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To determine a confidence interval around the predicted value from a simple linear regression, the appropriate degrees of freedom are:

n – 2.

An analyst announces that an increase in the discount rate next quarter will double her earnings forecast for a firm. This is an example of a:

conditional expectation.

The technique in which a machine learns to model a set of output data from a given set of inputs is best described as:

supervised learning.

Tina O'Fahey, CFA, believes a stock's price in the next quarter depends on two factors: the direction of the overall market and whether the company's next earnings report is good or poor. The possible outcomes and some probabilities are illustrated in the tree diagram shown below:
Based on this tree diagram, the expected value of the stock if the market decreases is closest to:

$57.00.

A researcher wants to test whether the weekly returns on two stocks are correlated. The test statistic for the appropriate test follows a:

t-distribution with n − 2 degrees of freedom.

Which of the following statements regarding the distribution of returns used for asset pricing models is most accurate?

Lognormal distribution returns are used for asset pricing models because they will not result in an asset return of less than -100%.

An executive describes her company's "low latency, multiple terabyte" requirements for managing Big Data. To which characteristics of Big Data is the executive referring?

Volume and velocity.

John purchased 60% of the stocks in a portfolio, while Andrew purchased the other 40%. Half of John's stock-picks are considered good, while a fourth of Andrew's are considered to be good. If a randomly chosen stock is a good one, what is the probability John selected it?

0.75.

Thomas Merton, a car industry analyst, wants to investigate a relationship between the types of ads used in advertising campaigns and sales to customers in certain age groups. In order to make sure he includes manufacturers of all sizes, Merton divides the industry into four size groups and draws random samples from each group. What sampling method is Merton using?

Stratified random sampling.

Which of the following is least likely an assumption of linear regression?

The error terms from a regression are positively correlated.

A test of independence based on contingency table data uses a(n):

chi-square statistic.

A simple linear regression is a model of the relationship between:

one dependent variable and one independent variable.

The strength of the relationship, as measured by the correlation coefficient, between the return on mid-cap stocks and the return on the S&P 500 for the period under study was:

0.774.

Which of the following is least likely a prediction of the central limit theorem?

The standard error of the sample mean will increase as the sample size increases.

In bootstrap resampling, a single observation from a full dataset:

may appear in multiple samples.

To account for logarithmic variables, functional forms of simple linear regressions are available if:

either or both of the dependent and independent variables are logarithmic.

There is a 40% probability that an investment will earn 10%, a 40% probability that the investment will earn 12.5%, and a 20% probability that the investment will earn 30%. What are the mean expected return and the standard deviation of expected returns, respectively?

15.0%; 7.58%.

A large investment company uses an enterprise risk management framework to assess the various risks in its organization. Some of the tools it uses to assess its risks include scenario analysis and simulations, which typically involve:

large amounts of quantitative and qualitative data.

According to the Central Limit Theorem, the distribution of the sample means is approximately normal if:

the sample size n > 30.

Which of the following statements describes a limitation of Monte Carlo simulation?

Outcomes of a simulation can only be as accurate as the inputs to the model.

Which of the following statements most accurately describes a data processing method?

Curation focuses on data quality and accuracy through data cleaning.

An auditor who decides to handpick rather than randomly select transactions to examine for instances of fraud is most likely using:

judgmental sampling.

In a test of independence based on contingency table data, degrees of freedom are the:

product of the number of rows minus one and the number of columns, minus one.

An investor is considering purchasing ACQ. There is a 30% probability that ACQ will be acquired in the next two months. If ACQ is acquired, there is a 40% probability of earning a 30% return on the investment and a 60% probability of earning 25%. If ACQ is not acquired, the expected return is 12%. What is the expected return on this investment?

16.5%.

A test of the hypothesis that two categorical variables are independent is most likely to employ:

contingency tables.

Which of the following statements regarding the central limit theorem (CLT) is least accurate? The CLT:

states that for a population with mean µ and variance σ², the sampling distribution of the sample means for any sample of size n will be approximately normally distributed.

Which of the following is least likely a step in stratified random sampling?

The size of each sub-sample is selected to be the same across strata.

