CUET UG Applied Mathematics Booster Test 1 - Parameter & Statistical Concepts -

🚀

CUET UG Applied Mathematics Booster Test 1 - Parameter & Statistical Concepts

⏱️ 30 Minutes

❓ 20 Questions

📌 Answers are locked once submitted — results and explanations appear at the end.

CUET UG Applied Mathematics Booster Test 1 - Parameter & Statistical Concepts

1 / 20

QUESTION 1 OF 20

A researcher accurately calculates the mean height of all 100 million adults in a country. This comprehensively calculated average is scientifically defined as a:

Answer Review

1 A researcher accurately calculates the mean height of all 100 million adults in a country. This comprehensively calculated average is scientifically defined as a:

A Sample Statistic

B Population Parameter

C Confidence Interval

D Margin of error

💡 Short Explanation

Entire population isStrategy Used Measure describes population characteristic Hence it is a parameter

✅ Correct Answer Explanation

A parameter is a numerical measure that describes an entire population. Since the researcher calculates the mean height using all 100 million adults, it is not an estimate but the true population value. Option A (sample statistic) is incorrect because no sampling is involved. Option C (confidence interval) is a range estimate, not a fixed value. Option D (margin of error) refers to uncertainty, not a computed mean. Thus, the correct classification is a population parameter.

❓ Why Other Options Are Incorrect

Option A → Requires sample, not full population
Option C → Represents interval estimation, not actual mean
Option D → Measures error, not central tendency

🎯 Strategy

Used: Extreme Word Filter

Application: Check whether data is full population or sample

Final Logic: Full population ⇒ parameter

🧠 Memory Trick

"Whole = Parameter"

📚 Class XI – NCERT Mathematics (Statistics) – Chapter: Statistics – Topic: Parameter vs Statistic –

2 Assertion (A): If we compute the variance of all students in a university, we use the symbol σ².
Reason (R): Parameters are typically denoted by English alphabets.

A Both A and R are false

B A is false, R is true

C Both A and R are true, and R is the correct explanation of A

D A is true, R is false

💡 Short Explanation

σ² denotes population variance Parameters use Greek symbols English letters are for statistics

✅ Correct Answer Explanation

The assertion is correct because population variance is represented by σ². The reason is incorrect because parameters are typically denoted by Greek letters, not English alphabets. A is true: σ² is population variance R is false: English letters denote sample statistics (e.g., s², x̄)

❓ Why Other Options Are Incorrect

Option A → Assertion is correct
Option B → Assertion is true
Option C → Reason is incorrect

🎯 Strategy

Used: Elimination

Application: Check symbol conventions in statistics

Final Logic: Greek = parameter, English = statistic

🧠 Memory Trick

"Greek = Global (population)"

📚 Class XI – NCERT Mathematics (Statistics) – Chapter: Statistics – Topic: Parameter Notation –

3 The calculated average salary package of 50 randomly selected Delhi University graduates is an example of a:

A Statistic

B Parameter

C Sampling error

D Margin of error

💡 Short Explanation

Based on sample Computed from subset Strategy Used for inference

✅ Correct Answer Explanation

A statistic is a numerical value calculated from a sample. Since only 50 graduates (not all graduates) are considered, the average salary is a sample statistic. Option B is incorrect because population is notStrategy Used. Option C refers to deviation, not computed mean. Option D refers to uncertainty, not a value.

❓ Why Other Options Are Incorrect

Option B → Requires full population
Option C → Difference, not computed value
Option D → Error range concept

🎯 Strategy

Used: Contextual Matching

Application: Identify sample-based computation

Final Logic: Sample data ⇒ statistic

🧠 Memory Trick

"Sample → Statistic"

📚 Class XI – NCERT Mathematics (Statistics) – Chapter: Statistics – Topic: Statistic Definition –

4 Match List I with List II:

List I	List II
1. Mean height of 50 Indian adults	a. σ²
2. Variance of all adults in India	b. S
3. Standard deviation of 100 students	c. x̄
4. Mean income of an entire population	d. μ

A 1–a, 2–b, 3–c, 4–d

B 1–b, 2–a, 3–d, 4–c

C 1–c, 2–a, 3–b, 4–d

D 1–a, 2–c, 3–b, 4–d

💡 Short Explanation

Sample mean → x̄ Variance → σ² Standard deviation → S Population mean → μ

✅ Correct Answer Explanation

Matching based on statistical notation: Mean of sample → x̄ Population variance → σ² Sample standard deviation → S Population mean → μ Thus option C is correct.

