Question 1

Secondary data is primarily sourced from:

Accepted Answer

The correct answer is: Publicly available databases. Secondary data refers to data that was collected by someone else in the past (e.g., publications, census reports, public databases). Personal interviews, experiments, and original surveys collect primary data.

Question 2

What is an example of a primary data collection method?

Accepted Answer

The correct answer is: Conducting interviews and surveys. Primary data is collected directly by the researcher for the specific research goal. Conducting interviews and surveys are active methods of primary data collection.

Question 3

Consider the following statements regarding questionnaire preparation:

- a. Questionnaires collect data by asking people to respond to different sets of questions.
- b. The validity and reliability of the data you collect depend on the design of questions.
- c. Collect the data without a pilot test of all questionnaires.
- d. When designing your questionnaire, you should consider the wording of individual questions prior to the order in which they appear.

Which of the following statements is/are correct?

Accepted Answer

The correct answer is: a and d. Statements a and d are correct. Statement c is incorrect because pilot testing is crucial to validate the questionnaire before collecting data. Statement b is also true conceptually, but among the given options, C (a and d) is the most standard combination matching standard research methodology.

Question 4

Which of the following statements regarding tabulation is FALSE?

Accepted Answer

The correct answer is: Tabulation facilitates comparison between rows and not columns. Statement D is false because tabulation is specifically designed to facilitate comparisons between both rows and columns simultaneously.

Question 5

Eight randomly selected college students slept for the following hours previous night: 4, 8, 7, 5, 3, 7, 7, 3.

Arrange the following values in decreasing order:
- a. Mean of sleeping hours of the students
- b. Median of sleeping hours of the students
- c. Mode of sleeping hours of the students
- d. Number of random Sample

Accepted Answer

The correct answer is: d, c, b, a. Calculating values: d (Sample size) = 8. Mean (a) = (4+8+7+5+3+7+7+3)/8 = 44/8 = 5.5. Sorted data: 3, 3, 4, 5, 7, 7, 7, 8. Median (b) = (5+7)/2 = 6. Mode (c) = 7. Decreasing order is: d (8) > c (7) > b (6) > a (5.5), which is d, c, b, a.

Question 6

Consider the following statements regarding probabilities:

- P: Probabilities can never add up to more than one.
- Q: Probabilities of mutually exclusive events always add up to one.
- R: Probabilities can never be zero.
- S: Probabilities are always positive.

Which of the following statements is/are correct?

Accepted Answer

The correct answer is: Pand S. P is correct (probabilities in a sample space sum to 1). S is considered correct in standard exam keys assuming probability is non-negative ($P(E) \ge 0$). Statement Q is false because mutually exclusive events only sum to 1 if they are also exhaustive. Statement R is false because impossible events have a probability of 0.

Question 7

In a class of 100 students, every student must pick exactly one sport to play:
- 28 students pick Football.
- 27 students pick Kho-Kho.
- 33 students pick Volleyball.
- 12 students pick Cricket.
- Total girls = 40. Total boys = 60.
- 13 girls play Kho-Kho.
- 13 boys play Volleyball.
- 10 boys play Cricket (written as 23 boys play Cricket due to a typo in the question).

Match the following:
- a. Boys who play Kho-Kho: 1. 2
- b. Girls who play cricket: 2. 10
- c. Boys who play cricket: 3. 14
- d. Total number of boys: 5. 60

Which of the pairs given above is/are correctly matched?

Accepted Answer

The correct answer is: a-3, b-1, c-2, d-5. Deductions: d) Total boys = 100 - 40 = 60 (d-5). a) Boys who play Kho-Kho = 27 total - 13 girls = 14 (a-3). c) Boys who play cricket = 10 (c-2). b) Girls who play cricket = 12 total - 10 boys = 2 (b-1). Correct match: a-3, b-1, c-2, d-5.

Question 8

An economist estimated that a commodity Y had a price index of 10, calculated for 1993 with a base year of 1990, and a quantity index of 0.5 when calculated for 1990 with a base year of 1993. What is the Fisher Ideal Value Index for 1993 with the base year taken to be 1990?

Accepted Answer

The correct answer is: 20. Price Index for 1993 with base 1990 ($P_{01}$) = 10. Quantity Index for 1990 with base 1993 ($Q_{10}$) = 0.5. Quantity Index for 1993 with base 1990 ($Q_{01}$) = 1 / $Q_{10}$ = 1 / 0.5 = 2. Value Index = $P_{01}$ * $Q_{01}$ = 10 * 2 = 20.

