Inspector of Statistics • Paper-III
Student’s t distribution is especially appropriate when:
A)
Sample size is large and variance known
B)
Sample size is small and population variance unknown
C)
Population is non normal
D)
Testing equality of several means
Student's t is especially useful with small samples when the population variance is unknown.
Inspector of Statistics • Paper-III
If two random variables X and Y are independent, which of the following is true?
A)
Their joint p.m.f/p.d.f. equals the product of their marginal p.m.f.s/p.d.f.s
B)
Their covariance is zero
C)
Their correlation is zero
D)
All of the above
Independence implies factorisation of the joint distribution and zero covariance/correlation when defined, so all listed statements are intended.
Inspector of Statistics • Paper-III
Which theorem provides a method to improve an unbiased estimator by conditioning on a sufficient statistic?
A)
Cramer-Rao inequality
B)
Factorization theorem
C)
Rao-Blackwell theorem
D)
Lehmann-Scheffe theorem
Rao–Blackwell improves an unbiased estimator by conditioning it on a sufficient statistic.
Inspector of Statistics • Paper-III
The function that gives the probability that a discrete random variable is exactly equal to some value is called:
A)
Probability density function (p.d.f.)
B)
Cumulative distribution function (c.d.f.)
C)
Probability mass function (p.m.f.)
D)
Moment generating function (m.g.f.)
For a discrete random variable, the probability at an exact value is given by the PMF.
Inspector of Statistics • Paper-III
The additive property is a key characteristic of which exact sampling distribution?
A)
Student’s t-distribution
B)
F-distribution
C)
Chi-square distribution
D)
Normal distribution
Chi-square distributions are additive: sums of independent chi-square variables with compatible degrees of freedom remain chi-square.
Inspector of Statistics • Paper-III
Pearson’s Chi-square test for goodness of fit is used to:
A)
Compare the means of two independent samples.
B)
Test the independence of two categorical variables in a contingency table.
C)
Assess how well a sample distribution fits a hypothesized population distribution.
D)
Test the equality of two population variances.
Goodness-of-fit chi-square tests compare observed frequencies with a hypothesised distribution.
Inspector of Statistics • Paper-III
Which design controls variation in two directions (rows and columns) and is particularly useful when there are two known sources of variability?
A)
Completely Randomized Design
B)
Randomized Block Design
C)
Latin Square Design
D)
Factorial Design
Latin Square Design controls two nuisance sources of variation through rows and columns.
Inspector of Statistics • Paper-III
What is the key distinction between a parameter and a statistic?
A)
A parameter describes a sample, while a statistic describes a population.
B)
A parameter is fixed for a population, while a statistic varies from sample to sample.
C)
A statistic is always known, while a parameter is always unknown.
D)
They are two terms for the same concept.
A parameter is a fixed population characteristic; a statistic is computed from a sample and varies across samples.
Inspector of Statistics • Paper-III
Which interpolation formula is used for unequal intervals?
A)
Newton–Gregory forward formula
B)
Newton–Gregory backward formula
C)
Lagrange’s interpolation formula
D)
Simpson’s rule
Lagrange interpolation works with unequal intervals; Newton–Gregory forward/backward formulas assume equally spaced data.
Inspector of Statistics • Paper-III
Which graphical representation is most appropriate for showing the distribution of a continuous variable?
A)
Bar chart
B)
Pie chart
C)
Histogram
D)
Scatter diagram
A histogram is the standard graphical display for the distribution of a continuous variable.
Inspector of Statistics • Paper-II
With reference to Eco-Sensitive Zones, which of the following statements are correct?
I. Eco-Sensitive Zones are areas notified under the Wildlife (Protection) Act, 1972
II. Eco-Sensitive Zones are designated to ban all forms of human activity within their boundaries, except for agricultural practices
Select the correct answer using the code given below:
A)
I only
B)
II only
C)
Both I and II
D)
Neither I nor II
Eco-Sensitive Zones are notified under the Environment (Protection) Act and are not blanket no-human-activity zones.
Inspector of Statistics • Paper-II
Which of the following are designated as ‘Protected Areas’ by Government of Mizoram?
I. Murlen National Park
II. Phawngpui National Park
III. Dampa Tiger Reserve
IV. Ngengpui Wildlife Sanctuary
Select the correct answer using the code below:
A)
I and II only
B)
I, II and IV only
C)
II, III and IV only
D)
I, II, III and IV
To determine the correct answer, we must verify the status of each listed area under the Government of Mizoram's environmental and wildlife protection framework:
1. **Murlen National Park**: This is a designated National Park in Mizoram, established to protect the biodiversity of the region.
2. **Phawngpui National Park**: Located at the highest peak of Mizoram (Blue Mountain), it is one of the most prominent National Parks in the state.
3. **Dampa Tiger Reserve**: This is the largest protected area in Mizoram and is designated as a Tiger Reserve (which falls under the broader category of 'Protected Areas').
