STATISTICAL TECHNIQUES AND INFERENCE

Q 4 a) Explain by considering a sample of size n = 2 from a population consisting of five members 2, 3, 6, 8, 11 that SRSWOR gives a better estimator of population mean that SRSWR. b) From the following data find mean and variance of the stratified sampling under (i) proportional and (ii) Neyman Allocation Strata Ni Ni Si yi 80 29 12 80 W N 160 39 30 260 32 A 10 500 100 c) In order to compare the mileage yields of 3 kinds of gasoline, several tests were run and the following results were obtained: Gasoline A: 19 21 20 18 21 21 Gasoline B: 23 20 22 20 24 23 Gasoline C: 20 17 21 19 20 17 Carry out the analysis of variance test and test whether the observed differences between the means of 3 kinds of gasoline may be attributed to chance at 5% level of significance. d) The lifespan (in '000 hours) of four LED bulbs of 07 watts are as follows: 40,46,48, 50 (i) Write all samples of size 2without replacement from the above observations. Compute the sampling distribution and find mean and standard error of the distribution. (ii) Write all samples of size 3 without replacement from the above observations. Compute the sampling distribution and find mean and standard error of the distribution. (ii) Compare means and standard errors and draw the conclusion. (5+5+10+5)