Question 9

One of the key features of the census is:

Accepted Answer

The correct answer is: Simultaneity. Simultaneity is a vital feature of the census, meaning the census data must refer to a well-defined point of time and be conducted simultaneously throughout the territory.

Question 10

Consider the following statements regarding Measures of Mortality:

- a. Gross Reproduction Rate: 5. Measures the number of daughters over a lifetime.
- b. Age-Specific Fertility Rate: 3. Has modal value between 20 and 25
- c. Net Reproduction Rate: 2. Affected by mortality rates
- d. Maternal Mortality Rate: 4. Is measured per 1000 live births.

Which of the pairs given above is/are correctly matched?

Accepted Answer

The correct answer is: a-5, b-3, c-2, d-4. Matches: GRR (Gross Reproduction Rate) measures daughters born per woman without considering mortality (a-5). ASFR usually peaks in age group 20-25 (b-3). NRR is NRR = GRR * survival rate, hence affected by mortality (c-2). MMR in this specific matching maps to 4. Correct match is a-5, b-3, c-2, d-4.

Question 11

The interest on Rs. 54,000 loan for nine months at 8% interest per year is:

Accepted Answer

The correct answer is: 3240. Simple Interest = Principal * Rate * Time = 54,000 * 0.08 * (9/12) = 54,000 * 0.08 * 0.75 = Rs. 3,240.

Question 12

Tom and Jerry went to a restaurant for dinner. Tom ordered 2 hamburgers and 1 soft drink, totalling Rs. 70. Jerry ordered 1 hamburger and 2 soft drinks, totalling Rs. 50. What is the cost of one hamburger and one soft drink?

Accepted Answer

The correct answer is: Hamburger - Rs.30, Soft Drink - Rs.10. Let H = hamburger, S = soft drink.
2H + S = 70  (Eq 1)
H + 2S = 50  (Eq 2)
Multiplying Eq 2 by 2: 2H + 4S = 100. Subtracting Eq 1: 3S = 30 => S = 10. Substituting in Eq 2: H + 20 = 50 => H = 30. Hamburger is Rs. 30, Soft Drink is Rs. 10.

Question 13

Consider the following statements:

- a. The number of ways to arrange the letters of the word "PEPPER" is 60.
- b. In a group of 20 people, the number of ways to select a committee of 3 members where the order doesn't matter is $\binom{20}{3}$.
- c. The expansion of $(2+x)^3$ using binomial theorem is $8+6x+12x^2+x^3$.
- d. The number of ways 3 boys and 3 girls can sit in a row is 360.

Which of the following statements is/are correct?

Accepted Answer

The correct answer is: a and b. Statement a is correct (PEPPER has 6 letters: 3 P's, 2 E's, 1 R. Arrangements = $6! / (3! 2!) = 60$). Statement b is correct (order does not matter, so combination $\binom{20}{3}$ is used). Statement c is incorrect (expansion is $8 + 12x + 6x^2 + x^3$). Statement d is incorrect (6 people in a row can sit in $6! = 720$ ways). Thus, a and b are correct.

Question 14

Consider the following statements:

- a. The limit of $\frac{x^2-1}{x-1}$ as x approaches 1 is 0.
- b. If $f(x)=\frac{1}{x}$ then the derivative of $f(x)$ with respect to x is $\frac{1}{x^2}$.
- c. The limit of $\frac{e^x-1}{x}$ as x approaches 0 is 1.
- d. The limit definition of a derivative for a function $f(x)$ is $\lim_{h 	o 0} \frac{f(x+h)-f(x)}{h}$.

Which of the following statements is/are correct?

Accepted Answer

The correct answer is: cand d. Statement c is correct (standard exponential limit = 1). Statement d is correct (definition of derivative). Statement a is incorrect (limit is 2). Statement b is incorrect (derivative of $1/x$ is $-1/x^2$, not $1/x^2$). Thus, c and d are correct.

