Statistical Methods & Experimental Designs

1

In drawing a Histogram for unequal class intervals, the height of the rectangle will be:

असमान वर्ग अंतरालों (Unequal class intervals) के लिए आयतचित्र (Histogram) बनाते समय आयत की ऊँचाई किसके समानुपाती होगी?

Collection, Classification and Tabulation of Data, Frequency Distributions and Graphical Representations Collection, Classification and Tabulation of Data, Frequency Distributions and Graphical Representations ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

2

The width of each of nine classes in a frequency distribution is 2.5 and the lower class boundary of the lowest class is 10.6. Which one of the following is the upper class boundary of the highest class?

एक बारंबारता बंटन में नौ वर्गों में से प्रत्येक की चौड़ाई 2.5 है और सबसे निचले वर्ग की निचली वर्ग सीमा 10.6 है। निम्नलिखित में से कौन-सी उच्चतम वर्ग की ऊपरी वर्ग सीमा (Upper class boundary) है?

Collection, Classification and Tabulation of Data, Frequency Distributions and Graphical Representations Collection, Classification and Tabulation of Data, Frequency Distributions and Graphical Representations ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

3

The median of a given frequency distribution is found graphically with the help of:

दिए गए बारंबारता बंटन की माध्यिका (Median) को आलेखीय रूप से किसकी सहायता से ज्ञात किया जाता है?

Collection, Classification and Tabulation of Data, Frequency Distributions and Graphical Representations Collection, Classification and Tabulation of Data, Frequency Distributions and Graphical Representations ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

4

Frequency distribution can be presented graphically by:

बारंबारता बंटन (Frequency distribution) को आलेखी (graphical) रूप से किसके द्वारा प्रदर्शित किया जा सकता है?

Collection, Classification and Tabulation of Data, Frequency Distributions and Graphical Representations Collection, Classification and Tabulation of Data, Frequency Distributions and Graphical Representations ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

5

The arithmetic mean of an $n$-number series is $\bar{x}$. The sum of the last $n-1$ numbers is $k$. Then the first number will be:

$n$ संख्याओं की एक श्रेणी का समांतर माध्य $\bar{x}$ है। अंतिम $n-1$ संख्याओं का योग $k$ है। तो पहली संख्या क्या होगी?

Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

6

The mean of two samples of sizes 50 and 100 are 53.7 and 52.3 respectively. Find the mean of the combined sample:

आकार 50 और 100 के दो प्रतिदर्शों (Samples) के माध्य क्रमशः 53.7 और 52.3 हैं। संयुक्त प्रतिदर्श (Combined sample) का माध्य ज्ञात कीजिए:

Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

7

The mean weight per bag in a group of 6 bags of rice is 119 kg. The individual weights of 5 of them are 115 kg, 109 kg, 129 kg, 117 kg and 114 kg. What is the weight of the other bag of the group?

चावल की 6 बोरियों के एक समूह में प्रति बोरी औसत वजन 119 किग्रा है। उनमें से 5 बोरियों का व्यक्तिगत वजन 115 किग्रा, 109 किग्रा, 129 किग्रा, 117 किग्रा और 114 किग्रा है। समूह की छठवीं बोरी का वजन क्या है?

Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

8

The following table gives the distribution of 100 families according to daily expenditure:

Expenditure (in Rs)	0-10	10-20	20-30	30-40	40-50
Number of families	14	$x$	27	$y$	15

Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

9

Which one of the following is a correct statement?

निम्नलिखित में से कौन-सा कथन सही है? [Note: NTA Official Final Answer Key accepted both Option 1 and Option 2 as correct responses] [नोट: एनटीए की अंतिम उत्तर कुंजी में विकल्प 1 और विकल्प 2 दोनों को सही माना गया है]

Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

10

A scooter rider covers a certain distance at a uniform speed of 45 km per hour and retraces the same path at a uniform speed of 55 km per hour to reach the starting point. His average speed during the whole journey is:

एक स्कूटर सवार एक निश्चित दूरी 45 किमी प्रति घंटे की समान गति से तय करता है और प्रारंभिक बिंदु पर वापस पहुँचने के लिए उसी रास्ते से 55 किमी प्रति घंटे की समान गति से लौटता है। पूरी यात्रा के दौरान उसकी औसत गति क्या है?

Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

11

The arithmetic mean of 21 numbers is 9. If the number 19 is deleted from the set, the mean of the remaining 20 numbers will be:

21 संख्याओं का समांतर माध्य 9 है। यदि इस समुच्चय से संख्या 19 हटा दी जाए, तो शेष 20 संख्याओं का माध्य होगा:

Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

12

The mean square deviation of the variate $X$ from ______ is minimum:

चर $X$ का ______ से माध्य वर्ग विचलन (Mean square deviation) न्यूनतम होता है:

Measures of Dispersion: Range, Quartile Deviation, Mean Deviation, Standard Deviation and Coefficient of Variation Measures of Dispersion: Range, Quartile Deviation, Mean Deviation, Standard Deviation and Coefficient of Variation ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

13

A distribution consists of 100 observations with a median of 36.9. If the largest 10 observations are each increased by 6, then the median of the new set of observations will be:

एक बंटन में 100 प्रेक्षण हैं जिनका माध्यिका (median) मान 36.9 है। यदि सबसे बड़े 10 प्रेक्षणों में से प्रत्येक में 6 की वृद्धि कर दी जाए, तो प्रेक्षणों के नए समुच्चय की माध्यिका होगी:

Measures of Dispersion: Range, Quartile Deviation, Mean Deviation, Standard Deviation and Coefficient of Variation Measures of Dispersion: Range, Quartile Deviation, Mean Deviation, Standard Deviation and Coefficient of Variation ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

14

For a discrete distribution, which of the following is correct?

एक असतत (खंडित) बंटन (Discrete distribution) के लिए निम्नलिखित में से कौन-सा सही है?

Moments, Skewness (Karl Pearson, Bowley) and Kurtosis Moments, Skewness (Karl Pearson, Bowley) and Kurtosis ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

15

Two unbiased dice are thrown simultaneously. Then the possible number of outcomes will be:

दो निष्पक्ष पासों (Unbiased dice) को एक साथ फेंका जाता है। तो परिणामों की कुल संभव संख्या होगी:

Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

16

If $C_1$ and $C_2$ are subsets of sample space $S$, then which is correct?

यदि $C_1$ और $C_2$ प्रतिदर्श समष्टि $S$ के उपसमुच्चय (Subsets) हैं, तो कौन-सा कथन सही है?

Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

17

Two dice are rolled simultaneously. What is the probability that the sum of numbers on the dice is 9?

दो पासे एक साथ फेंके जाते हैं। पासों पर आने वाली संख्याओं का योग 9 होने की प्रायिकता क्या है?

Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

18

Given $P(A) = p_1$, $P(B) = p_2$, and $P(A \cap B) = p_3$. Then $P(A' \cap B')$ will be:

यदि $P(A) = p_1$, $P(B) = p_2$, और $P(A \cap B) = p_3$ दिया गया है, तो $P(A' \cap B')$ का मान क्या होगा?

Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

19

If $P(A \cup B) = 5/6$, $P(A \cap B) = 1/3$ and $P(\overline{B}) = 1/2$, then the events $A$ and $B$ are:

यदि $P(A \cup B) = 5/6$, $P(A \cap B) = 1/3$ और $P(\overline{B}) = 1/2$ हो, तो घटनाएं $A$ और $B$ हैं:

Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

20

If $P(A) = 0.25$, $P(B) = 0.50$ and $P(A \cap B) = 0.14$, then the probability that neither $A$ nor $B$ occurs is:

यदि $P(A) = 0.25$, $P(B) = 0.50$ और $P(A \cap B) = 0.14$ हो, तो न तो $A$ और न ही $B$ के घटित होने की प्रायिकता है:

Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

21

Bonferroni's inequality states that for any two events $C_1$ and $C_2$:

बोनफेरोनी की असमिका (Bonferroni's inequality) के अनुसार किन्हीं दो घटनाओं $C_1$ और $C_2$ के लिए:

Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

22

A bowl contains 8 chips, 3 marked Red and 5 marked Blue. Two chips are drawn at random without replacement. What is the probability that the first chip is Red and the second chip is Blue?