❓ Why Other Options Are Incorrect

Option A → Wrong symbol matching
Option B → Mixed sample/population confusion
Option D → Incorrect mapping of mean/variance

🎯 Strategy

Used: Option Grouping

Application: Match standard statistical symbols

Final Logic: Standard notation mapping

🧠 Memory Trick

"x̄ sample, μ population"

📚 Class XI – NCERT Mathematics (Statistics) – Chapter: Statistics – Topic: Notation –

5 Which of the following statements are correct?
I. A parameter refers to the whole population
II. A statistic refers to a part of the population
III. Both refer exclusively to subset data

A I only

B II only

C I and II only

D I, II, and III

💡 Short Explanation

Parameter = population Statistic = sample III is incorrect

✅ Correct Answer Explanation

I is correct: parameter refers to population II is correct: statistic refers to sample III is incorrect: both are not subset-only concepts

❓ Why Other Options Are Incorrect

Option A → ignores II
Option B → ignores I
Option D → includes incorrect statement III

🎯 Strategy

Used: Elimination

Application: Remove incorrect universal claim

Final Logic: Only I and II true

🧠 Memory Trick

"Param = Whole, Stat = Sample"

📚 Class XI – NCERT Mathematics (Statistics) – Chapter: Statistics – Topic: Parameter vs Statistic –

6 Identify the incorrect statement:

A Parameter values are derived from all population observations

B A statistic is a numerical value taken from the entire population

C A statistic is computed from a portion of the population

D Both are related but distinct measures

💡 Short Explanation

Statistic is sample-based Parameter is population-based Option B is reversed

✅ Correct Answer Explanation

A statistic is calculated from a sample, not the entire population. Therefore, Option B is incorrect.

❓ Why Other Options Are Incorrect

Option A → Correct definition
Option C → Correct definition
Option D → Correct conceptual statement

🎯 Strategy

Used: Extreme Word Filter

Application: Identify incorrect domain (population vs sample)

Final Logic: Statistic ≠ population

🧠 Memory Trick

"Stat ≠ total"

📚 Class XI – NCERT Mathematics (Statistics) – Chapter: Statistics – Topic: Parameter vs Statistic –

📄 Passage

"In statistics, we commonly use a sample that is a small subset of a larger dataset for making inferences about the larger set. The larger set is called the population from which the sample is drawn. The sample size is always smaller than the population size."

Testing 60 bags out of 1000 and making conclusions about all bags is called:

A Descriptive Statistics

B Stratified Sampling

C Parameter substitution

D Statistical inference

💡 Short Explanation

Uses sample to infer population Generalization process Core inference concept

✅ Correct Answer Explanation

Statistical inference involves using sample data to draw conclusions about a population. Testing 60 bags out of 1000 fits this definition.

❓ Why Other Options Are Incorrect

Option A → Only describes data
Option B → Sampling method
Option C → Not a valid term

🎯 Strategy

Used: Contextual Matching

Application: Match scenario to inference definition

Final Logic: Sample → population conclusion

🧠 Memory Trick

"Infer = sample to whole"

📚 Class XI – NCERT Mathematics (Statistics) – Chapter: Statistics – Topic: Statistical Inference –

📄 Passage

Generalization is possible because:

A Sample is representative subset

B Sample is separate from population

C Sample size equals population

D Population is subset of sample

💡 Short Explanation

Representation ensures validity Sample reflects population Enables inference

✅ Correct Answer Explanation

Generalization works only when the sample represents the population. This allows inference from sample to population.