Question 15

Let $A=\{x: x\in\mathbb{R}, |x|<1\}$ and $B=\{x: x\in\mathbb{R}, |x-1|\ge1\}$. If $A \cup B = \mathbb{R} \setminus D$, then the set D is:

Accepted Answer

The correct answer is: {x\in\mathbb{R}: 1\le x<2}. $A = (-1, 1)$. $|x-1| \ge 1 \implies x-1 \ge 1$ or $x-1 \le -1 \implies x \ge 2$ or $x \le 0$. Thus $B = (-\infty, 0] \cup [2, \infty)$. $A \cup B = (-\infty, 1) \cup [2, \infty)$. The complement is $D = \mathbb{R} \setminus (A \cup B) = [1, 2) = \{x\in\mathbb{R}: 1 \le x < 2\}$.

Question 16

Consider the following relations/functions and their properties:

- a. $F=\{(x,y)\in\mathbb{R}	imes\mathbb{R}: x^2+y=2\}$
- b. $F=\{(x,y)\in\mathbb{R}	imes\mathbb{R}: x^2+y^2=25\}$
- c. $F=\{(x,y)\in\mathbb{R}	imes\mathbb{R}: y=2x+1\}$
- d. $F=\{(x,y)\in\mathbb{R}	imes\mathbb{R}: y=x^2\}$

Matches:
- 1. $F \circ F = \{(x,z)\in\mathbb{R}	imes\mathbb{R}: z=4x+3\}$
- 2. F is increasing on $(0,\infty)$ but not on \mathbb{R}
- 3. F is one-one but not onto
- 4. Range of $F = [-2,\infty)$ (assuming $y=x^2-2$ in the paper's original intended equation)
- 5. F is not a function

Which of the pairs given above is/are correctly matched?

Accepted Answer

The correct answer is: a-4, b-5, c-1, d-2. F in (b) is a circle equation, which is not a function (b-5). F in (c) has $F(F(x)) = 2(2x+1)+1 = 4x+3$ (c-1). F in (d) is $y=x^2$, which is increasing on positive real numbers but not on the whole real line (d-2). This makes D (a-4, b-5, c-1, d-2) the correct match.

Question 17

Consider the following matrices and their determinants:

- a. Square matrix has two identical rows
- b. $3	imes3$ Identity matrix
- c. $3	imes3$ diagonal matrix with diagonal entries 1, 2 and 3
- d. P and Q are two $3	imes3$ matrices with $\det(P)=2$ and $\det(Q)=4$. Determinant of $P Q^T$ is:

Matches:
- 1. Determinant = 1
- 2. Determinant = 4
- 3. Determinant = 0
- 4. Determinant = 6
- 5. Determinant = 8

Which of the pairs given above is/are correctly matched?

Accepted Answer

The correct answer is: a-3, b-1, c-4, d-5. Determinant properties: Identical rows result in determinant 0 (a-3). Identity matrix determinant is 1 (b-1). Diagonal matrix determinant is the product of diagonals = 1*2*3 = 6 (c-4). $\det(PQ^T) = \det(P)\det(Q) = 2*4 = 8$ (d-5). Correct match: a-3, b-1, c-4, d-5.

Question 18

Arrange the following events in increasing order of probability:

- a. Picking a diamond from a well-shuffled deck of 52 playing cards.
- b. Drawing a King from a standard deck of 52 cards.
- c. Rolling a number between 1 and 6 on a fair six-sided die.
- d. Getting heads on a fair coin toss.

Accepted Answer

The correct answer is: b, a, d, c. Calculating probabilities: $P(b) = 4/52 \approx 0.077$. $P(a) = 13/52 = 0.25$. $P(d) = 0.5$. $P(c) = 4/6 \approx 0.67$ (strictly between 1 and 6 is {2,3,4,5}). Increasing order: b, a, d, c.

Question 19

The area of the triangle determined by the three points A(1,2,3), B(3,2,1) and C(2,4,5) is:

Accepted Answer

The correct answer is: \sqrt{29}. Using vectors: $\vec{AB} = B - A = (2, 0, -2)$ and $\vec{AC} = C - A = (1, 2, 2)$. Cross product $\vec{AB} 	imes \vec{AC} = (4, -6, 4)$. Magnitude $= \sqrt{4^2 + (-6)^2 + 4^2} = \sqrt{68} = 2\sqrt{17}$. Area $= 1/2 * 2\sqrt{17} = \sqrt{17}$. Note: $\sqrt{17}$ is the mathematically correct answer, but due to a question error, the official JKSSB answer key marked it as option D (\sqrt{29}).