एक पात्र में 8 चिप्स हैं, जिनमें 3 लाल (Red) और 5 नीली (Blue) हैं। बिना प्रतिस्थापन (without replacement) के यादृच्छिक रूप से दो चिप्स निकाली जाती हैं। पहली चिप लाल और दूसरी चिप नीली होने की प्रायिकता क्या है?

Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

23

If $A$ and $B$ are two mutually exclusive events with $P(A) > 0$ and $P(B) > 0$, then the conditional probability $P(B|A)$ is:

यदि $A$ और $B$ दो परस्पर अपवर्जी (mutually exclusive) घटनाएं हैं जिनमें $P(A) > 0$ और $P(B) > 0$ है, तो सप्रतिबंध प्रायिकता $P(B|A)$ होगी:

Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

24

If $X$ is a random Poisson variate with $P(X=1) = P(X=2)$, then $P(X=4)$ is:

यदि $X$ एक यादृच्छिक प्वासों चर (Poisson variate) है जिसमें $P(X=1) = P(X=2)$ है, तो $P(X=4)$ का मान है:

Theoretical Discrete Probability Distributions: Bernoulli, Binomial, Poisson, Geometric and Hypergeometric Theoretical Discrete Probability Distributions: Bernoulli, Binomial, Poisson, Geometric and Hypergeometric ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

25

If for a binomial distribution the mean is 8 and variance is 6, then the mode is:

यदि एक द्विपद बंटन (binomial distribution) के लिए माध्य 8 और प्रसरण 6 है, तो इसका बहुलक (mode) क्या होगा?

Theoretical Discrete Probability Distributions: Bernoulli, Binomial, Poisson, Geometric and Hypergeometric Theoretical Discrete Probability Distributions: Bernoulli, Binomial, Poisson, Geometric and Hypergeometric ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

26

If the mean of a Poisson distribution is 36, then its coefficient of variation is:

यदि एक प्वासों बंटन (Poisson distribution) का माध्य 36 है, तो इसका विचरण गुणांक (coefficient of variation) क्या होगा?

Theoretical Discrete Probability Distributions: Bernoulli, Binomial, Poisson, Geometric and Hypergeometric Theoretical Discrete Probability Distributions: Bernoulli, Binomial, Poisson, Geometric and Hypergeometric ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

27

A die is thrown 100 times. If getting an even number is considered a success, then the variance of the number of successes is:

एक पासे को 100 बार फेंका जाता है। यदि सम संख्या (even number) प्राप्त करने को सफलता माना जाए, तो सफलताओं की संख्या का प्रसरण (variance) होगा:

Theoretical Discrete Probability Distributions: Bernoulli, Binomial, Poisson, Geometric and Hypergeometric Theoretical Discrete Probability Distributions: Bernoulli, Binomial, Poisson, Geometric and Hypergeometric ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

28

In a random sample of 10 people, if the probability of a person being left-handed is 0.16, then the mean and standard deviation of the number of left-handed people are respectively:

10 व्यक्तियों के एक यादृच्छिक प्रतिदर्श में, यदि किसी व्यक्ति के बाएं हाथ से काम करने वाले (left-handed) होने की प्रायिकता 0.16 है, तो बाएं हाथ से काम करने वाले व्यक्तियों की संख्या का माध्य और मानक विचलन क्रमशः हैं:

Theoretical Discrete Probability Distributions: Bernoulli, Binomial, Poisson, Geometric and Hypergeometric Theoretical Discrete Probability Distributions: Bernoulli, Binomial, Poisson, Geometric and Hypergeometric ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

29

For a Poisson distribution, if $P(X = 1) = P(X = 3)$, then its mode is:

एक प्वासों बंटन (Poisson distribution) के लिए, यदि $P(X = 1) = P(X = 3)$ है, तो इसका बहुलक (mode) क्या होगा?

