SPRT and also calculate the approximate mean sample sizes needed under each hypothesis. (8 Marks) (a) (b) Cont/ Suppose that the first three observations are 2.6. 1.1.1.5. Carry out the steps in constructing the SPRT for these data. (4 Marks) B4 Observations are available sequentially from a distribution with unknown parameter The null hypothesis H₁:0=0, is to be tested against the alternative H₁:0=0 with Type I and Type II error probabilities of approximately a and ß respectively. (i) Give instructions, in terms of a and, as to how to perform the sequential probability ratio test (SPRT), and state, without proof, Wald's formulae for the (approximate) mean sample sizes needed, under each hypothesis. (8 Marks) Without doing any calculations, discuss briefly the sample sizes needed for the above SPRT compared to the sample size of the corresponding most powerful fixed sample size test when the true value of lies strictly between 0 and ₁. (5 Marks) Now suppose that the observations come from a Normal N(0,0²) population and we wish (ii) to test H₁:0=1 against the alternative Ho=2 with the Type I and Type II error probabilities approximately being equal to 0.05 and 0.10 respectively. (iii) Obtain the SPRT and also calculate the approximate mean sample sizes needed under each hypothesis. (8 Marks) (a) (b) Cont/ Suppose that the first three observations are 2.6. 1.1.1.5. Carry out the steps in constructing the SPRT for these data. (4 Marks)

Answer rating: 100% (QA)

i Instructions for performing the SPRT The SPRT is a sequential hypothesis test that uses the likelihood ratio test statistic to compare two hypothese... View the full answer