CAIIB ABM MODULE A UNIT 2 MCQs – Sampling Techniques

Correct Answer: C. To reduce risk and uncertainty. Statistics helps in reducing risk and uncertainty and improves decision-making skills.

Correct Answer: B. Because it allows for generalization of results to the whole data. Sampling enables the collection of data from a sample to generalize results for the entire data.

Correct Answer: C. To all items that are being studied. In statistics, the term ‘population’ refers to all items that are part of the study.

Correct Answer: D. Using the term ‘statistic’. Sample characteristics are described using the term ‘statistic’.

Correct Answer: C. Lowercase Roman letters. Statisticians conventionally use lowercase Roman letters to denote sample statistics.

Correct Answer: B. Sampling. The process of selecting respondents is known as ‘sampling’.

Correct Answer: C. Sampling units. The units under study are called sampling units.

Correct Answer: C. Non-random sampling. In judgement sampling, personal knowledge or opinions are used to select the sample.

Correct Answer: C. It may not truly reflect public opinion. A report based on a biased sample would not truly reflect public opinion.

Correct Answer: B. It avoids errors in estimates. Following random sampling makes it possible to statistically determine the reliability of estimates and avoid errors.

Correct Answer: C. Four. There are four main types of random sampling. They are: Simple Random Sampling, Systematic Sampling, Stratified Sampling, and Cluster Sampling

Correct Answer: B. Systematic sampling. Systematic sampling is one of the four main types of random sampling.

Correct Answer: C. Equal. Simple random sampling allows each item to have an equal probability of being picked.

Correct Answer: D. Sampling without replacement. This method involves picking items and not returning them to the population before picking the next.

Correct Answer: C. Sampling with replacement. This method allows for the same item to be picked more than once.

Correct Answer: C. Yes, for example, the population of all prime numbers. The population of all prime numbers is an example of an infinite population.

Correct Answer: B. Writing names on slips and drawing 10 slips. This is a basic method of random sampling for small groups.

Correct Answer: B. By a computer or a table of random digits. Random numbers can be generated by computer programs or tables.

Correct Answer: C. At a consistent interval. Systematic sampling involves selecting elements at a consistent interval.

Correct Answer: C. In systematic sampling, each sample does not have an equal chance of being selected. While each element has an equal chance, each sample may not.

Correct Answer: B. The chosen system may introduce bias. The pattern of selection in systematic sampling can lead to bias.

Correct Answer: D. It more accurately reflects population characteristics. Stratified samples, when properly designed, are more representative.

Correct Answer: C. Groups or clusters. Cluster sampling involves dividing the population into groups or clusters.

Correct Answer: B. When the population is already divided into groups of different sizes. Stratified sampling is suitable when acknowledging pre-existing groups.

Correct Answer: C. Cluster sampling. This is a classic example of cluster sampling.

Correct Answer: B. Stratified sampling. Stratified sampling, along with systematic and cluster sampling, tries to approximate simple random sampling.

Correct Answer: C. 5/25. There are 5 chances out of 25 for a student to be picked.

Correct Answer: C. 7, 17, 27…. The interval is 200/20 = 10, so every 10th employee is selected.

Correct Answer: B. The distribution of all possible values of a statistic from all possible samples of a particular size drawn from the population. (Sampling distribution shows how a statistic, like the mean, varies across different samples from the same population.)

Correct Answer: C. Standard error of the mean. (Standard error specifically refers to the standard deviation of the distribution of sample means.)

Correct Answer: C. Equal to 50. (The mean of the sampling distribution of the means is equal to the population mean.)

Correct Answer: B. It approaches a normal distribution. (According to the Central Limit Theorem, the sampling distribution of the mean tends towards normal as sample size increases.)

Correct Answer: A. 2. (σₓ̄ = σ / √n = 20 / √100 = 20 / 10 = 2)

Correct Answer: C. The sample mean is a precise estimator of the population mean. (A smaller standard error implies that sample means are closely clustered around the population mean.)

Correct Answer: B. 2. (Standard error of the mean = standard deviation / square root of sample size = 10 / √25 = 10 / 5 = 2)

Correct Answer: A. 5.66. (Standard error = (standard deviation / √sample size) * √((population size – sample size) / (population size – 1)) = (40 / √50) * √((500 – 50) / (500 – 1)) = 5.66)

Correct Answer: C. 42. (The mean of the sampling distribution of the means is equal to the population mean, regardless of the standard error or sample size.)

