READING 7 ESTIMATION AND INFERENCE Flashcards by Abdulmjeed Almutairi

Which of the following sampling methods gives each member of the population an equal probability of being selected?

(A) Convenience Sampling
(B) Simple Random Sampling
(C) Judgmental Sampling
(D) Stratified Random Sampling

(B) Simple Random Sampling

Simple random sampling ensures that every individual or item in the population has the same chance of being included in the sample.

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An analyst wants to estimate the average return of all technology stocks listed on a major exchange. To ensure that both large and small tech companies are adequately represented in the sample, which sampling method would be most appropriate?

(A) Cluster Sampling
(B) Convenience Sampling
(C) Stratified Random Sampling
(D) Simple Random Sampling

Stratified random sampling allows the analyst to divide the population (all technology stocks) into subgroups (e.g., based on market capitalization) and then take a random sample from each subgroup, ensuring representation across different sizes.

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Which of the following sampling methods is most susceptible to researcher bias?

(A) Simple Random Sampling
(B) Stratified Random Sampling
(C) Cluster Sampling
(D) Judgmental Sampling

(D) Judgmental Sampling

In judgmental sampling, the researcher uses their own expertise to select the sample, which introduces the potential for their personal biases to influence the selection process.

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A portfolio manager wants to quickly get a sense of the market sentiment by surveying the first 50 clients who respond to an email questionnaire. This is an example of:

(A) Simple Random Sampling
(B) Stratified Random Sampling
(C) Convenience Sampling
(D) Cluster Sampling

Convenience sampling involves selecting individuals or data points that are easily accessible to the researcher, as in this case with the readily responding clients.

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To reduce the cost of data collection for a study on the performance of investment advisors across a large country, a researcher randomly selects five major cities and then includes all registered investment advisors within those cities in the sample. This is an example of:

(A) Stratified Random Sampling
(B) Simple Random Sampling
(C) Cluster Sampling
(D) Judgmental Sampling

Cluster sampling involves dividing the population into groups (clusters), randomly selecting a few clusters, and then including all members within the selected clusters in the sample.

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Which sampling method is particularly useful when the population is difficult or costly to access directly?

(A) Simple Random Sampling
(B) Stratified Random Sampling
(C) Judgmental Sampling
(D) Cluster Sampling

(D) Cluster Sampling

Cluster sampling can be more practical and cost-effective when the population is geographically dispersed or when obtaining a list of all individuals is challenging.

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An analyst is constructing a bond portfolio to match the characteristics of a broad market index. They categorize the bonds in the index by maturity and credit rating and then randomly select bonds from each category in proportion to their representation in the index. This is an example of:

(A) Convenience Sampling
(B) Simple Random Sampling
(C) Stratified Random Sampling
(D) Cluster Sampling

By categorizing the bonds and sampling proportionally from each category (stratum), the analyst is using stratified random sampling to ensure the portfolio reflects the index’s structure.

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Which sampling method generally has the lowest potential for sampling error, assuming the strata are well-defined and relevant?

(A) Convenience Sampling
(B) Simple Random Sampling
(C) Cluster Sampling
(D) Stratified Random Sampling

(D) Stratified Random Sampling

When done correctly, stratified random sampling can reduce sampling error by ensuring that key subgroups within the population are adequately represented in the sample.

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A researcher wants to gather preliminary data on the trading strategies used by successful day traders. Based on their network, they select a few traders known for their consistent profitability to participate in the study. This is an example of:

(A) Simple Random Sampling
(B) Convenience Sampling
(C) Cluster Sampling
(D) Judgmental Sampling

(D) Judgmental Sampling

The researcher is using their judgment to select participants who they believe will provide valuable insights based on their success.

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In which sampling method is the representativeness of the sample most dependent on the researcher’s expertise?

(A) Simple Random Sampling
(B) Stratified Random Sampling
(C) Cluster Sampling
(D) Judgmental Sampling

(D) Judgmental Sampling

The validity of the findings from judgmental sampling hinges on the researcher’s ability to select a sample that accurately reflects the population’s characteristics.

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If a researcher selects every 10th stock from a list of all publicly traded companies, ordered alphabetically, this would be an example of:

(A) Simple Random Sampling
(B) Systematic Sampling
(C) Convenience Sampling
(D) Cluster Sampling

(B) Systematic Sampling

Systematic sampling involves selecting members of the population at regular intervals after a random starting point. While not strictly simple random sampling, it aims for a degree of randomness.

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Which of the following is a key disadvantage of convenience sampling?

(A) It requires a complete list of the population.
(B) It can be time-consuming and costly.
(C) It often results in a non-representative sample.
(D) It requires dividing the population into subgroups.

Convenience samples are typically drawn from easily accessible individuals or data, which may not reflect the characteristics of the broader population, leading to biased results.

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Which sampling method is most likely to have higher sampling error if the clusters are not representative of the overall population?

(A) Stratified Random Sampling
(B) Simple Random Sampling
(C) Cluster Sampling
(D) Judgmental Sampling

The effectiveness of cluster sampling depends on the assumption that each selected cluster mirrors the characteristics of the entire population. If this assumption doesn’t hold, the sampling error can be significant.