4. **Ngengpui Wildlife Sanctuary**: This is a officially notified Wildlife Sanctuary in Mizoram.
Under the Wildlife (Protection) Act, 1972, 'Protected Areas' is an umbrella term that includes National Parks, Wildlife Sanctuaries, Conservation Reserves, and Community Reserves. Since all four listed entities (Murlen, Phawngpui, Dampa, and Ngengpui) are officially notified as either National Parks, Tiger Reserves, or Wildlife Sanctuaries by the Government of Mizoram, all four are designated as Protected Areas.
Therefore, the correct combination is I, II, III, and IV.
Inspector of Statistics • Paper-II
Which article of the Indian Constitution deals with the administration of Autonomous District Councils in North East India through Governors’ rule?
A)
Article 244 (2)
B)
Article 240
C)
Article 371-G
D)
Article 356
Article 244(2) applies the Sixth Schedule framework for administration of tribal areas in specified North-Eastern states.
Inspector of Statistics • Paper-II
Which banking indicator is used to assess credit flow in Mizoram?
A)
Credit–Deposit Ratio
B)
Repo Rate
C)
Cash Reserve Ratio
D)
Priority Sector Target
The Credit-Deposit Ratio (CD Ratio) is the primary banking indicator used to assess the efficiency of credit flow in a specific region or state, including Mizoram. It measures how much of the deposits collected by banks in that region are being lent back to the local borrowers as loans. A low CD ratio in a state like Mizoram would indicate that banks are collecting deposits but not deploying them as credit locally, whereas a high ratio indicates a healthy flow of credit to the local economy.
Why other options are incorrect:
- b. Repo Rate: This is a monetary policy tool set by the Reserve Bank of India (RBI) at the national level; it is not a regional indicator for credit flow.
- c. Cash Reserve Ratio (CRR): This is the percentage of total deposits that commercial banks must keep as reserves with the RBI; it is a regulatory requirement, not a measure of regional credit flow.
- d. Priority Sector Target: While this dictates the percentage of loans that must go to specific sectors (like agriculture or MSMEs), it is a regulatory target/benchmark rather than an indicator used to assess the actual overall flow of credit relative to deposits in a state.
Inspector of Statistics • Paper-II
In statistics, if observations are arranged either in ascending or descending order of magnitude, then the value of observation which lies exactly in the middle is :
A)
Mean
B)
Mode
C)
Median
D)
Range
The middle observation in ordered data is the median.
Inspector of Statistics • Paper-II
With reference to the geography of Mizoram, consider the following statements:
I. Mizoram lies entirely in the Purvanchal Hill range
II. The state has a higher north–south extension than east–west extension
III. Most rivers of Mizoram drain into the Bay of Bengal
Which of the statements given above are correct?
A)
1 and 2 only
B)
2 and 3 only
C)
1 and 3 only
D)
1, 2 and 3
Step-by-step analysis of the statements:
1. Statement I is correct: Mizoram is located in the Purvanchal range (the eastern extension of the Himalayas). The state's terrain is characterized by north-south trending hill ranges and deep valleys, which are typical of the Purvanchal hills.
2. Statement II is correct: Geographically, Mizoram is elongated. Its north-south extension is significantly greater than its east-west width. This is evident from the state's map, where the distance from the northern border (Manipur/Assam) to the southern border (Myanmar/Bangladesh) is much longer than the distance from the western border (Tripura/Bangladesh) to the eastern border (Myanmar).
3. Statement III is correct: The major rivers of Mizoram, such as the Tlawng, Tuirial, and Chhimtuipui (Kolodyne), flow generally in a south-westerly or southerly direction. These rivers eventually join larger river systems (like the Surma/Kushiyara in Bangladesh) which drain into the Bay of Bengal.
Since all three statements are geographically accurate, the correct option is 'd'.
Inspector of Statistics • Paper-II
Consider the following statements:
I: Article 4 of the Paris Agreement is central to global climate action and is often cited in international climate negotiations
II: Article 4 of the Paris Agreement requires all Parties to prepare, communicate, and maintain successive Nationally Determined Contributions (NDCs)
III: Article 4 of the Paris Agreement mandates legally binding emission reduction targets for both developed and developing countries
Which one of the following is correct in respect of the above statements?
A)
Both II and III are correct and both of them explain I
B)
Both II and III are correct but only one of them explains I
C)
Only Statement II is correct and it explains I
D)
Neither Statement II nor Statement III is correct
Article 4 requires successive NDCs, but it does not impose legally binding quantified emission-reduction targets on countries, so only II is correct.
Inspector of Statistics • Paper-II
Consider the following statements:
I. In India, Biodiversity Management Committees play a crucial role in achieving the objectives of the Nagoya Protocol
II. These committees have significant responsibilities in regulating access and benefit-sharing, including the authority to impose collection charges for the use of biological resources within their jurisdiction
Which of the statements given above is/are correct?
A)
I only
B)
II only
C)
Both I and II
D)
Neither I nor II
Biodiversity Management Committees are part of access-and-benefit-sharing implementation and can levy collection charges.