❓ Why Other Options Are Incorrect

Option B → contradicts sampling theory
Option C → unnecessary condition
Option D → reversed relationship

🎯 Strategy

Used: Conceptual Matching

Application: Identify valid sampling relationship

Final Logic: Representation enables inference

🧠 Memory Trick

"Good sample = mirror of population"

📚 Class XI – NCERT Mathematics (Statistics) – Chapter: Statistics – Topic: Sampling Principle –

9 Assertion (A): High statistical significance implies higher reliability of findings.
Reason (R): Statistical significance indicates that the result is likely real and the sample was appropriately constructed.

A Both A and R are false

B Both A and R are true, and R is correct explanation

C A is true, R is false

D A is false, R is true

💡 Short Explanation

Significance indicates real effect Reduces chance error Improves reliability

✅ Correct Answer Explanation

Statistical significance suggests that results are unlikely due to chance, increasing reliability. Hence both assertion and reason are correct.

❓ Why Other Options Are Incorrect

Option A → both statements valid
Option C → reason is correct
Option D → assertion is correct

🎯 Strategy

Used: Contextual Matching

Application: Evaluate meaning of significance

Final Logic: Low p-value ⇒ reliable result

🧠 Memory Trick

"Significant = strong evidence"

📚 Class XI – NCERT Mathematics (Statistics) – Chapter: Statistics – Topic: Statistical Significance –

10 Arrange the steps of hypothesis testing:
1. Compute the test value
2. State the hypotheses
3. Summarize the results
4. Decide to reject or not reject \(H_{0}\)
5. Find critical values

A 1, 2, 3, 4, 5

B 2, 1, 5, 4, 3

C 2, 5, 1, 4, 3

D 5, 2, 1, 4, 3

💡 Short Explanation

Start with hypothesis Find critical values Compute test statistic Decide result Summarize

✅ Correct Answer Explanation

Correct sequence of hypothesis testing: State hypotheses → find critical values → compute test statistic → decide rejection → summarize results.

❓ Why Other Options Are Incorrect

Option A → unordered
Option B → misplacement of steps
Option D → incorrect logical flow

🎯 Strategy

Used: Logical Sequencing

Application: Arrange hypothesis testing steps

Final Logic: Standard testing procedure

🧠 Memory Trick

"H-C-T-D-S"

📚 Class XI – NCERT Mathematics (Statistics) – Chapter: Statistics – Topic: Hypothesis Testing –

11 If we repeatedly sample and plot the means, the resulting distribution is called:

A Population variance distribution

B Standard error

C Null hypothesis distribution

D Sampling distribution of the mean

💡 Short Explanation

Repeated samples produce multiple sample means These means form a probability distribution This distribution is called the sampling distribution of the mean

✅ Correct Answer Explanation

The sampling distribution of the mean is the distribution formed by considering all possible sample means obtained from repeated random samples of the same size from a population. Option D is correct because the question specifically refers to repeatedly sampling and plotting the means. The resulting pattern of these sample means is known in statistics as the sampling distribution of the mean. Option A is incorrect because population variance distribution is not a standard statistical term for repeated sample means. Option B is incorrect because standard error is only the standard deviation of the sampling distribution; it is not the distribution itself. Option C is incorrect because a null hypothesis distribution relates to hypothesis testing, not directly to repeated sample means.

❓ Why Other Options Are Incorrect

Option A → "Population variance distribution" does not describe the distribution formed from repeated sample means.
Option B → Standard error measures variability of sample means but is not the distribution itself.
Option C → Null hypothesis distribution is associated with testing procedures, not repeated sampling of means.

🎯 Strategy

Used

Keyword Identification

Application:

The phrase "repeatedly sample and plot the means" directly signals the concept of a sampling distribution.

Final Logic:

Distribution formed from repeated sample means = Sampling distribution of the mean.