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When is judgmental sampling potentially more useful than probability sampling methods in investment analysis?

(A) When aiming for statistical inference about the entire market.
(B) When the researcher has strong theoretical reasons to believe specific data points are most relevant.
(C) When cost and time are major constraints and a quick overview is needed.
(D) When the population is large and easily accessible.

(B) When the researcher has strong theoretical reasons to believe specific data points are most relevant.

In specific situations where expert knowledge suggests certain data points hold key information, judgmental sampling can be targeted and potentially insightful, even though it lacks the statistical rigor of probability sampling.

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According to the Central Limit Theorem, for a sufficiently large sample size, the sampling distribution of the sample mean will:

(A) Have the same shape as the population distribution.
(B) Be approximately a uniform distribution.
(C) Be approximately a normal distribution.
(D) Have a mean equal to the sample mean.

The Central Limit Theorem states that regardless of the shape of the original population’s distribution, the distribution of the sample means will approach a normal distribution as the sample size increases.

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The mean of the sampling distribution of the sample mean is:

(A) Always equal to zero.
(B) Equal to the sample mean.
(C) Equal to the population mean.
(D) Dependent on the sample size.

One of the key properties of the Central Limit Theorem is that the mean of the distribution of all possible sample means is equal to the true mean of the original population.

The standard error of the sample mean measures:

(A) The dispersion of the population around its mean.
(B) The specific difference between a single sample mean and the population mean (i.e., sampling error for one sample).
(C) The dispersion of the sample means (calculated from many different samples) around the population mean.
(D) The range of values observed in a single sample.

The standard error of the sample mean quantifies the variability of the sample means that would be obtained from repeated sampling of the population. It estimates how much these sample means tend to deviate from the true population mean.

Option (B) describes sampling error, which is the difference for a single sample, while standard error describes the typical size of that error across many samples.

As the sample size (n) increases, the standard error of the sample mean will:

(A) Increase.
(B) Decrease.
(C) Remain the same.
(D) Increase proportionally to the square root of n.

(B) Decrease.

The formula for standard error shows an inverse relationship with the square root of the sample size. Larger samples lead to smaller standard errors.

When the population standard deviation is unknown, the standard error of the sample mean is estimated using:

(A) The population variance divided by the sample size.
(B) The sample standard deviation divided by the square root of the sample size.
(C) The population standard deviation divided by the sample size.
(D) The sample variance divided by the sample size.

(B) The sample standard deviation divided by the square root of the sample size.

In the common scenario where σ is unknown, we use the sample standard deviation (s) to estimate it

The Central Limit Theorem is most applicable when the sample size is:

(A) Very small (e.g., less than 5).
(B) Small to moderate (e.g., around 10-20).
(C) Sufficiently large (e.g., generally n ≥ 30).
(D) Equal to the population size.

The CLT’s approximation to a normal distribution improves as the sample size increases, with a common guideline being a sample size of 30 or more.

An analyst takes multiple samples of 50 stocks from a large market and calculates the average return for each sample. The distribution of these average returns is best described by the:

(A) Population distribution.
(B) Sample distribution of one particular sample.
(C) Sampling distribution of the sample mean.
(D) Uniform distribution.

The distribution of the means of all possible samples of a given size taken from a population is called the sampling distribution of the sample mean.

For a population with a mean (μ) of 10% and a standard deviation (σ) of 5%, what is the standard error of the sample mean for a sample size of 100?

(B) 0.5%

Why is the Central Limit Theorem important in investment analysis?

(A) It allows us to know the exact distribution of individual asset returns.
(B) It guarantees that any sample will perfectly represent the population.
(C) It allows us to make statistical inferences about population parameters (like average returns) based on sample statistics, even when the population distribution is unknown.
(D) It simplifies the calculation of individual asset risk.

(C) It allows us to make statistical inferences about population parameters (like average returns) based on sample statistics, even when the population distribution is unknown.

The CLT’s power lies in enabling us to use the normal distribution for inference about the population mean based on sample means, regardless of the original distribution, provided the sample size is large enough.

A researcher is studying the average dividend yield of all REITs. They take a sample of 40 REITs. If the sample standard deviation of the dividend yield is 2%, the estimated standard error of the sample mean is:

(B) 0.32%

Resampling techniques like the bootstrap and jackknife are primarily used to: (A) Estimate the population parameters directly from a single sample. (B) Reduce the size of the original dataset for computational efficiency. (C) Estimate the sampling distribution of a statistic. (D) Eliminate bias in the original sample.

(C) Estimate the sampling distribution of a statistic. Resampling methods involve repeatedly drawing samples from the original dataset to approximate how a statistic would vary across different samples from the population.

The jackknife method estimates the sampling distribution of a statistic by: (A) Repeatedly drawing samples with replacement of the same size as the original. (B) Creating multiple sub-samples, each with one observation removed from the original sample. (C) Randomly selecting a subset of the original data without replacement. (D) Dividing the original data into non-overlapping intervals.