Question 20

The unit vector having the opposite direction of the vector (1,-1) is:

Accepted Answer

The correct answer is: \frac{-1}{\sqrt{2}}(1,-1). Vector $\vec{v} = (1, -1)$. Magnitude $= \sqrt{1^2 + (-1)^2} = \sqrt{2}$. The unit vector in the same direction is $\frac{1}{\sqrt{2}}(1, -1)$. The unit vector in the opposite direction is obtained by multiplying with -1, which is $\frac{-1}{\sqrt{2}}(1, -1)$.

Question 21

The English word "Statistics" is derived from

i. Latin word "Status"
ii. Italian word "Statista"
iii. German word "Statistik"

Accepted Answer

The correct answer is: i, ii & iii. The word 'Statistics' has been derived from the Latin word 'Status', Italian word 'Statista', and the German word 'Statistik'. All refer to the political state or data concerning it.

Question 22

Which of the following is NOT a characteristic of data?

Accepted Answer

The correct answer is: Data are personal facts. Statistical data represent aggregate facts rather than individual or personal subjective facts.

Question 23

If the class-intervals in a frequency distribution are 72-73.9, 74-75.9, 76-77.9, 78-79.9, then the mid-value of the class 74-75.9 is:

Accepted Answer

The correct answer is: 74.95. The mid-value (class mark) is calculated as (Lower limit + Upper limit) / 2 = (74 + 75.9) / 2 = 149.9 / 2 = 74.95.

Question 24

Which of the following is a positional average?

Accepted Answer

The correct answer is: Mode. Mode and Median are positional averages because their values depend on their position in the distribution. Arithmetic, Geometric, and Harmonic means are mathematical averages.

Question 25

Marks obtained by 9 students in mathematics as 52, 75, 40, 70, 43, 40, 65, 35, 48. The arithmetic mean is:

Accepted Answer

The correct answer is: 52. Sum of values = 52 + 75 + 40 + 70 + 43 + 40 + 65 + 35 + 48 = 468. Number of observations = 9. Arithmetic Mean = 468 / 9 = 52.

Question 26

Which of the following is considered as the highest level of measurement?

Accepted Answer

The correct answer is: Ratio. The four levels of measurement in increasing order are Nominal, Ordinal, Interval, and Ratio. Ratio scale is the highest level as it has a true zero point.

Question 27

Consider the following statements and choose the best alternative:

Assertion (A): Histogram is a graphical presentation of data
Reason (R): Statistical data can be represented in the form of graphs.

i. A is true
ii. R is true
iii. A is False
iv. R is False

Accepted Answer

The correct answer is: i & ii. Both Assertion A (Histogram is a graphical presentation) and Reason R (data can be represented as graphs) are true statements.

Question 28

Match the following:

*List-I*
i. Mean
ii. Median
iii. Mode
iv. Range

*List-II*
a. Difference between largest and smallest value
b. Precise
c. Middle most term
d. Highest Frequency

Accepted Answer

The correct answer is: i-b, ii-c, iii-d, iv-a. The correct matches are: Mean is a precise mathematical average (i-b); Median is the middlemost term (ii-c); Mode corresponds to the highest frequency (iii-d); Range is the difference between largest and smallest values (iv-a).

Question 29

Match the following:

*List-I*
i. Chi-square test
ii. F-test
iii. T-test
iv. Z-test

*List-II*
a. Analyze the difference between the means of more than two groups.
b. For known variance and large sample size, test that determines whether two population means are different.
c. Used to compare means of two groups
d. Compares two categorical variables.

Accepted Answer

The correct answer is: i-d, ii-a, iii-c, iv-b. The correct matches are: Chi-square test compares categorical variables (i-d); F-test compares means of more than two groups (ii-a); T-test compares means of two groups (iii-c); Z-test compares means for large samples with known variance (iv-b).

Question 30

Which of the following are categorical variable?

i. Age of a person
ii. Gender of a person
iii. Race of a person

Accepted Answer

The correct answer is: ii & iii. Gender and Race are categorical (qualitative) variables. Age is a quantitative (numerical) continuous variable.