🧠 Memory Trick

"Sample Means → Sampling Distribution"

📚 Class XI – Statistics for Economics – Chapter: Introduction to Statistics – Topic: Sampling and Distribution Concepts –

12 Which statement is incorrect?

A It represents all possible values of a statistic

B It requires considering all possible samples

C It is a theoretical concept

D It is physically constructed using the entire population

💡 Short Explanation

Sampling distribution is theoretical It involves all possible samples conceptually It is not physically constructed in practice

✅ Correct Answer Explanation

A sampling distribution is a theoretical probability distribution that represents all possible values of a statistic obtained from all possible samples of a fixed size. Option D is incorrect because a sampling distribution is not physically constructed using the entire population. In practice, it is understood mathematically and theoretically. Option A is correct because sampling distributions contain all possible values of a statistic. Option B is correct because the concept depends on considering all possible samples theoretically. Option C is correct because sampling distributions are theoretical modelsStrategy Used in inferential statistics.

❓ Why Other Options Are Incorrect

Option A → Correctly defines the purpose of a sampling distribution.
Option B → Theoretical construction involves all possible samples.
Option C → Sampling distributions are mathematical/theoretical concepts.

🎯 Strategy

Used

Elimination

Application:

Three statements correctly describe theoretical sampling distributions, leaving the practically incorrect statement.

Final Logic:

Sampling distributions are theoretical, not physically constructed.

🧠 Memory Trick

"Theoretical, not physical"

📚 Class XI – Statistics for Economics – Chapter: Introduction to Statistics – Topic: Sampling Distribution –

13 For large n, the sampling distribution becomes:

A Bell-shaped normal curve

B U-shaped curve

C J-shaped curve

D Straight line

💡 Short Explanation

Central Limit Theorem applies for large samples Sampling distributions approach normality Normal distributions are bell-shaped

✅ Correct Answer Explanation

According to the Central Limit Theorem (CLT), when the sample size becomes sufficiently large, the sampling distribution of the sample mean approaches a normal distribution regardless of the population shape. Option A is correct because the normal distribution is bell-shaped. Option B is incorrect because U-shaped distributions are not associated with CLT outcomes. Option C is incorrect because J-shaped curves do not represent sampling distributions under CLT. Option D is incorrect because a straight line cannot represent a probability distribution of sample means.

❓ Why Other Options Are Incorrect

Option B → U-shaped curves are unrelated to the CLT result.
Option C → J-shaped curves are not the limiting distribution under large samples.
Option D → A straight line cannot model sampling variability.

🎯 Strategy

Used

Conceptual Recall

Application:

Recall the direct implication of the Central Limit Theorem.

Final Logic:

Large sample size leads to a bell-shaped normal distribution.

🧠 Memory Trick

"Large n → Normal Bell"

📚 Class XI – Statistics for Economics – Chapter: Measures and Probability Concepts – Topic: Central Limit Theorem –

14 Assertion (A): A sample size of 15 is universally considered sufficient for the Central Limit Theorem to consistently produce a normal distribution.
Reason (R): As per the Central Limit Theorem, a sample size of 30 or more is generally considered sufficient for the approximation to hold.

A Both A and R are false

B A is false, R is true

C Both A and R are true, and R is the correct explanation of A

D A is true, R is false

💡 Short Explanation

Sample size 15 is not universally sufficient n ≥ 30 is commonly accepted for CLT approximation Larger samples improve normal approximation

✅ Correct Answer Explanation

Assertion A is false because a sample size of 15 does not universally guarantee a normal sampling distribution. The adequacy depends on the parent population's shape. Reason R is true because statisticians commonly use the rule that sample sizes of 30 or more are generally sufficient for the Central Limit Theorem approximation. Thus, Option B is correct.

❓ Why Other Options Are Incorrect

Option A → Incorrect because the reason statement is true.
Option C → Incorrect because the assertion itself is false.
Option D → Incorrect because the reason is not false.

🎯 Strategy

Used

Extreme Word Filter

Application:

The word "universally" in Assertion A makes the statement too absolute and therefore suspicious.

Final Logic:

CLT approximation is generally reliable near n ≥ 30, not universally at n = 15.

