Obtain seasonal Indices by the “Moving average” method from the following data:
| Quarterly output of a Factory | ||||
| Year | I | II | III | IV |
| 2010 | 65 | 58 | 56 | 61 |
| 2011 | 68 | 63 | 63 | 67 |
| 2012 | 70 | 59 | 56 | 52 |
| 2013 | 60 | 55 | 51 | 58 |
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Verify whether the series is Stationary
A chemist developing insect repellents wishes to know if a newly developed formula gives greater protection from insect bites than that given by the leading product on the market. In the experiment, 14 volunteers each had one arm spayed with the old product and the other sprayed with the new formula. Then each subject placed his arms into two chambers filled with equal number of mosquitoes, gnats and other biting insects. The numbers of bites received on each arm are as follows:
| Subject | Old formula | New formula | Subject | Old formula | New formula |
| 1 | 5 | 3 | 8 | 4 | 2 |
| 2 | 2 | 1 | 9 | 2 | 5 |
| 3 | 5 | 5 | 10 | 6 | 2 |
| 4 | 4 | 1 | 11 | 5 | 3 |
| 5 | 3 | 1 | 12 | 7 | 3 |
| 6 | 6 | 4 | 13 | 4 | 1 |
| 7 | 2 | 4 | 14 | 3 | 3 |
If a researcher wants to half the standard error of the estimator of the mean then he/she will increase the sample size 4 times.
In a certain book, there is one misprint per two pages, on the average. What is the probability that there are two or more misprints on a randomly chosen page?
(b) A coal-fired power plant is considering two different systems for pollution abatement. The first system has reduced the emission of pollutants to acceptable levels 68 percent of the time, as determined from 200 air samples. The second, more expensive system has reduced the emission of pollutants to acceptable levels 76 percent of the time, as determine from 250 air samples. If the expensive system is significantly more effective than the inexpensive system in reducing pollutants to acceptable levels, then the management of the power plant will install the expensive system. To decide that
(i) State null and alternative hypotheses
(ii) Name the test which is suitable in this situation and why?
(iii)Calculate the value of test statistic and critical value.
(iv)Which system will be installed if management uses a significance level 0.01 in making decision?
From the following data find mean and variance of the stratified sampling under (i) proportional and (ii) Neyman Allocation
| Strata | Ni | Ni | Si | |
| 1 | 80 | 29 | 12 | 80 |
| 2 | 160 | 39 | 8 | 30 |
| 3 | 260 | 32 | 4 | 10 |
| 500 | 100 |
If X1, X2, X3, X4 and X5 is a random sample of size 5 taken from anExponential distribution, then estimator T1 is more efficient than T2.