(a) What is Student's t-test and its significance in biological research? Write the formula of t-test and its various steps using…

(a) Student's t-test: significance, formula and steps

Student's t-test, published in 1908 by W.S. Gosset under the pen-name "Student", tests whether a sample mean differs from a hypothesised value, or whether two means differ, when samples are small (conventionally n < 30) and the population variance is unknown and must be estimated from the sample. It assumes that the variable is approximately normally distributed, that observations are independent and randomly sampled, and, for the pooled two-sample test, that the two groups have equal variances.

Significance in biological research: most experiments compare a treatment group with a control on small samples (drug versus placebo, fertiliser versus none, polluted versus clean site, diet A versus diet B). The t-test tells whether the observed difference is larger than would be expected from sampling variation alone, at a chosen risk of a Type I error (α, usually 0.05). Its forms are the one-sample test, the independent (unpaired) two-sample test, and the paired test for before-after measurements on the same individuals; Welch's version is used when variances are unequal.

Formula for two independent samples:

t = (x̄₁ − x̄₂) / √[sₚ² (1/n₁ + 1/n₂)]

where the pooled variance sₚ² = [Σ(x₁ − x̄₁)² + Σ(x₂ − x̄₂)²] / (n₁ + n₂ − 2), with degrees of freedom df = n₁ + n₂ − 2. For paired data, t = d̄ / (s_d/√n) with df = n − 1, where d are the differences within pairs.

Worked example: weight gain (g) of fish on a control diet A (4, 5, 6) and a supplemented diet B (7, 8, 9).

1. State hypotheses: H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂ (two-tailed), α = 0.05.
2. Means: n₁ = 3, x̄₁ = 5; n₂ = 3, x̄₂ = 8.
3. Sums of squared deviations: Σ(x₁ − x̄₁)² = 1 + 0 + 1 = 2; Σ(x₂ − x̄₂)² = 1 + 0 + 1 = 2.
4. Pooled variance: sₚ² = (2 + 2)/(3 + 3 − 2) = 1.0.
5. Standard error of the difference: SE = √[1.0 × (1/3 + 1/3)] = √0.667 = 0.816.
6. Calculated t: t = |5 − 8| / 0.816 = 3.67, with df = 4.
7. Decision: the table value of t at df = 4 and α = 0.05 (two-tailed) is 2.776. Since 3.67 > 2.776 (p ≈ 0.02), H₀ is rejected: the supplemented diet gives a significantly greater weight gain.

(b) Fluorescence microscope

Principle: certain molecules (fluorochromes) absorb light of a shorter wavelength and, after a very brief interval (nanoseconds), emit light of a longer wavelength; the difference between the excitation and emission peaks is the Stokes shift. By illuminating the specimen with the excitation wavelength and allowing only the emitted wavelength to reach the eye or camera, labelled structures appear bright against a dark background. Unlike bright-field microscopy, which depends on absorption of transmitted light, this gives very high contrast and specificity, and structures smaller than the resolution limit can be detected if they fluoresce.

Instrumentation (epifluorescence microscope, in which the objective also serves as the condenser):

• Light source: a mercury or xenon arc lamp, now often LEDs or lasers, giving intense short-wavelength light.
• Excitation filter: passes only the band that excites the fluorochrome (e.g., blue about 490 nm for FITC).
• Dichroic (beam-splitting) mirror: set at 45°, it reflects the short excitation wavelength down through the objective onto the specimen but transmits the longer emitted wavelength.
• Objective: focuses excitation light on the specimen and collects emitted fluorescence.
• Emission (barrier) filter: blocks scattered excitation light and passes only the fluorescence (e.g., green about 520 nm).
• Detector: eyepieces or a sensitive CCD/sCMOS camera.

The excitation filter, dichroic mirror and emission filter are mounted together as a filter cube matched to each fluorochrome.

Applications:

• Immunofluorescence: fluorescent-labelled antibodies localise specific proteins, pathogens or autoantibodies (e.g., the FTA-ABS test for syphilis, antinuclear antibodies).
• Nucleic-acid stains and FISH: DAPI and Hoechst stain DNA; fluorescence in situ hybridisation maps genes and detects chromosome abnormalities such as translocations in cancers.
• Live-cell imaging: green fluorescent protein (GFP, from the jellyfish Aequorea victoria) and its variants tag proteins to follow their movement; calcium indicators (Fura-2) track signalling.
• Microbiology and diagnosis: auramine–rhodamine staining detects Mycobacterium tuberculosis in sputum.
• Advanced forms: confocal laser scanning microscopy gives optical sections and 3-D images, and TIRF and super-resolution methods (STED, PALM/STORM) resolve structures below 200 nm.

(c) Species suitable for prawn culture and methods of culture

Suitable species:

• Penaeus vannamei (Pacific white shrimp, formerly Litopenaeus vannamei): introduced in India in 2009 using specific-pathogen-free (SPF) broodstock; fast-growing, tolerant of a wide salinity range and high densities, it now forms the bulk of India's farmed shrimp.
• Penaeus monodon (giant tiger prawn): the largest native penaeid, traditionally the main brackishwater species; SPF domesticated stocks have revived its culture.
• Penaeus indicus (Indian white prawn, Fenneropenaeus indicus): native, suited to low-cost and traditional systems.
• Macrobrachium rosenbergii (giant freshwater prawn, "scampi") and M. malcolmsonii (monsoon river prawn): freshwater species, grown alone or with carps.

Methods of culture:

• Site selection and pond preparation: clay-loam soil, access to good water, away from mangroves and agricultural land as required by the Coastal Aquaculture Authority. Ponds of 0.5–1 ha are drained, dried and ploughed, limed according to soil pH, fertilised to raise plankton, screened against predators, and filled to about 1–1.5 m.
• Seed: hatchery-reared, disease-screened post-larvae (PL 10–15, PCR-tested for white spot virus) are acclimatised to pond temperature and salinity, often after a nursery phase.
• Extensive culture: traditional tidal systems such as the pokkali and kaipad rice fields of Kerala and the bheris of West Bengal, with natural seed or low stocking (below about 5 per m²), no feed and tidal water exchange; yields are low.
• Semi-intensive culture: stocking about 5–20 PL per m² for P. monodon (higher for P. vannamei), with formulated feed, fertilisation, some aeration and water exchange.
• Intensive culture: P. vannamei at about 40–100 or more per m² in lined or biosecure ponds with continuous paddle-wheel aeration, feeding trays, probiotics, and minimal-exchange or biofloc systems.
• Freshwater prawn culture: Macrobrachium is stocked at 2–5 per m², alone or in polyculture with Indian major carps, with shelters to reduce cannibalism and size-graded harvesting.
• Water quality and feeding: dissolved oxygen above 4 mg/L, pH 7.5–8.5, salinity 10–25 ppt (brackishwater), total ammonia kept low; feed is given 4–5 times daily and adjusted by check trays.
• Health management: biosecurity, bird and crab fencing, reservoir ponds and disinfection guard against white spot syndrome virus, acute hepatopancreatic necrosis disease (early mortality syndrome, caused by Vibrio parahaemolyticus) and Enterocytozoon hepatopenaei.
• Harvest and post-harvest: after about 100–120 days (P. vannamei) the pond is drained and shrimp collected with bag nets at the sluice, or partially harvested by cast nets; they are chilled in ice slurry at once, washed, graded, iced and sent to processing plants that follow export hygiene standards.
• Regulation: coastal aquaculture must be registered with the Coastal Aquaculture Authority (Act of 2005, amended in 2023), and MPEDA supports hatcheries, residue control and exports.