Theoretical Discrete Probability Distributions: Bernoulli, Binomial, Poisson, Geometric and Hypergeometric Theoretical Discrete Probability Distributions: Bernoulli, Binomial, Poisson, Geometric and Hypergeometric ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

30

If $X \sim N(\mu, \sigma^2)$, the maximum ordinate is at $X = \mu$ and is given by:

यदि $X \sim N(\mu, \sigma^2)$ है, तो अधिकतम कोटि (Maximum ordinate) $X = \mu$ पर होती है और इसका मान किसके द्वारा दिया जाता है?

Theoretical Continuous Probability Distributions: Uniform, Normal, Exponential, Beta and Gamma Distributions Theoretical Continuous Probability Distributions: Uniform, Normal, Exponential, Beta and Gamma Distributions ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

31

If the random variable $X$ has normal distribution with probability density function $f(x) = \frac{1}{\sqrt{2\pi}} e^{-(x-1)^2/2}, -\infty < x < \infty$, then the value of $\int_1^\infty f(x) dx$ is:

यदि यादृच्छिक चर $X$ का प्रायिकता घनत्व फलन (pdf) $f(x) = \frac{1}{\sqrt{2\pi}} e^{-(x-1)^2/2}, -\infty < x < \infty$ के साथ प्रसामान्य बंटन (normal distribution) है, तो समाकल $\int_1^\infty f(x) dx$ का मान है:

Theoretical Continuous Probability Distributions: Uniform, Normal, Exponential, Beta and Gamma Distributions Theoretical Continuous Probability Distributions: Uniform, Normal, Exponential, Beta and Gamma Distributions ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

32

The annual rainfall at a place is normally distributed with mean 1200 mm and standard deviation 200 mm. What is the probability that in a randomly selected year, the rainfall will be greater than 1400 mm? [Given that the area under the standard normal curve between $Z = 0$ and $Z = 1$ is 0.34]

एक स्थान पर वार्षिक वर्षा प्रसामान्य रूप से बंटित है जिसका माध्य 1200 मिमी और मानक विचलन 200 मिमी है। यादृच्छिक रूप से चुने गए वर्ष में वर्षा 1400 मिमी से अधिक होने की प्रायिकता क्या है? [दिया गया है कि मानक प्रसामान्य वक्र के तहत $Z = 0$ और $Z = 1$ के बीच का क्षेत्रफल 0.34 है]

Theoretical Continuous Probability Distributions: Uniform, Normal, Exponential, Beta and Gamma Distributions Theoretical Continuous Probability Distributions: Uniform, Normal, Exponential, Beta and Gamma Distributions ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

33

The unit of coefficient of correlation is:

सहसंबंध गुणांक (Coefficient of correlation) की इकाई (Unit) क्या होती है?

Correlation Analysis: Simple, Partial, Multiple Correlation, Pearson Coefficient and Rank Correlation Correlation Analysis: Simple, Partial, Multiple Correlation, Pearson Coefficient and Rank Correlation ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

34

Which of the following provides the best and most consistent estimate of the population mean $\mu$?

निम्नलिखित में से कौन समष्टि माध्य $\mu$ का सर्वोत्तम और सबसे संगत आकलन (most consistent estimate) प्रदान करता है?

Regression Analysis: Simple and Multiple Linear Regression, Least Squares Principle, Properties and R-Squared Regression Analysis: Simple and Multiple Linear Regression, Least Squares Principle, Properties and R-Squared ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

35

The arithmetic mean of the two regression coefficients $b_{yx}$ and $b_{xy}$ is:

दो समाश्रयण गुणांकों $b_{yx}$ और $b_{xy}$ का समांतर माध्य (arithmetic mean) होता है:

Sampling Theory: Census vs Sample Survey, Sampling Errors, SRSWOR, SRSWR, Stratified, Systematic and Cluster Sampling Sampling Theory: Census vs Sample Survey, Sampling Errors, SRSWOR, SRSWR, Stratified, Systematic and Cluster Sampling ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

36

A researcher wants to test whether the mean yield of a crop has changed from the standard 50 q/ha. A sample of 16 plots gave a mean of 52 q/ha. The population standard deviation is known to be $\sigma = 3.2$ q/ha. Which test should be used?