Question 31

Arrange the stages of statistical investigation in their correct order.

a. Classification of Data
b. Collection of Data
c. Interpretation of Data
d. Analysis of Data
e. Planning the purpose of Investigation

Accepted Answer

The correct answer is: e, b, a, d, c. The correct logical order of statistical investigation is: Planning (e) -> Collection of Data (b) -> Classification of Data (a) -> Analysis (d) -> Interpretation (c).

Question 32

Which of the following are Non sampling statistical errors?

i. Coverage error
ii. Non-response error
iii. Response error

Accepted Answer

The correct answer is: i, ii & iii. Non-sampling errors are errors that occur during data collection processes other than active sampling. Coverage, non-response, and response errors are all classified under non-sampling errors.

Question 33

In hypothesis testing, what is a type II error?

Accepted Answer

The correct answer is: If the investigator fails to reject a null hypothesis that is false in the population.. A Type II error (beta error) occurs when the null hypothesis is false but the investigator fails to reject it.

Question 34

What is the value with the most instances or occurrences in the list called?

Accepted Answer

The correct answer is: Mode. In statistics, the mode is the value that appears most frequently in a data set.

Question 35

What is random sampling?

Accepted Answer

The correct answer is: When each item has an equal chance of selection it is called random sampling. Simple random sampling is a selection method where every individual member of the population has an equal probability of being chosen.

Question 36

What is the formula for Chi square test?

Accepted Answer

The correct answer is: x^{2}=\Sigma\frac{(Observed~value-Expected~value)^{2}}{Expected~value}. The Chi-square formula is: χ² = Σ [(O - E)² / E], where O is the observed frequency and E is the expected frequency.

Question 37

There are two events "I" and "J". The events occurring are mutually exclusive for example "I" or "J", its probability is given by which of the laws of probability?

Accepted Answer

The correct answer is: Addition rule. For mutually exclusive events, the probability of I or J occurring is the sum of their individual probabilities (Addition Rule): P(I ∪ J) = P(I) + P(J).

Question 38

Which of the following tests is used to check the equality of variances between two populations?

Accepted Answer

The correct answer is: F-test. The F-test is a statistical test used to compare the variances of two independent populations.

Question 39

If the F statistic is larger than the critical F value.

Accepted Answer

The correct answer is: Accept the alternate hypothesis, H,. If the calculated F-statistic exceeds the critical value, we reject the null hypothesis (H₀) and accept the alternate hypothesis (H₁).

Question 40

The simplest measurement of central tendency is

Accepted Answer

The correct answer is: Mean. The arithmetic mean (average) is considered the simplest and most commonly used measure of central tendency.

Question 41

______ is defined as the difference between the value of the extreme items of a series

Accepted Answer

The correct answer is: Range. Range is the simplest measure of dispersion, defined as the difference between the maximum (largest) and minimum (smallest) values in a data set.

Question 42

In which of the following situations is the measured value most likely to be the true value of the quantity being measure?

Accepted Answer

The correct answer is: When the measurement has both high precision and high accuracy. High accuracy ensures the measured value is close to the true value, while high precision ensures consistency, making a high accuracy and high precision measurement the closest to the true value.

Question 43

The error caused by poor calibration of the instrument is called

Accepted Answer

The correct answer is: Systematic Error. Systematic errors are reproducible inaccuracies that are consistently in the same direction, often caused by poorly calibrated instruments or flawed experimental design.

Question 44

Which of the following correctly describes F distributions?

Accepted Answer

The correct answer is: Valid for all real values. The F-distribution is a continuous distribution (defined for positive real values, i.e. x >= 0). Thus, it is valid for real values (unlike discrete/integer distributions).

Question 45

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the sample mean will be larger than 82 is

Accepted Answer

The correct answer is: 0.0228. Standard error = 7 / sqrt(49) = 1. The Z-score for sample mean 82 = (82 - 80) / 1 = 2. P(X > 82) = P(Z > 2) = 1 - 0.9772 = 0.0228.

Question 46

The mean of 11 number is 7 if one of the numbers, 7 is deleted, what will be the mean of remaining 10 number?

Accepted Answer

The correct answer is: 7.0. Sum of 11 numbers = 11 * 7 = 77. If 7 is deleted, new sum = 77 - 7 = 70. New mean of 10 numbers = 70 / 10 = 7.0.

Question 47

What is the variance of a constant 'x'?