Inspector of Statistics • Paper-II
The Yuktdhara Portal is a GIS-enabled platform developed to support which government scheme?
A)
MGNREGS
B)
Pradhan Mantri Gram Sadak Yojana
C)
PM Awas Yojana–Gramin
D)
Jal Jeevan Mission
Yuktdhara is the GIS-based planning portal for MGNREGS.
Inspector of Statistics • Paper-II
Which sector contributes the largest share to Mizoram’s Gross State Domestic Product?
A)
Agriculture
B)
Industry
C)
Services
D)
Mining
In the context of Mizoram's economy, the Gross State Domestic Product (GSDP) is divided into three primary sectors: Primary (Agriculture & Allied), Secondary (Industry), and Tertiary (Services). While a large portion of the population is engaged in agriculture (jhum cultivation), the economic value added by the Services sector is the highest. The Services sector includes government administration, trade, hotels, restaurants, transport, and communication. In recent economic surveys of Mizoram, the Tertiary/Services sector consistently contributes the largest share to the GSDP, often exceeding 50-60%, followed by Agriculture and then Industry. Therefore, option (c) is correct. Option (a) is incorrect because while agriculture employs many, its GSDP share is lower than services. Option (b) and (d) are incorrect as the industrial and mining sectors are relatively underdeveloped in the state.
Inspector of Statistics • Paper-II
Which of the following indicators are used in the Statistical Handbook of Mizoram to assess the fiscal health of the state?
I. Gross Fiscal Deficit as a percentage of GSDP
II. Outstanding Debt to GSDP ratio
III. Revenue Surplus/Deficit
IV. Current Account Deficit
Select the correct answer using the code below:
A)
I and IV only
B)
II and III only
C)
I, II and III only
D)
I, II, III and IV
In the Statistical Handbook of Mizoram (published by the Directorate of Economics and Statistics), the 'Finance' section focuses on the state's fiscal health using standard macroeconomic indicators.
1. Gross Fiscal Deficit as a percentage of GSDP: This is the primary indicator used to measure the total borrowing requirements of the state relative to its economy.
2. Outstanding Debt to GSDP ratio: This indicates the sustainability of the state's debt burden over the long term.
3. Revenue Surplus/Deficit: This measures whether the state's current revenues are sufficient to cover its current expenditures (excluding capital expenditure).
4. Current Account Deficit: This tracks the gap between current receipts and current payments, reflecting the state's reliance on borrowings or grants for day-to-day functioning.
All four indicators are standard components of the fiscal analysis provided in the state's statistical reports to assess financial stability and sustainability.
Inspector of Statistics • Paper-II
The term ‘blue carbon’ refers to:
A)
Carbon captured by oceans and coastal ecosystems
B)
Carbon sequestered in forest biomass and agricultural soils
C)
Carbon contained in petroleum and natural gas
D)
Carbon present in atmosphere
Blue carbon is the carbon captured and stored in marine and coastal ecosystems.
Inspector of Statistics • Paper-II
Which of the following is correct about ozone?
A)
It is a red coloured gas
B)
It is odourless
C)
It is harmless in small concentrations
D)
None of the above
Ozone is a pale-blue gas with a characteristic pungent smell and is harmful at elevated concentrations, so A–C are false.
Inspector of Statistics • Paper-II
With reference to health indicators in Mizoram, consider the following statements:
I. Infant Mortality Rate in Mizoram is lower than the national average
II. Health statistical data are drawn from the Civil Registration System
III. Universal Immunisation Programme is implemented through Integrated Child Development Service (ICDS)
Which of the statements given above are correct?
A)
I and II only
B)
II and III only
C)
I and III only
D)
I, II and III
Step-by-step analysis of the statements:
1. Statement I is CORRECT: Mizoram consistently reports an Infant Mortality Rate (IMR) that is lower than the national average of India. This is attributed to better community health awareness and the effectiveness of primary healthcare delivery in the state.
2. Statement II is CORRECT: The Civil Registration System (CRS) is the official mechanism for the continuous, permanent, and compulsory recording of vital events (births and deaths). Health statistical data regarding mortality and fertility are primarily drawn from the CRS to ensure accuracy in public health planning.
3. Statement III is INCORRECT: The Universal Immunisation Programme (UIP) is implemented primarily through the health infrastructure (Primary Health Centres, Community Health Centres, and Sub-centres) under the Ministry of Health and Family Welfare. While the Integrated Child Development Services (ICDS) provides nutritional support and assists in mobilizing mothers and children for vaccination (convergence), the actual implementation and administration of the vaccines are handled by the health department, not the ICDS.
Therefore, only statements I and II are correct.
Inspector of Statistics • Paper-II
Which among the following taxes is levied by state government only?
A)
Wealth tax
B)
Estate duty
C)
Entertainment tax
D)
Corporation tax
Entertainment tax was a state-level tax before being subsumed/altered by GST; the other listed taxes are not state-only taxes.
