Reading 5: Sampling and Estimation
50 questions available
Key Points
- Probability sampling allows for error estimation; non-probability sampling relies on judgment.
- Simple random sampling: Equal probability of selection for each item.
- Stratified random sampling: Samples drawn from specific subgroups; ensures representation.
- Cluster sampling: Samples entire groups (clusters); cost-effective but potentially less precise.
- Systematic sampling: Selecting every nth member of a population.
Key Points
- CLT applies when n >= 30, ensuring the sampling distribution is approximately normal.
- Standard Error (SE) measures the dispersion of sample means around the population mean.
- SE formula: Population standard deviation divided by the square root of n.
- If population variance is unknown, use the sample standard deviation (s) to estimate SE.
- Larger sample sizes reduce the standard error.
Key Points
- Unbiasedness: Expected value of estimator equals the parameter.
- Efficiency: Smallest variance among unbiased estimators.
- Consistency: Probability of estimate being close to the parameter increases with sample size.
- The sample mean is an unbiased and efficient estimator of the population mean.
Key Points
- Confidence Interval = Point Estimate +/- (Reliability Factor * Standard Error).
- Use z-statistic when population variance is known.
- Use t-statistic when population variance is unknown (requires assumption of normality for small samples).
- Common z-values: 1.65 (90 percent), 1.96 (95 percent), 2.58 (99 percent).
- t-distribution has fatter tails; intervals are wider than z-intervals.
Key Points
- Jackknife: Re-calculates statistic leaving one observation out each time.
- Bootstrap: Repeated sampling from the original data set with replacement.
- Data snooping bias: Finding spurious patterns due to extensive testing.
- Survivorship bias: Overestimating performance by excluding failed firms/funds.
- Look-ahead bias: Using future data for past simulations.
- Time-period bias: Results valid only for a specific time period.
Questions
Which of the following best describes a simple random sample?
View answer and explanationIn stratified random sampling, how are samples drawn?
View answer and explanationWhich sampling method involves dividing the population into subsets and assuming each subset is representative of the overall population?
View answer and explanationWhat is the primary difference between one-stage and two-stage cluster sampling?
View answer and explanationWhich of the following is an example of non-probability sampling?
View answer and explanationSampling error is best defined as:
View answer and explanationAccording to the Central Limit Theorem, the sampling distribution of the sample mean will be approximately normal if:
View answer and explanationThe Central Limit Theorem states that the mean of the distribution of sample means is equal to:
View answer and explanationIf a population has a mean of 50 and a standard deviation of 10, what is the standard error of the sample mean for a sample size of 25?
View answer and explanationWhen the population standard deviation is unknown, the standard error of the sample mean is estimated by:
View answer and explanationA sample of 100 observations has a standard deviation of 20. The standard error of the sample mean is:
View answer and explanationAs the sample size increases, what happens to the standard error of the sample mean?
View answer and explanationAn estimator is considered unbiased if:
View answer and explanationWhich property of an estimator refers to having the smallest variance among all unbiased estimators?
View answer and explanationA consistent estimator is one where:
View answer and explanationA point estimate is best described as:
View answer and explanationA confidence interval is constructed using which of the following formulas?
View answer and explanationFor a normal distribution, the reliability factor for a 90 percent confidence interval is approximately:
View answer and explanationThe reliability factor for a 95 percent confidence interval using the standard normal distribution is:
View answer and explanationA sample of 64 observations has a mean of 20 and a population standard deviation of 4. What is the 95 percent confidence interval for the population mean?
View answer and explanationWhen constructing a confidence interval for the population mean of a normal distribution with unknown variance, which statistic should be used?
View answer and explanationThe degrees of freedom for a t-statistic calculated from a sample of size n is:
View answer and explanationCompared to the standard normal distribution, the Student's t-distribution has:
View answer and explanationAs the degrees of freedom increase, the Student's t-distribution:
View answer and explanationIf a population is nonnormal and the variance is unknown, which test statistic is appropriate for a large sample (n > 30)?
View answer and explanationIf sampling from a nonnormal distribution with unknown variance and a small sample size (n < 30), which test statistic is available?
View answer and explanationThe Jackknife method of resampling involves:
View answer and explanationThe Bootstrap method involves:
View answer and explanationData snooping bias occurs when:
View answer and explanationSurvivorship bias is a form of:
View answer and explanationWhich bias occurs when a study tests a relationship using sample data that was not available on the test date?
View answer and explanationTime-period bias results when:
View answer and explanationA mutual fund database that only includes funds currently in existence likely suffers from:
View answer and explanationA sample has a mean of 5 percent and a standard deviation of 10 percent. If the sample size is 100, what is the standard error of the sample mean?
View answer and explanationWith a sample size of 200 and a standard deviation of 20 percent, the standard error is 1.4 percent. If the sample size increases, the standard error will:
View answer and explanationIn a random sample of 50 items with a known population standard deviation, the standard error is 2. If the sample size is increased to 200, the new standard error will be:
View answer and explanationIf a confidence interval is 95 percent, the significance level (alpha) is:
View answer and explanationUsing a z-table, the probability that a standard normal random variable is less than -1.96 is:
View answer and explanationFor a t-distribution with 29 degrees of freedom, the critical value for a 95 percent confidence interval is 2.045. A sample of 30 has a mean of 2 and a standard deviation of 20. The confidence interval is closest to:
View answer and explanationSystematic sampling involves:
View answer and explanationWhich sampling method is often used in bond indexing to approximate the index without purchasing every bond?
View answer and explanationIn the context of sampling distributions, the standard error decreases when:
View answer and explanationWhen using the t-distribution, if the degrees of freedom increase, the confidence interval for a given significance level will:
View answer and explanationA 99 percent confidence interval using the z-statistic includes the mean plus or minus:
View answer and explanationSuppose a researcher tests a trading rule using the same database repeatedly until a significant result is found. This is an example of:
View answer and explanationUsing a price-to-book ratio based on year-end prices and year-end book values (available months later) to test a trading strategy is an example of:
View answer and explanationIf a study covers a time period where a fundamental structural change occurred (e.g., changing inflation dynamics), the study may suffer from:
View answer and explanationConvenience sampling is best described as:
View answer and explanationWhich of the following is NOT a desirable property of an estimator?
View answer and explanationTo calculate the standard error of the sample mean when the population variance is known, one divides the population standard deviation by:
View answer and explanation