Accepted Answer

The correct answer is: 0. The variance measures dispersion. A constant does not vary, so its deviation from its mean is always zero, resulting in a variance of 0.

Question 48

Find the median of 4, 5, 6, 3, 2, 6, 4.

Accepted Answer

The correct answer is: 4. Sort the data: 2, 3, 4, 4, 5, 6, 6. The middle (4th) value in this 7-item sorted list is 4. Thus, the median is 4.

Question 49

If 35 is removed from the data, 30, 34, 35, 36, 37, 38, 39, 40 then the median increased by

Accepted Answer

The correct answer is: 0.5. For 8 sorted numbers, Median = (36 + 37)/2 = 36.5. If 35 is removed, remaining 7 numbers have 4th value = 37. Median increase = 37 - 36.5 = 0.5.

Question 50

In a simultaneous throw of two dice, what is the probability of getting a total of 10 or 11?

Accepted Answer

The correct answer is: 5/36. Total outcomes = 36. Favorable outcomes for 10 are (4,6), (5,5), (6,4) [3 outcomes]. Favorable outcomes for 11 are (5,6), (6,5) [2 outcomes]. Total favorable outcomes = 5. Probability = 5/36.

Question 51

Two unbiased coins are tossed. What's the probability of having access to at most one head?

Accepted Answer

The correct answer is: 3/4. Outcomes are HH, HT, TH, TT (4 outcomes). 'At most one head' means 0 or 1 head. Favorable outcomes are HT, TH, TT (3 outcomes). Probability = 3/4.

Question 52

IP P(A U B)=7/12 P(A)=1/3, are for two independent events A and B, then P(B) is

Accepted Answer

The correct answer is: 3/8. P(A U B) = P(A) + P(B) - P(A)*P(B) since A and B are independent. 7/12 = 1/3 + P(B) - P(B)/3 => 3/12 = 2/3 * P(B) => P(B) = (3/12) * (3/2) = 9/24 = 3/8.

Question 53

The relation between mean, median and mode in a moderately skewed distribution is

Accepted Answer

The correct answer is: 3 Median = 2 Mean + Mode. The empirical relationship for moderately skewed distributions is: Mode = 3 Median - 2 Mean, which can be rearranged as 3 Median = 2 Mean + Mode.

Question 54

A TDMA system uses 25 MHz for the forward link, which is broken into radio channels of 200, kHz. If 8 speech channels are supported on a single radio channel, how many simultaneous users can be accommodated?

Accepted Answer

The correct answer is: 1000. Number of radio channels = 25 MHz / 200 kHz = 25,000 / 200 = 125. Since each channel supports 8 users, total simultaneous users = 125 * 8 = 1000.

Question 55

Consider the following pairs:
i. Mean - Most occurring value in a sample
ii. Mode - Value of the middle one of a number of vectors ordered in increasing magnitude
iii. Median - An arithmetic average of all values
iv. Standard deviation - Measure of dispersion around mean
Which of the above pairs are correctly matched?

Accepted Answer

The correct answer is: iv only. Only pair iv is correctly matched. The Mean is the arithmetic average (iii is incorrect), Mode is the most frequently occurring value (i is incorrect), and Median is the middle value of a sorted dataset (ii is incorrect).

Question 56

The second law of probability, the addition rule is used for which of the following events?

Accepted Answer

The correct answer is: Mutually exclusive events. The addition rule of probability states that for mutually exclusive events (events that cannot happen at the same time), the probability of either event occurring is the sum of their individual probabilities: P(A or B) = P(A) + P(B).

Question 57

In hypothesis testing, what is a type I error?

Accepted Answer

The correct answer is: Rejection of H0 when H is true. In hypothesis testing, a Type I error (false positive) occurs when the null hypothesis H0 is rejected when it is actually true.

Question 58

What does the F--test measure?

Accepted Answer

The correct answer is: Check equality of variances between two populations. The F-test is a statistical test used primarily to compare the variances of two populations or samples to check if they are significantly different.

Question 59

What is systemic sampling?

Accepted Answer

The correct answer is: When sample is chosen at a regular interval from population. Systematic sampling is a probability sampling method where elements are selected from an ordered population at a predetermined, regular periodic interval (e.g. selecting every k-th individual).

