ASRB NET and ARS: dairy disciplines · India · Agricultural Scientists Recruitment Board (ICAR)
Original practice questions written to the published syllabus · not past papersThe calculus, differential equations and statistics that dairy engineering problems, kinetics and quality control need.
In the exams: Supports numerical items across ICAR AICE subject 38 (Dairy Engineering) and GATE XL-U Section 4; statistics recurs in ASRB NET dairy disciplines and in quality-control units
How our questions for ASRB NET and ARS spread across the units of Mathematics & Statistics for Dairy Science. Difficulty: 10 easy, 17 medium, 1 hard.
| Tests of significance: t, chi-square and F | 8 | |
| Analysis of variance and basic experimental designs | 8 | |
| Descriptive statistics and probability distributions | 5 | |
| Sampling theory and confidence intervals | 4 | |
| Correlation and regression | 3 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
Five fat tests read 3.2, 3.4, 3.6, 3.8 and 4.0%. What is the sample standard deviation (divisor n − 1)?
A. 0.316%
Deviations −0.4, −0.2, 0, 0.2, 0.4; sum of squares 0.40; variance 0.40/4 = 0.10; s = √0.10 = 0.316%. Dividing by n gives 0.283%; 0.100 is the variance; 0.632 forgets to divide the sum of squares at all.
Further reading: Snedecor and Cochran, Statistical Methods
Which sampling method divides farm suppliers into collection routes and samples randomly within each route?
A. Stratified random sampling
Sampling within each defined group (stratum) is stratified sampling. Cluster sampling would select whole routes at random and test all farms in them.
Further reading: Snedecor and Cochran, Statistical Methods
If the sample size used for a confidence interval for a mean is increased from 25 to 100, the width of the interval becomes approximately:
B. Half as wide
Width is proportional to 1/√n; √(100/25) = 2, so the interval halves. One quarter would need a sixteenfold larger sample.
Further reading: Snedecor and Cochran, Statistical Methods
Of 300 farm milk samples, 18 fail an antibiotic screening test. What is the approximate 95% confidence interval for the failure rate?
C. 3.3% to 8.7%
p̂ = 0.06; SE = √(0.06 × 0.94/300) = 0.0137; half-width 1.96 × SE = 0.027, giving 3.3% to 8.7%. Forgetting to divide by n gives an impossible negative lower limit.
Further reading: Snedecor and Cochran, Statistical Methods
Pearson's r between two variables is close to zero. Which conclusion is justified?
C. There is little linear relation, though a curved relation may still exist
r measures linear association only; a strong U-shaped relation can give r ≈ 0. Zero correlation does not prove independence.
Further reading: Snedecor and Cochran, Statistical Methods
Fisher's three basic principles of experimental design are:
B. Replication, randomisation and local control
Replication estimates and reduces error, randomisation prevents bias, and local control (blocking) removes known variation.
Further reading: Montgomery, Design and Analysis of Experiments
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