Use the following data to calculate the standard deviation of the return:

• 50% chance of a 12% return

• 30% chance of a 10% return

• 20% chance of a 15% return

1.7%.

An advantage of the bootstrap method of estimating the standard error of sample means, compared to estimating it based on a sample variance, is that the bootstrap method:

can be applied to complex statistics.

Stratified random sampling is most often used to preserve the distribution of risk factors when creating a portfolio to track an index of:

corporate bonds.

A conditional expectation involves:

refining a forecast because of the occurrence of some other event.

An economist estimates a 60% probability that the economy will expand next year. The technology sector has a 70% probability of outperforming the market if the economy expands and a 10% probability of outperforming the market if the economy does not expand. Given the new information that the technology sector will not outperform the market, the probability that the economy will not expand is closest to:

67%.

The central limit theorem states that, for any distribution with a finite mean and variance, as n gets larger, the sampling distribution:

approaches a normal distribution.

An analyst expects that 20% of all publicly traded companies will experience a decline in earnings next year. The analyst has developed a ratio to help forecast this decline. If the company has a decline in earnings, there is a 90% probability that this ratio will be negative. If the company does not have a decline in earnings, there is only a 10% probability that the ratio will be negative. The analyst randomly selects a company with a negative ratio. Based on Bayes' theorem, the updated probability that the company will experience a decline is:

69%.

For a test of independence based on contingency table data, the test statistic is calculated as the:

sum of squared differences between each table cell’s actual value and its expected value, if the two characteristics are independent.

To test a hypothesis that the population correlation coefficient of two variables is equal to zero, an analyst collects a sample of 24 observations and calculates a sample correlation coefficient of 0.37. Can the analyst test this hypothesis using only these two inputs?

Yes.

In a simple regression model, the least squares criterion is to minimize the sum of squared differences between:

the predicted and actual values of the dependent variable.

When resampling is done, the subsamples that are repeatedly drawn from the original observed samples will:

remain the same size.

If a random variable x is lognormally distributed then ln x is:

normally distributed.

Which of the following statements is most accurate regarding the dataset and samples used in bootstrap resampling?

The full dataset is used, and the samples are all the same size.

One of the major limitations of Monte Carlo simulation is that it:

cannot provide the insight that analytic methods can.

Suppose the mean debt/equity ratio of the population of all banks in the United States is 20 and the population variance is 25. A banking industry analyst uses a computer program to select a random sample of 50 banks from this population and compute the sample mean. The program repeats this exercise 1000 times and computes the sample mean each time. According to the central limit theorem, the sampling distribution of the 1000 sample means will be approximately normal if the population of bank debt/equity ratios has:

any probability distribution.

An equity analyst needs to select a representative sample of manufacturing stocks. Starting with the population of all publicly traded manufacturing stocks, she classifies each stock into one of the 20 industry groups that form the Index of Industrial Production for the manufacturing industry. She then selects four stocks from each industry. The sampling method the analyst is using is best characterized as:

stratified random sampling.

There is a 60% chance that the economy will be good next year and a 40% chance that it will be bad. If the economy is good, there is a 70% chance that XYZ Incorporated will have EPS of $5.00 and a 30% chance that their earnings will be $3.50. If the economy is bad, there is an 80% chance that XYZ Incorporated will have EPS of $1.50 and a 20% chance that their earnings will be $1.00. What is the firm's expected EPS?

$3.29.

Given the relationship: Y = 2.83 + 1.5X

What is the predicted value of the dependent variable when the value of the independent variable equals 2?

5.83.

A simple linear regression is said to exhibit heteroskedasticity if its residual term:

does not have a constant variance.

Based on a sample correlation coefficient of −0.525 from a sample size of 19, an analyst calculates a t-statistic of −0.525√19−2√1−(−0.525)2 = −2.5433. The analyst can reject the hypothesis that the population correlation coefficient equals zero:

at a 5% significance level, but not at a 2% significance level.

Which of the following statements about fintech is most accurate?

Fintech companies include those that develop technology for the financial services industry.