Question 60

How are degrees of freedom calculated in Chi square test? (where r is number of rows and c is number of columns)

Accepted Answer

The correct answer is: df=(r-1)(c-1). In a contingency table of a Chi-square test, the degrees of freedom (df) are calculated as: df = (r - 1) * (c - 1), where r is the number of rows and c is the number of columns.

Question 61

What is the median of the following set of numbers?
10, 15, 8, 20, 12

Accepted Answer

The correct answer is: 12. First, arrange the numbers in ascending order: 8, 10, 12, 15, 20. The middle value of this sorted set of 5 numbers is 12, which is the median.

Question 62

If the variance of the dataset is zero, what can be said about the values in the dataset?

Accepted Answer

The correct answer is: All values are the same. Variance measures how much values spread out from the mean. If the variance is zero, there is no dispersion at all, meaning all data values in the set are identical.

Question 63

In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?

Accepted Answer

The correct answer is: 68%. According to the empirical rule (68-95-99.7 rule) for a normal distribution, approximately 68.27% of the data falls within one standard deviation (±1σ) of the mean.

Question 64

What does the term p-value represent in hypothesis testing?

Accepted Answer

The correct answer is: Probability of obtaining observed results by chance. The p-value is the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is correct. It represents the likelihood of the result occurring due to random chance.

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Secondary data is primarily sourced from:

What is an example of a primary data collection method?

Which of the following statements regarding tabulation is FALSE?

An economist estimated that a commodity Y had a price index of 10, calculated for 1993 with a base year of 1990, and a quantity index of 0.5 when calculated for 1990 with a base year of 1993. What is the Fisher Ideal Value Index for 1993 with the base year taken to be 1990?

One of the key features of the census is:

The interest on Rs. 54,000 loan for nine months at 8% interest per year is:

Tom and Jerry went to a restaurant for dinner. Tom ordered 2 hamburgers and 1 soft drink, totalling Rs. 70. Jerry ordered 1 hamburger and 2 soft drinks, totalling Rs. 50. What is the cost of one hamburger and one soft drink?

Let $A=\{x: x\in\mathbb{R}, |x|<1\}$ and $B=\{x: x\in\mathbb{R}, |x-1|\ge1\}$. If $A \cup B = \mathbb{R} \setminus D$, then the set D is:

Arrange the following events in increasing order of probability: - a. Picking a diamond from a well-shuffled deck of 52 playing cards. - b. Drawing a King from a standard deck of 52 cards. - c. Rolling a number between 1 and 6 on a fair six-sided die. - d. Getting heads on a fair coin toss.

The area of the triangle determined by the three points A(1,2,3), B(3,2,1) and C(2,4,5) is:

The unit vector having the opposite direction of the vector (1,-1) is:

The English word "Statistics" is derived from i. Latin word "Status" ii. Italian word "Statista" iii. German word "Statistik"

Which of the following is NOT a characteristic of data?

If the class-intervals in a frequency distribution are 72-73.9, 74-75.9, 76-77.9, 78-79.9, then the mid-value of the class 74-75.9 is:

Which of the following is a positional average?

Marks obtained by 9 students in mathematics as 52, 75, 40, 70, 43, 40, 65, 35, 48. The arithmetic mean is:

Which of the following is considered as the highest level of measurement?

Consider the following statements and choose the best alternative: Assertion (A): Histogram is a graphical presentation of data Reason (R): Statistical data can be represented in the form of graphs. i. A is true ii. R is true iii. A is False iv. R is False

Match the following: *List-I* i. Mean ii. Median iii. Mode iv. Range *List-II* a. Difference between largest and smallest value b. Precise c. Middle most term d. Highest Frequency

Which of the following are categorical variable? i. Age of a person ii. Gender of a person iii. Race of a person

Arrange the stages of statistical investigation in their correct order. a. Classification of Data b. Collection of Data c. Interpretation of Data d. Analysis of Data e. Planning the purpose of Investigation

Which of the following are Non sampling statistical errors? i. Coverage error ii. Non-response error iii. Response error

In hypothesis testing, what is a type II error?

What is the value with the most instances or occurrences in the list called?

What is random sampling?

What is the formula for Chi square test?

There are two events "I" and "J". The events occurring are mutually exclusive for example "I" or "J", its probability is given by which of the laws of probability?

Which of the following tests is used to check the equality of variances between two populations?

If the F statistic is larger than the critical F value.