एक शोधकर्ता यह परीक्षण करना चाहता है कि क्या किसी फसल की औसत उपज मानक 50 क्विंटल/हेक्टेयर से बदल गई है। 16 भूखंडों के एक प्रतिदर्श में 52 क्विंटल/हेक्टेयर का औसत प्राप्त हुआ। समष्टि का मानक विचलन $\sigma = 3.2$ क्विंटल/हेक्टेयर ज्ञात है। इसके लिए किस परीक्षण का उपयोग किया जाना चाहिए?

Sampling Theory: Census vs Sample Survey, Sampling Errors, SRSWOR, SRSWR, Stratified, Systematic and Cluster Sampling Sampling Theory: Census vs Sample Survey, Sampling Errors, SRSWOR, SRSWR, Stratified, Systematic and Cluster Sampling ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

37

The probability of rejecting the null hypothesis $H_0$ when it is actually true is known as:

निराकरणीय परिकल्पना $H_0$ के वास्तव में सत्य होने पर उसे अस्वीकार (reject) करने की प्रायिकता कहलाती है:

Testing of Hypotheses: Null and Alternative Hypotheses, Type I and II Errors, Significance Level, Large Sample Tests (Z-test) Testing of Hypotheses: Null and Alternative Hypotheses, Type I and II Errors, Significance Level, Large Sample Tests (Z-test) ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

38

In Simple Random Sampling Without Replacement (SRSWOR) from a finite population of size $N$, the probability of selecting any specified population unit at the $k$-th draw ($1 \le k \le N$) is:

$N$ आकार की परिमित समष्टि से बिना प्रतिस्थापन के सरल यादृच्छिक प्रतिचयन (SRSWOR) में, $k$-वें निष्कर्षण ($1 \le k \le N$) पर किसी निर्दिष्ट समष्टि इकाई के चयनित होने की प्रायिकता होती है:

Testing of Hypotheses: Null and Alternative Hypotheses, Type I and II Errors, Significance Level, Large Sample Tests (Z-test) Testing of Hypotheses: Null and Alternative Hypotheses, Type I and II Errors, Significance Level, Large Sample Tests (Z-test) ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

39

Which statistical test is appropriate for testing a hypothesis about a single population mean when the population variance is KNOWN, even if the sample size is small?

जब समष्टि प्रसरण (population variance) ज्ञात हो, तो प्रतिदर्श का आकार छोटा होने पर भी एकल समष्टि माध्य के परीक्षण के लिए कौन सा सांख्यिकीय परीक्षण उपयुक्त है?

Small Sample Tests: Students t-test, Snedecors F-test, Chi-Square Test of Goodness of Fit and Contingency Tables Small Sample Tests: Students t-test, Snedecors F-test, Chi-Square Test of Goodness of Fit and Contingency Tables ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

40

In a two-sample pooled t-test for comparing the means of two independent normal populations with sample sizes $n_1$ and $n_2$ and equal variances, the degrees of freedom associated with the test statistic is:

समान प्रसरण वाली दो स्वतंत्र प्रसामान्य समष्टियों के माध्यों की तुलना के लिए $n_1$ और $n_2$ आकार के दो प्रतिदर्शों वाले संयुक्त t-परीक्षण (pooled t-test) में परीक्षण सांख्यिकी से संबद्ध स्वातंत्र्य कोटि (degrees of freedom) होती है:

Small Sample Tests: Students t-test, Snedecors F-test, Chi-Square Test of Goodness of Fit and Contingency Tables Small Sample Tests: Students t-test, Snedecors F-test, Chi-Square Test of Goodness of Fit and Contingency Tables ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