Consider the following analysis of variance (ANOVA) table:

The F-statistic for the test of the fit of the model is closest to:

27.87.

Bill Phillips is developing a Monte Carlo simulation to value a complex and thinly traded security. Phillips wants to model one input variable to have negative skewness and a second input variable to have positive excess kurtosis. In a Monte Carlo simulation, Phillips can appropriately use:

both of these variables.

The probability of A is 0.4. The probability of A^C is 0.6. The probability of (B | A) is 0.5, and the probability of (B | A^C) is 0.2. Using Bayes' formula, what is the probability of (A | B)?

0.625.

The estimated slope coefficient in a simple linear regression is:

the ratio of the covariance of the regression variables to the variance of the independent variable.

When there is a linear relationship between an independent variable and the relative change in the dependent variable, the most appropriate model for a simple regression is:

the log-lin model.

A researcher wants to test a hypothesis that two variables have a population correlation coefficient equal to zero. For a sample size of 30, the appropriate critical value for this test is plus-or-minus:

2.048.

In linear regression, an indicator variable is best described as a variable whose values:

must equal zero or one.

The coefficient of determination for a linear regression is best described as the:

percentage of the variation in the dependent variable explained by the variation of the independent variable.

Artificial intelligence is best described as:

computer systems that emulate human thinking.

Which of the following uses of data is most accurately described as curation?

An analyst adjusts daily stock index data from two countries for their different market holidays.

Which technique for estimating the standard error of the sample mean involves calculating multiple means from the same sample, each with one observation removed from the sample?

Jackknife.

Under which of these conditions is a machine learning model said to be underfit?

The model treats true parameters as noise.

An analyst is asked to select a sample of securities from those included in a broad-based index that can be expected to have the same return as the index while preserving the key risk exposures of the index. The analyst should most appropriately use:

stratified random sampling.

Monte Carlo simulation is necessary to:

approximate solutions to complex problems.

A lognormal distribution is least likely to be:

negatively skewed.

To estimate the average time Level I CFA candidates spend preparing for the exam, an employee of ABC Investments decides to randomly survey candidates who work at ABC's offices, although he is unsure how well they represent the candidate population. This is most likely an example of:

convenience sampling.

A data analyst uses fintech to evaluate the number of times the words buy or sell appear in a company's quarterly filings in a given fiscal year. This is most likely an example of which form of fintech?

Text analytics.

If random variable Y follows a lognormal distribution then the natural log of Y must be:

normally distributed.

An analyst divides the population of U.S. stocks into 10 equally sized sub-samples based on market value of equity. Then he takes a random sample of 50 from each of the 10 sub-samples and pools the data to create a sample of 500. This is an example of:

stratified random sampling.

If the true mean of a population is 16.62, according to the central limit theorem, the mean of the distribution of sample means, for all possible sample sizes n will be:

16.62.

The goal of resampling and the use of subsamples is to estimate parameters for the:

overall population.

Consider the following analysis of variance (ANOVA) table:
The R² for this regression is closest to:

0.45

A two-sided but very thick coin is expected to land on its edge twice out of every 100 flips. And the probability of face up (heads) and the probability of face down (tails) are equal. When the coin is flipped, the prize is $1 for heads, $2 for tails, and $50 when the coin lands on its edge. What is the expected value of the prize on a single coin toss?

$2.47.

A parking lot has 100 red and blue cars in it.

• 40% of the cars are red.

• 70% of the red cars have radios.

• 80% of the blue cars have radios.

What is the probability that the car is red given that it has a radio?

37%.

The central limit theorem concerns the sampling distribution of the:

sample mean.

Tully Advisers, Inc., has determined four possible economic scenarios and has projected the portfolio returns for two portfolios for their client under each scenario. Tully's economist has estimated the probability of each scenario as shown in the table below. Given this information, what is the expected return on Portfolio A?

11.55%.

Bonds rated B have a 25% chance of default in five years. Bonds rated CCC have a 40% chance of default in five years. A portfolio consists of 30% B and 70% CCC-rated bonds. If a randomly selected bond defaults in a five-year period, what is the probability that it was a B-rated bond?

0.211.