The simplest measurement of central tendency is

______ is defined as the difference between the value of the extreme items of a series

In which of the following situations is the measured value most likely to be the true value of the quantity being measure?

The error caused by poor calibration of the instrument is called

Which of the following correctly describes F distributions?

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the sample mean will be larger than 82 is

The mean of 11 number is 7 if one of the numbers, 7 is deleted, what will be the mean of remaining 10 number?

What is the variance of a constant 'x'?

Find the median of 4, 5, 6, 3, 2, 6, 4.

If 35 is removed from the data, 30, 34, 35, 36, 37, 38, 39, 40 then the median increased by

In a simultaneous throw of two dice, what is the probability of getting a total of 10 or 11?

Two unbiased coins are tossed. What's the probability of having access to at most one head?

IP P(A U B)=7/12 P(A)=1/3, are for two independent events A and B, then P(B) is

The relation between mean, median and mode in a moderately skewed distribution is

A TDMA system uses 25 MHz for the forward link, which is broken into radio channels of 200, kHz. If 8 speech channels are supported on a single radio channel, how many simultaneous users can be accommodated?

The second law of probability, the addition rule is used for which of the following events?

In hypothesis testing, what is a type I error?

What does the F--test measure?

What is systemic sampling?

How are degrees of freedom calculated in Chi square test? (where r is number of rows and c is number of columns)

What is the median of the following set of numbers? 10, 15, 8, 20, 12

If the variance of the dataset is zero, what can be said about the values in the dataset?

In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?

What does the term p-value represent in hypothesis testing?

If a dataset has a positively skewed distribution, where is the mean in relation to the median?

In a t-test for independent samples, what does the p-value indicate?

What is the purpose of F-test in analysis of variance (ANOVA)?

In a Chi-square test for independence, what is a null hypothesis?

In a paired-sample t-test, what does a p-value less than the chosen level of significance (e.g; 0.05) indicate?

In an analysis of variance (ANOVA) comparing the performance of three different study techniques, the mean scores are 75, 80, and 85 for groups 1, 2, and 3, respectively. The overall mean is 80, and the total sum of squares is 300. What is the between-group sum of squares?

In a study of preferences among three different colors (red, blue, and green), the observed frequencies are 25, 30, and 15, respectively. If the expected frequencies are 20 for each color, what is the chi-square statistic for this test?

What is the formula to calculate theoretical plates, where V is retention time and W_b is peak width

In which of the following ways, absorption is related to transmittance?

The relationship between m/e and magnetic field H in a sector mass spectrometer is:

Measures of central tendency are:

The ________ of a sample is the middle value when the data are arranged in ascending or descending rank order.

A table with all possible value of a random variable and its corresponding probabilities is called

How much of 0.6N NaOH must be added to 750 mL 0.2N NaOH in order to prepare a solution of 0.3N?

Solvent extraction is improved if done using

When dealing with ballistic trajectories in physics, which metric unit is commonly used to measure projectile velocity?

A compound exhibits two distinct NMR peaks at chemical shifts of 1.2 ppm and 2.8 ppm. If the magnetic field strength is 7 Tesla, what is the corresponding frequency difference between these peaks?

A substance with a gyromagnetic ratio ($\gamma$) of $26.75 \times 10^7 \text{ rad/Ts}$ in a magnetic field of 9 Tesla. Calculate the Larmor frequency ( ) of the substance

In forensic analysis, if the probability of a match between a suspect's DNA and evidence DNA is 1 in 1 million, what is the likelihood of an unrelated person having the same DNA profile?

In a forensic investigation involving categorical data, which statistical test is used to determine if there is a significant association between two variables?

If the mean length of hair samples is 10 cm, and the standard deviation is 2 cm, what is the variation coefficient?

In a forensic probability matrix, if the probability of Event A is 0.2 and the probability of Event B is 0.3, what is the joint probability of both events occurring?

Which principle underlies the forensic technique of density comparison for glass fragments?

Among the properties of textile fibbers, how does the orientation of molecular chains within a fibber contribute to its mechanical characteristics, such as tensile strength?

When identifying adulterated cement in forensic analysis, what specific property is often assessed to determine the quality and purity of the cement sample?

Match the following: List-I i. Mean ii. Median iii. Mode iv. Range List-II a. Difference between largest and smallest value b. Precise c. Middle most term d. Highest Frequency