Statistical Inference for SSC CGL Tier 2, Paper 2

In the SSC CGL Tier 2 SSC JSO Paper, questions from Statistical Inference test your understanding of how conclusions are drawn from data. This topic includes Estimation (Point and Interval) and Hypothesis Testing using different statistical tests like Z, t, Chi-square, and F tests. This blog explains each of these concepts in simple terms, with formulas and examples to help you prepare effectively.

What is Statistical Inference?

Statistical Inference means using sample data to make conclusions or generalizations about a larger population. Since collecting data for an entire population is often not possible, we analyze a sample and use statistical methods to estimate population parameters or test assumptions. There are two main parts of statistical inference:

1. Estimation – Finding approximate values of population parameters.
2. Hypothesis Testing – Checking whether assumptions about the population are true or not.

Also check out Most Repeated Quantitative Aptitude Questions for SSC CGL Tier 2

1. Estimation

What is Estimation?

Estimation is the process of finding the approximate value of an unknown population parameter (like mean or proportion) based on sample data.

There are two types of estimation:

• Point Estimation
• Interval Estimation

Point Estimation

Point estimation gives a single best value of a population parameter.

Parameter	Point Estimator	Example
Population Mean (μ)	Sample Mean (x̄)	Average height of 100 students used to estimate population mean height
Population Proportion (p)	Sample Proportion (p̂)	Proportion of voters supporting a candidate from a small survey
Population Variance (σ²)	Sample Variance (s²)	Variance of sample marks used to estimate total variance

Also check out Most Repeated Quantitative Aptitude Questions for SSC CGL Tier 2

Interval Estimation

Interval estimation gives a range of values within which the population parameter is expected to lie, along with a certain level of confidence.

So, Confidence Interval = (68.04, 71.96)

This means we are 95% confident that the true population mean lies between 68.04 and 71.96.

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2. Hypothesis Testing

What is Hypothesis Testing?

Hypothesis testing is a method to decide whether there is enough statistical evidence in a sample to support or reject a claim (called a hypothesis) about a population parameter. Below are the steps in hypothesis testing:

Step	Description
1. Formulate Hypotheses	Set Null Hypothesis (H₀) and Alternative Hypothesis (H₁)
2. Select Significance Level	Usually α = 0.05 or 0.01
3. Choose Appropriate Test	Z, t, Chi-square, or F test
4. Compute Test Statistic	Using formulas based on sample data
5. Decision	Compare test statistic with critical value to accept or reject H₀

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Types of Errors

Error Type	Description
Type I Error	Rejecting H₀ when it is true (False positive)
Type II Error	Accepting H₀ when it is false (False negative)

Common Statistical Tests

Depending on the type of data and sample size, different tests are used in hypothesis testing.

1. Z-Test

Used when:

• Population standard deviation (σ) is known
• Sample size is large (n ≥ 30)

Test Type	Purpose
One-sample Z-test	To test if sample mean = population mean
Two-sample Z-test	To compare means of two samples
Proportion Z-test	To test equality of proportions

2. t-Test

Used when:

• Population standard deviation (σ) is unknown
• Sample size is small (n < 30)

Test Type	Purpose
One-sample t-test	Test sample mean vs population mean
Two-sample t-test	Compare two independent sample means
Paired t-test	Compare before-after observations of same group

3. Chi-Square (χ²) Test

Used for:

• Testing goodness of fit or independence of two attributes in a contingency table.

where,
O = Observed frequency,
E = Expected frequency.

Test Type	Purpose
Goodness of Fit	Check if observed data follows a theoretical distribution
Test of Independence	Check if two categorical variables are related

4. F-Test

Used for:
Comparing variances of two populations.

Example:
Used in ANOVA (Analysis of Variance) to test if means of multiple groups are equal.

Test Type	Purpose
Two-Sample F-test	Compare variances
ANOVA	Compare means of more than two groups

Confidence Intervals and Hypothesis Testing – Connection

Both estimation and hypothesis testing are linked:

• A confidence interval provides a range for the parameter.
• A hypothesis test checks if a specific value (like population mean) lies inside or outside that range.

If the hypothesized value lies outside the confidence interval, H₀ is rejected.

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Key Takeaways

• Statistical inference helps draw conclusions about populations using sample data.
• Point and Interval estimation give single or range-based parameter estimates.
• Z-test, t-test, Chi-square, and F-test are the core hypothesis tests for SSC CGL Tier 2 (JSO).
• Always identify the test type based on sample size, data type, and whether variance is known.
• Practice questions based on test statistic formulas and decision-making rules for better accuracy in the exam.

FAQs

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