ICAR AICE-JRF/SRF - Agricultural Statistics, Computer Application, Bioinformatics (PhD admission and fellowship) · India · National Testing Agency for ICAR
Original practice questions written to the published syllabus · not past papersThe first statistics course of every agricultural degree, which is also the statistics unit of AIEEA-PG Group 07: frequency distributions, averages and dispersion, probability and the three named distributions, tests of significance, correlation and regression, and the CRD and RBD. Laisha teaches it to the depth the entrance examines; the Veterinary, Agribusiness and Agricultural Engineering tracks have their own introductory versions.
In the exams: AIEEA-PG Group 07 statistics unit (heavy: the whole unit); AICE-JRF Agronomy Unit 6 and other agricultural subjects' statistics units (present); ASRB NET general statistics (present); SSC CGL JSO statistics paper (heavy)
How our questions for ICAR AICE-JRF/SRF spread across the units of Statistical Methods for Agricultural Sciences. Difficulty: 0 easy, 9 medium, 19 hard.
| Basic principles of experimental design, ANOVA, CRD and RBD | 5 | |
| Skewness, kurtosis and moments | 3 | |
| Student's t-test: one sample, two samples and paired | 3 | |
| Correlation and regression and their tests of significance | 3 | |
| Measures of dispersion: range, mean deviation, quartile deviation, variance and coefficient of variation | 2 | |
| Random sampling and standard error | 2 | |
| Tests of significance: errors, null hypothesis and level of significance | 2 | |
| F-test for equality of variances | 2 | |
| Chi-square tests for goodness of fit and independence of attributes | 2 | |
| Measures of central tendency: arithmetic, geometric and harmonic means, median and mode | 1 | |
| Probability: addition and multiplication laws, conditional probability and Bayes' theorem | 1 | |
| Binomial, Poisson and normal distributions in agricultural data | 1 | |
| Large-sample (SND) tests for one and two means | 1 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
Using the normal approximation with continuity correction, what is the probability that 60 or more of 100 calves are female, if each birth is female with probability 0.5?
A. 0.0287
Mean = 50, SD = √25 = 5. With continuity correction, P(X ≥ 60) ≈ P(Z > (59.5 − 50)/5 = 1.9) = 0.0287. Without the correction Z = 2.0 gives 0.0228; using 60.5 gives 0.0179, which corrects in the wrong direction.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
A two-treatment trial with 3 replications finds no significant difference at 5%. What is the soundest conclusion?
A. The trial failed to detect a difference; with 3 replications its power is likely low
Failing to reject H₀ is not evidence that H₀ is true; small trials have low power. The correct report gives the estimated difference with its confidence interval and notes the power.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
In village A, 60 of 200 farmers adopted drip irrigation; in village B, 40 of 200. Using the pooled proportion, what is Z for the difference?
C. 2.31
p₁ = 0.30, p₂ = 0.20, pooled p = 100/400 = 0.25; SE = √(0.25 × 0.75 × (1/200 + 1/200)) = 0.0433; Z = 0.10/SE = 2.31. Unpooled SE (√(0.21/200 + 0.16/200)) gives 2.32.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
If T follows Student's t with 12 df, what distribution does T² follow?
B. F with (1, 12) df
t² with ν df is F(1, ν), since t is a standard normal over √(χ²_ν/ν) and the square of a standard normal is χ² with 1 df.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
A Poisson distribution is fitted to counts grouped into 7 classes, with its mean estimated from the data. After pooling, 5 classes remain. What are the df for the χ² goodness-of-fit test?
A. 3
df = k − 1 − (parameters estimated) = 5 − 1 − 1 = 3. Using the 7 classes before pooling, or forgetting the estimated mean, gives 5 or 4.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
Across 300 farms, fertiliser use and yield are strongly correlated (r = 0.7). An official concludes that each extra kilogram of fertiliser raises yield by the regression slope. What is the main objection?
C. Correlation across farms does not show causation; irrigation, soil and management may drive both
With 300 farms r = 0.7 is highly significant, but observational association can be confounded: better-irrigated farms use more fertiliser and also yield more. A dose-response needs a designed experiment.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
Through which point do both regression lines (y on x, and x on y) pass?
C. (x̄, ȳ)
Least-squares lines satisfy a = ȳ − b x̄, so each passes through the means; the two lines intersect there. They pass through the origin only if both means are zero.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
An RBD with 5 treatments and 4 blocks has one missing plot. Over the observed plots, the total of its treatment is 60, of its block 48, and of the whole experiment 240. What is Yates' estimate of the missing value?
D. 21.00
x = (tT + rB − G)/((t − 1)(r − 1)) = (5 × 60 + 4 × 48 − 240)/(4 × 3) = (300 + 192 − 240)/12 = 21.00. Error df then falls from 12 to 11. 20.00 is the treatment's mean over its 3 observed plots.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
Counts of insects per plant in a trial range from 0 to 30 and their variance rises with the mean. Which transformation is usual before ANOVA?
D. Square root, √(x + 0.5) when zeros occur
Counts with variance proportional to the mean are stabilised by the square root; the 0.5 handles zeros. Angular transformation is for percentages; log(x) fails at zero counts.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
What are the assumptions of the analysis of variance for an RBD?
C. Additive treatment and block effects, independent errors, normality and homogeneous error variance
The RBD model yᵢⱼ = μ + tᵢ + bⱼ + eᵢⱼ assumes additivity (no treatment × block interaction), and errors that are independent, normal and of constant variance. Equal treatment means is the null hypothesis being tested, not an assumption.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
Ten here, 28 in the app. The Laisha app has every practice question we have written to ICAR AICE-JRF/SRF in this subject, marked as you go, with timed papers, a jump-to-unanswered list and a certificate when you pass at 70 per cent.
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