(B) Creating multiple sub-samples, each with one observation removed from the original sample. The jackknife generates n samples of size n−1 by systematically leaving out one observation at a time from the original sample of size n.

A key advantage of the jackknife method is its: (A) Ability to estimate the full shape of the sampling distribution for complex statistics. (B) High computational efficiency, especially with smaller datasets. (C) Superior accuracy in estimating standard errors compared to the bootstrap. (D) Capability to handle very large datasets.

(B) High computational efficiency, especially with smaller datasets. The jackknife requires only n resamples, making it computationally simpler than the bootstrap, which often uses thousands.

A key advantage of the bootstrap method is its: (A) Simplicity in calculation for small sample sizes. (B) Ability to estimate the sampling distribution of various statistics, including those without analytical forms. (C) Guaranteed reduction of bias in all statistical estimates. (D) Lower computational demand compared to the jackknife.

(B) Ability to estimate the sampling distribution of various statistics, including those without analytical forms. The bootstrap's strength lies in its versatility to estimate the distribution and standard errors for a wide range of statistics, even complex ones.

The bootstrap method estimates the sampling distribution of a statistic by: (A) Creating multiple sub-samples, each with one observation removed from the original sample. (B) Randomly selecting a subset of the original data without replacement. (C) Repeatedly drawing samples with replacement of the same size as the original. (D) Dividing the original data into non-overlapping intervals.

(C) Repeatedly drawing samples with replacement of the same size as the original. The bootstrap involves drawing many samples of size n from the original dataset of size n, with replacement, to simulate the sampling process.

Which resampling method is particularly useful for assessing the stability of a statistic with respect to the removal of a single data point? (A) Bootstrap (B) Jackknife (C) Both bootstrap and jackknife (D) Neither bootstrap nor jackknife

(B) Jackknife By systematically leaving out each observation, the jackknife helps in understanding the influence of individual data points on the statistic.

Which resampling method allows for the construction of confidence intervals by examining the percentiles of the resampled statistics? (A) Jackknife (B) Bootstrap (C) Both jackknife and bootstrap (D) Neither bootstrap nor jackknife

(B) Bootstrap The distribution of the bootstrap statistics can be directly used to estimate confidence intervals by finding the relevant percentiles.

Compared to using only the data in a single sample, the bootstrap method can potentially: (A) Decrease accuracy due to the introduction of replacement. (B) Improve accuracy by simulating the sampling distribution. (C) Only provide information about the mean of the statistic. (D) Only be used for normally distributed data.

(B) Improve accuracy by simulating the sampling distribution. By generating many resamples, the bootstrap provides a more robust estimate of the statistic's variability and potential distribution.

For a very small sample size (e.g., n < 10), which resampling method might be preferred due to its lower computational demands? (A) Bootstrap with a large number of resamples. (B) Jackknife. (C) Bootstrap with a very small number of resamples (e.g., equal to n). (D) Neither method is reliable with very small sample sizes.

(B) Jackknife. The jackknife's computational simplicity with n resamples makes it more manageable for small datasets compared to the bootstrap, which typically requires many more resamples for reliable estimates.

Resampling methods like the bootstrap can be particularly useful when: (A) The population distribution is well-known and follows a standard form. (B) Analytical formulas for the standard error of a statistic are readily available. (C) The statistic of interest is complex and its theoretical sampling distribution is unknown. (D) The sample size is extremely large (e.g., millions of observations).

(C) The statistic of interest is complex and its theoretical sampling distribution is unknown. Bootstrap shines when traditional statistical methods relying on distributional assumptions or formulas are not applicable, allowing for a data-driven estimation of the sampling distribution.

The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. Under what condition might this approximation be less reliable, even with a sample size of 30 or more? (A) When the population standard deviation is very small. (B) When the population mean is close to zero. (C) When the population distribution is extremely skewed or has very heavy tails. (D) When the sample is drawn without replacement.

(C) When the population distribution is extremely skewed or has very heavy tails. While the CLT is powerful, if the original population is drastically non-normal (e.g., highly skewed with extreme outliers), a larger sample size than the typical rule of thumb might be needed for the sampling distribution of the mean to become approximately normal.

If you repeatedly draw large, random samples from a population and calculate the mean of each sample, what will be the shape of the distribution of these sample means? (A) It will have the same shape as the original population. (B) It will be a uniform distribution. (C) It will be approximately a normal distribution. (D) It will be impossible to predict the shape without knowing the population distribution.

(C) It will be approximately a normal distribution. This is the core of the Central Limit Theorem. The distribution of sample means tends towards normality as the sample size increases.

A researcher is studying the average income of individuals in a large city. The distribution of incomes in this city is known to be right-skewed. If the researcher takes a large random sample (n = 100) and calculates the sample mean, what can be said about the distribution of sample means if this process were repeated many times? (A) It would also be right-skewed, similar to the population. (B) It would be approximately normally distributed. (C) It would be uniformly distributed. (D) It would be skewed to the left.

(B) It would be approximately normally distributed. Despite the right-skewed population, the Central Limit Theorem tells us that with a large sample size (n=100), the distribution of the sample means will tend towards a normal distribution.