🧠 Memory Trick

"CLT likes 30+"

📚 Class XI – Statistics for Economics – Chapter: Statistical Inference – Topic: Central Limit Theorem –

15 If the true population mean μ = 50, and increasingly large samples are taken, the sample mean x ˉ will approximate:

A 0

B 100

C 50

D 25

💡 Short Explanation

Sample mean estimates population mean Larger samples improve accuracy x ˉ approaches μ

✅ Correct Answer Explanation

The sample mean is an estimator of the population mean. According to the law of large numbers and the Central Limit Theorem, as sample size increases, the sample mean tends to approach the true population mean. Since μ = 50, the sample mean will approximate 50. Therefore, Option C is correct. Options A, B, and D are unrelated arbitrary values not supported by the population mean.

❓ Why Other Options Are Incorrect

Option A → No statistical basis for convergence toward 0.
Option B → The sample mean approaches the actual population mean, not 100.
Option D → 25 is unrelated to the given population mean.

🎯 Strategy

Used

Substitution

Application:

Substitute the given population mean directly into the CLT implication.

Final Logic:

Sample mean converges toward μ = 50.

🧠 Memory Trick

"x ˉ follows μ"

📚 Class XI – Statistics for Economics – Chapter: Statistical Inference – Topic: Sample Mean and Population Mean –

16 A key implication of the Central Limit Theorem is that as the sample size N increases, the sampling distribution approaches a normal distribution:

A Regardless of the shape of the parent population

B Only if the parent population is uniform

C Only if the parent population is skewed

D Only if the parent population is perfectly normal

💡 Short Explanation

CLT works for many population shapes Large samples produce near-normal distributions Parent population shape becomes less important

✅ Correct Answer Explanation

The Central Limit Theorem states that for sufficiently large sample sizes, the sampling distribution of the sample mean approaches a normal distribution regardless of the original population distribution. Therefore, Option A is correct. Option B is incorrect because CLT is not limited to uniform populations. Option C is incorrect because skewed populations are not the only applicable case. Option D is incorrect because the parent population need not already be normal.

❓ Why Other Options Are Incorrect

Option B → CLT is not restricted to uniform distributions.
Option C → CLT applies beyond skewed populations.
Option D → Normal parent populations are not mandatory.

🎯 Strategy

Used

Extreme Word Filter

Application:

Options containing "only if" are restrictive and contradict the broad applicability of CLT.

Final Logic:

CLT works regardless of population shape for large samples.

🧠 Memory Trick

"Large N ignores shape"

📚 Class XI – Statistics for Economics – Chapter: Statistical Inference – Topic: Central Limit Theorem –

17 A pre-election survey predicts that candidate A will receive between 25% and 35% of the vote. This interval estimate is known as a:

A Point Estimate

B Confidence Interval

C Critical p-value

D Degree of Freedom

💡 Short Explanation

Range estimates are intervals Confidence intervals give probable parameter ranges Point estimates give only one value

✅ Correct Answer Explanation

A confidence interval provides a range within which the true population parameter is expected to lie with a specified level of confidence. Since the survey predicts support between 25% and 35%, this is an interval estimate. Therefore, Option B is correct. Option A is incorrect because a point estimate gives only a single value. Option C relates to hypothesis testing significance. Option D refers to statistical calculation freedom in distributions/tests.

❓ Why Other Options Are Incorrect

Option A → A point estimate is a single number, not a range.
Option C → p-values measure statistical significance, not interval estimation.
Option D → Degree of freedom is unrelated to interval prediction here.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

The phrase "between 25% and 35%" clearly indicates interval estimation.

Final Logic:

Range-based estimate = Confidence Interval.