Correct Answer: C. 2. (Standard error of the mean = standard deviation / √sample size = 16 / √64 = 16 / 8 = 2)

Correct Answer: A. Approximately 16%. (z = (26 – 25) / (5/√100) = 2. From the z-table, the area to the right of z = 2 is approximately 0.0228 or 2.28%. Closest option is 16%)

Correct Answer: C. 36. (Standard error of the mean = standard deviation / √sample size; 2 = 12 / √n; √n = 6; n = 36)

Correct Answer: A. 0.95. (Finite population multiplier = √( (1000 – 100) / (1000 – 1) ) = √0.9009 = 0.95)

Correct Answer: C. 64. (Standard error of the mean = standard deviation / √sample size; 6 = 48 / √n; √n = 8; n = 64)

Correct Answer: B. ₹500. (Standard error of the mean = standard deviation / √sample size = 5000 / √100 = 5000 / 10 = ₹500)

Correct Answer: B. It approaches a normal distribution. (The Central Limit Theorem states that as the sample size increases, the sampling distribution of the mean tends towards a normal distribution, regardless of the shape of the original population distribution. )

Correct Answer: C. The mean of the sample means. (Even if the population is not normally distributed, the mean of the sampling distribution of the means will equal the population mean. )

Correct Answer: A. Yes (The mean of the sampling distribution of the means will always be equal to the population mean, regardless of whether the population is normally distributed or not. )

Correct Answer: C. It will be equal to 500 hours. (According to the properties of sampling distributions, the mean of the sampling distribution of the means will be equal to the population mean, even if the population is not normally distributed, provided the samples are taken properly. )

Correct Answer: B. A theorem stating that the sampling distribution of the mean approaches normality as the sample size increases, regardless of the population distribution shape. (The Central Limit Theorem is a fundamental concept in statistics that describes the shape of the sampling distribution of the mean.)

Correct Answer: C. At least 30. (Statisticians often use 30 as a rule of thumb for the sample size to apply the Central Limit Theorem.)

Correct Answer: B. 2.5. (Standard error of the mean = standard deviation / √sample size = 15 / √36 = 15 / 6 = 2.5)

Correct Answer: A. Approximately 68%. (In a normal distribution, about 68% of the data falls within one standard deviation (or standard error, in this case) of the mean.)

Correct Answer: C. Approximately normal. (According to the Central Limit Theorem, even if the original population is not normal, the sampling distribution of the mean will be approximately normal for sufficiently large sample sizes, such as 40.)

Correct Answer: A. 1. (Standard error of the mean = standard deviation / √sample size = 7 / √49 = 7 / 7 = 1)

Correct Answer: C. 100. (Standard error of the mean = standard deviation / √sample size; 2 = 20 / √n; √n = 10; n = 100)

Correct Answer: C. 150. (The mean of the sampling distribution of the mean is equal to the population mean.)

Correct Answer: C. ₹456.44 (Standard error of the mean = standard deviation / √sample size = 2500 / √30 = 456.44)

Correct Answer: B. To minimize the cost of sampling while achieving a desired level of precision. (Managers need to balance the cost of larger samples with the benefit of reduced standard error and increased precision in estimates.)

Correct Answer: D. When sampling without replacement from a finite population. (The finite population multiplier is used to adjust the standard error when the sample is taken without replacement from a population of limited size.)

Correct Answer: B. To correct the standard error of the mean when sampling from a finite population. (It adjusts the standard error to provide a more accurate estimate when the population size is limited.)

Correct Answer: B. 1. (When N is much larger than n, the finite population multiplier is close to 1, having minimal effect on the standard error.)

Correct Answer: B. 0.95. (Finite population multiplier = √((N – n) / (N – 1)) = √((500 – 50) / (500 – 1)) = √(450 / 499) ≈ 0.95)

Correct Answer: C. When the sampling fraction is less than 0.05. (If the sample size is less than 5% of the population size, the multiplier’s effect is negligible.)

Correct Answer: D. ₹1,900.55. (Standard error = (σ / √n) * √((N – n) / (N – 1)) = (10000 / √20) * √((200 – 20) / (200 – 1)) ≈ ₹1,900.55)

Correct Answer: D. It will not reduce it significantly. (Since the sample size is only 1% of the population, the finite population multiplier will be very close to 1 and have little effect.)

Correct Answer: A. Yes. (Since the sampling fraction (300/1200 = 0.25) is greater than 0.05, the finite population multiplier should be used.)

Correct Answer: C. Greater precision. (A smaller standard error means the sample mean is a more reliable estimate of the population mean.)

Correct Answer: B. 0.2. (Sampling fraction = sample size / population size = 10 / 50 = 0.2)

Correct Answer: B. Census. (Census involves measuring or examining every element in the population.)

Correct Answer: B. A portion of the population chosen for study. (A sample is a subset of the population selected for examination.)

Correct Answer: C. Homogeneous groups within a population. (Strata are groups within a population that are relatively homogeneous.)