41

While testing the significance of a sample correlation coefficient $r$ calculated from a sample of size $n$, the null hypothesis $H_0: \rho = 0$ is tested using a t-statistic with degrees of freedom:

$n$ आकार के प्रतिदर्श से परिकलित प्रतिदर्श सहसंबंध गुणांक $r$ की सार्थकता का परीक्षण करते समय, निराकरणीय परिकल्पना $H_0: \rho = 0$ का परीक्षण कितनी स्वातंत्र्य कोटि (degrees of freedom) वाले t-सांख्यिकी से किया जाता है?

Small Sample Tests: Students t-test, Snedecors F-test, Chi-Square Test of Goodness of Fit and Contingency Tables Small Sample Tests: Students t-test, Snedecors F-test, Chi-Square Test of Goodness of Fit and Contingency Tables ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

42

When observations in two samples are paired and correlated (e.g., before and after measurements on the same $n$ subjects), the null hypothesis $H_0: \mu_D = 0$ is tested using:

जब दो प्रतिदर्शों में प्रेक्षण युग्मित और सहसंबंधित हों (उदा. समान $n$ विषयों पर 'पहले' और 'बाद' के माप), तो निराकरणीय परिकल्पना $H_0: \mu_D = 0$ का परीक्षण किसके द्वारा किया जाता है?

Small Sample Tests: Students t-test, Snedecors F-test, Chi-Square Test of Goodness of Fit and Contingency Tables Small Sample Tests: Students t-test, Snedecors F-test, Chi-Square Test of Goodness of Fit and Contingency Tables ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

43

For an $r \times s$ contingency table with total frequency $N$, the exact mean (expected value) of the Pearson chi-square statistic $X^2$ as derived by Haldane is:

कुल बारंबारता $N$ वाली एक $r \times s$ प्रसंग सारणी (contingency table) के लिए, हाल्डेन (Haldane) द्वारा व्युत्पन्न पियर्सन काई-वर्ग सांख्यिकी $X^2$ का सटीक माध्य (प्रत्याशित मान) है:

Small Sample Tests: Students t-test, Snedecors F-test, Chi-Square Test of Goodness of Fit and Contingency Tables Small Sample Tests: Students t-test, Snedecors F-test, Chi-Square Test of Goodness of Fit and Contingency Tables ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

44

The geometric mean of the two numbers 625 and 1 is:

दो संख्याओं 625 और 1 का गुणोत्तर माध्य (Geometric Mean) क्या है?

Design of Experiments: Principles of Experimentation, CRD, RBD, Latin Square Design (LSD) and Factorial Experiments Design of Experiments: Principles of Experimentation, CRD, RBD, Latin Square Design (LSD) and Factorial Experiments ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

45

The harmonic mean of the two regression coefficients $b_{yx}$ and $b_{xy}$ is:

दो समाश्रयण गुणांकों (regression coefficients) $b_{yx}$ और $b_{xy}$ का हरात्मक माध्य (harmonic mean) होता है:

Design of Experiments: Principles of Experimentation, CRD, RBD, Latin Square Design (LSD) and Factorial Experiments Design of Experiments: Principles of Experimentation, CRD, RBD, Latin Square Design (LSD) and Factorial Experiments ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1

46

If the estimated linear regression equation of $Y$ on $X$ is given by $Y = 100 + 7X$, then the predicted value of $Y$ when $X = 20$ is:

यदि $X$ पर $Y$ का आकलित रैखिक समाश्रयण समीकरण $Y = 100 + 7X$ दिया गया है, तो $X = 20$ होने पर $Y$ का अनुमानित मान क्या होगा?

Design of Experiments: Principles of Experimentation, CRD, RBD, Latin Square Design (LSD) and Factorial Experiments Design of Experiments: Principles of Experimentation, CRD, RBD, Latin Square Design (LSD) and Factorial Experiments ICAR PG Statistical Sciences 2024 Shift 1 MCQ (Single Correct) +4 / −1