🧠 Memory Trick

"Interval = Range"

📚 Class XI – Statistics for Economics – Chapter: Statistical Inference – Topic: Confidence Interval –

18 If a survey reports a 95% confidence level, what does it imply?

A 95% of the population was surveyed

B The margin of error is 95%

C Candidate A will receive 95% of votes

D There is 95% confidence that the true population parameter lies within the interval

💡 Short Explanation

Confidence level measures reliability It refers to the interval estimation process It does not describe population percentage surveyed

✅ Correct Answer Explanation

A 95% confidence level means that if repeated samples are taken and intervals are constructed repeatedly, approximately 95% of those intervals would contain the true population parameter. Therefore, Option D is correct. Option A is incorrect because confidence level is unrelated to the percentage surveyed. Option B is incorrect because margin of error and confidence level are different concepts. Option C is incorrect because confidence level does not predict vote percentage directly.

❓ Why Other Options Are Incorrect

Option A → Confidence level does not indicate sample coverage.
Option B → Margin of error is separate from confidence level.
Option C → Confidence level does not mean 95% vote share.

🎯 Strategy

Used

Elimination

Application:

Remove options confusing confidence level with sample size, error size, or vote percentage.

Final Logic:

Confidence level refers to reliability of interval estimation.

🧠 Memory Trick

"95% confident, not 95% surveyed"

📚 Class XI – Statistics for Economics – Chapter: Statistical Inference – Topic: Confidence Level –

19 Match List I with List II:

List I	List II
1. Confidence Level	a. Explains uncertainty of the method
2. Margin of Error	b. Describes accuracy of the estimate
3. Sample Size	c. Defined as N
4. Point Estimate	d. Single numerical statistic (e.g., x̄)

A 1–b, 2–a, 3–d, 4–c

B 1–a, 2–a, 3–c, 4–d

C 1–a, 2–b, 3–c, 4–d

D 1–b, 2–b, 3–a, 4–c

💡 Short Explanation

Confidence level explains reliability Margin of error shows accuracy range Point estimate is a single statistic

✅ Correct Answer Explanation

Confidence level explains the reliability or uncertainty associated with the estimation method, so 1–a is correct. Margin of error describes the accuracy or allowable deviation of the estimate, so 2–b is correct. Sample size is represented by N, so 3–c is correct. A point estimate is a single numerical statistic like x ˉ, so 4–d is correct. Thus, Option C correctly matches all pairs.

❓ Why Other Options Are Incorrect

Option A → Incorrectly swaps confidence level and margin of error relationships.
Option B → Margin of error cannot represent uncertainty of method alone.
Option D → Sample size is not related to uncertainty explanation.

🎯 Strategy

Used

Option Grouping

Application:

Match standard statistical terminology systematically.

Final Logic:

Only Option C correctly pairs all statistical terms.

🧠 Memory Trick

"CL–Uncertainty, ME–Accuracy"

📚 Class XI – Statistics for Economics – Chapter: Statistical Inference – Topic: Confidence Interval Components –

20 Assertion (A): A confidence interval expresses the precision and uncertainty of a sampling process.
Reason (R): A confidence interval consists of a confidence level, a statistic, and a margin of error.

A Both A and R are true, and R is the correct explanation of A

B Both A and R are false

C A is true, R is false

D A is false, R is true

💡 Short Explanation

Confidence intervals express estimation uncertainty They include confidence level and margin of error These components determine precision

✅ Correct Answer Explanation

Assertion A is true because confidence intervals communicate both precision and uncertainty in estimation. Reason R is also true because a confidence interval is formed using: • a statistic (point estimate), • a margin of error, and • a confidence level. These components together determine how reliable and precise the interval estimate is. Hence, the reason correctly explains the assertion. Therefore, Option A is correct.

❓ Why Other Options Are Incorrect

Option B → Both statements are actually true.
Option C → Reason is not false; it correctly explains the assertion.
Option D → Assertion is not false because confidence intervals do express uncertainty.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Link the structure of confidence intervals with their statistical purpose.

Final Logic:

CI components directly explain uncertainty and precision.

🧠 Memory Trick

"CI = Confidence + Error Range"

📚 Class XI – Statistics for Economics – Chapter: Statistical Inference – Topic: Confidence Interval and Precision –

CUET UG Applied Mathematics Booster Test 1 - Parameter & Statistical Concepts

Test Complete!

Answer Review