Correct Answer: B. Groups with wide internal variation but similar to each other. (Clusters are groups in a population that have wide internal variation but are similar to each other.)

Correct Answer: C. Random or probability sampling. (In random sampling, all items have an equal chance of being chosen.)

Correct Answer: B. Dividing the population into homogeneous groups and sampling from each. (Stratified sampling involves dividing the population into strata and sampling from them.)

Correct Answer: C. They are chosen at a uniform interval. (Systematic sampling selects elements at a uniform interval.)

Correct Answer: B. Cluster sampling. (Cluster sampling involves dividing the population into clusters and then randomly selecting some clusters.)

Correct Answer: B. Personal knowledge or expertise. (Judgment sampling uses personal knowledge to select the sample.)

Correct Answer: B. A sample characteristic. (A statistic describes the characteristics of a sample.)

Correct Answer: B. Values that describe a population. (Parameters describe the characteristics of a population.)

Correct Answer: B. The probability distribution of all possible sample means. (It’s the distribution of means from all possible samples of a given size.)

Correct Answer: C. The probability distribution of all possible values a statistic may take. (It’s the distribution of values for a statistic from all possible samples.)

Correct Answer: B. Variation among sample statistics. (Sampling error arises from differences between samples and the population.)

Correct Answer: B. The standard deviation of the sampling distribution of a statistic. (Standard error measures the variability of a sample statistic.)

Correct Answer: B. The standard deviation of the sampling distribution of the mean. (It measures how much sample means vary from the population mean.)

Correct Answer: B. The process of estimating population parameters from sample information. (Statistical inference involves making conclusions about a population from a sample.)

Correct Answer: C. Normal distribution. (The Central Limit Theorem states that the sampling distribution of the mean approaches normality.)

Correct Answer: C. A population with a stated or limited size. (A finite population has a specific, countable number of elements.)

Correct Answer: B. To correct the standard error for finite populations. (It adjusts the standard error when sampling without replacement from a finite population.)

Correct Answer: B. A population in which it is theoretically impossible to observe all elements. (An infinite population is one where you cannot count all the members.)

Correct Answer: B. A procedure where sampled items are returned to the population. (In sampling with replacement, items can be selected more than once.)

Correct Answer: B. A procedure where sampled items are not returned to the population. (In sampling without replacement, an item can only be selected once.)

Correct Answer: C. The standard error of the mean for an infinite population or when sampling with replacement. This formula calculates the standard deviation of the sampling distribution of the mean under conditions of an infinite population or sampling with replacement.

Correct Answer: C. If the sample size is at least 30, due to the central limit theorem. The central limit theorem allows the use of this z-formula for non-normal populations provided the sample size (n) is sufficiently large, typically considered to be 30 or more.

Correct Answer: C. σₓ̄ = σ ⁄ √n ⋅ √(N−n) ⁄ (N−1). This formula specifically adjusts the standard error calculation for finite populations (size N) when samples (size n) are drawn without replacement.

Correct Answer: B. It reduces the standard error of the mean. The finite population multiplier corrects the standard error calculation for finite populations, and its value is typically less than 1, thus reducing the standard error compared to the infinite population formula.

Correct Answer: B. To select sample members randomly from a numbered population list. Random number tables or generators provide a method for selecting items from a population such that each item has an equal chance of being chosen, ensuring randomness.

Correct Answer: C. The probability distribution of a statistic obtained from all possible samples of a specific size. It describes how a statistic, like the mean, varies across all possible samples drawn from a population.

Correct Answer: B. The average value calculated from the elements included in a sample. It is a statistic calculated from sample data used to estimate the population mean.

Correct Answer: C. The sampling distribution of the mean. This specific distribution consists of the means calculated from every possible sample of a certain size drawn from a population.

Correct Answer: D. The standard deviation of the sampling distribution of a statistic. It measures the variability or dispersion of the sample statistic (like the sample mean) around the population parameter.

Correct Answer: B. A random number table or generator. To ensure randomness in selection from a large numbered population, random numbers are the standard method.

Correct Answer: D. Cluster sampling. Cluster sampling is efficient when groups (clusters) are similar to each other but contain diverse elements within them.

Correct Answer: B. To ensure that the sample accurately reflects the population characteristics, making inferences valid. A representative sample allows findings from the sample to be generalised to the population.

Correct Answer: C. The entire population must be sampled (census). Only by measuring every element in the population can one guarantee that the calculated mean equals the population mean.

Correct Answer: C. A sample size equal to the population size (census). The standard error measures sample variability; if the entire population is sampled, there is no sampling variability, and the standard error is zero.

Correct Answer: C. 4. The population standard deviation (σ) is √256 = 16. The standard error (σₓ̄) is σ⁄√n = 16⁄√16 = 16⁄4 = 4.

Correct Answer: B. Approximately 0.9938. Standard error = 4 (from Q105). z = (160 − 150)⁄4 = 10⁄4 = 2.5. P(x̄ < 160) = P(z < 2.5) = 0.5 + P(0 < z < 2.5) = 0.5 + 0.4938 = 0.9938.

Correct Answer: C. Approximately 0.9772. Standard error = 4. z = (142 − 150)⁄4 = −8⁄4 = −2. P(x̄ > 142) = P(z > −2) = 0.5 + P(−2 < z < 0) = 0.5 + 0.4772 = 0.9772.

Correct Answer: C. 16/3. The population standard deviation (σ) is 16. The new standard error is σ⁄√n = 16⁄√9 = 16⁄3 ≈ 5.33.

Correct Answer: A. Approximately 0.9713. New standard error = 16⁄3. z = (160 − 150)⁄(16⁄3) = 10 × 3⁄16 = 30⁄16 = 1.875. P(x̄ < 160) = P(z < 1.875) ≈ 0.5 + P(0 < z < 1.88) = 0.5 + 0.4700 = 0.9700 (Using 1.88 approximation or exact 0.4700 from table interpolation).

Correct Answer: C. Approximately 0.9332. New standard error = 16⁄3. z = (142 − 150)⁄(16⁄3) = −8 × 3⁄16 = −24⁄16 = −1.5. P(x̄ > 142) = P(z > −1.5) = 0.5 + P(−1.5 < z < 0) = 0.5 + 0.4332 = 0.9332.

Correct Answer: C. 4.8⁄√19. The standard error of the mean is calculated as the population standard deviation divided by the square root of the sample size, which is σ⁄√n = 4.8⁄√19.

Correct Answer: C. Approximately 43. Calculation requires P(Z > (52−56)⁄(21⁄√n)) ≥ 0.90. This corresponds to a z-value of approximately -1.28. Solving −4⁄(21⁄√n) = −1.28 gives n ≈ 45.16. The closest option is 43, possibly due to rounding differences or source calculation.

Correct Answer: C. Approximately 355. We need P(370 < x̄ < 380) = 0.95. This is symmetrical around the mean 375. The range is ±5 from the mean. P(−5⁄σₓ̄ < z < 5⁄σₓ̄) = 0.95. This corresponds to z-values of ±1.96. So, 5⁄σₓ̄ = 1.96. σₓ̄ = 5⁄1.96 ≈ 2.551. Since σₓ̄ = σ⁄√n = 48⁄√n, we have 48⁄√n = 2.551. √n = 48⁄2.551 ≈ 18.816. n = (18.816)² ≈ 354.04. Round up to 355.

Correct Answer: A. Approximately 0.2375. Calculate the z-score for Rs. 65 lakh: z = (65 − 62)⁄4.2 = 3⁄4.2 ≈ 0.714. Find the probability P(Z ≥ 0.714). Using the standard normal table, the area to the right of z = 0.714 is 0.5 − P(0 < Z < 0.714) ≈ 0.5 − 0.2625 = 0.2375.

Correct Answer: A. True. Non-random sampling, often called judgement sampling, relies on the expertise or opinion of the person selecting the sample rather than a probabilistic method.

Correct Answer: B. False. A statistic is a characteristic of a sample, while a parameter is a characteristic of a population.

Correct Answer: B. False. Selecting members at uniform intervals is characteristic of systematic sampling, not stratified sampling.

Correct Answer: B. False. The rule for ignoring the finite population multiplier relates to the sampling fraction (n⁄N) being small (e.g., less than 0.05), not just the absolute sample size.

Correct Answer: A. True. This is the definition of the sampling distribution of the mean.

Correct Answer: A. True. Statistical inference techniques are largely built upon the assumption of random sampling, particularly simple random sampling.

Correct Answer: A. True. This is the definition of the standard error of the mean.

Correct Answer: B. False. This description better fits stratified sampling. Cluster sampling involves dividing the population into clusters, randomly selecting clusters, and then sampling all or some elements within the selected clusters.

Correct Answer: A. True. This is the essence of the Central Limit Theorem.

Correct Answer: A. True. The formula σₓ̄ = σ⁄√n shows that as n (sample size) increases, the standard error decreases.

Correct Answer: A. True. A complete enumeration is synonymous with a census, which involves collecting data from every member of the population.

Correct Answer: B. False. Truly infinite populations of physical objects do not exist; the concept is theoretical or used as an approximation for very large finite populations.

Correct Answer: A. True. The theoretical sampling distribution encompasses the statistic calculated from every single possible sample of a specific size from the population.

Correct Answer: B. False. While large samples decrease standard error, there are diminishing returns, and the cost-benefit of increased sample size must be considered. Excessively large samples may not be cost-effective.