Stats - 2

If we did a test for equality or inequality what would we use?

F distribution

Compared with historical simulation, Monte Carlo simulation is most appropriate when: probability distributions are unavailable. "what if" analysis is required. analytical methods are required.

"what if" analysis is required

Z ratio

(Xbar - u) / (std dev)

If a stock's continuously compounded return is normally distributed, then the distribution of the future stock price is best described as being: normal. a Student's t. lognormal.

lognormal.

A random number between zero and one is generated according to a continuous uniform distribution. What is the probability that the first number generated will have a value of exactly 0.30? 0% 30% 70%

0%

Power of test

1 - Type II error

A hypothesis test for a normally-distributed population at a 0.05 significance level implies a: 95% probability of rejecting a true null hypothesis. 95% probability of a Type I error for a two-tailed test. 5% critical value rejection region in a tail of the distribution for a one-tailed test.

5% critical value rejection region in a tail of the distribution for a one-tailed test.

Intergenerational data mining

A form of data mining that applies information developed by previous researchers using a dataset to guide current research using the same or a related dataset.

Which of the following represents a correct statement about the p-value? The p-value offers less precise information than does the rejection points approach. A larger p-value provides stronger evidence in support of the alternative hypothesis. A p-value less than the specified level of significance leads to rejection of the null hypothesis.

A p-value less than the specified level of significance leads to rejection of the null hypothesis.

Which of the following assets most likely requires the use of a multivariate distribution for modeling returns? A call option on a bond A portfolio of technology stocks A stock in a market index

A portfolio of technology stocks

When doing a test concerning the variance of a single normally distributed population we would use A. Z B. T C. Chi squared

C.

definition of consistent

more accurate as the population increases

Type 2 error

Accepting null hypothesis when you should have rejected it false negative

Chi squared distribution is A. symmetrical B. asymmetrical

B. asymmetrical

In the step "stating a decision rule" in testing a hypothesis, which of the following elements must be specified? Critical value Power of a test Value of a test statistic

Critical value The critical value in a decision rule is the rejection point for the test. It is the point with which the test statistic is compared to determine whether to reject the null hypothesis, which is part of the fourth step in hypothesis testing.

definition of efficiency

If no other estimator of te same parameter has a sampling distribution with a smaller variance

An analyst is examining a large sample with an unknown population variance. To test the hypothesis that the historical average return on an index is less than or equal to 6%, which of the following is the most appropriate test? One-tailed z-test Two-tailed z-test One-tailed F-test

One-tailed z-test

Type 1 error

Rejecting null hypothesis when it is true False positive

Which of the following statements about hypothesis testing is correct? The null hypothesis is the condition a researcher hopes to support. The alternative hypothesis is the proposition considered true without conclusive evidence to the contrary. The alternative hypothesis exhausts all potential parameter values not accounted for by the null hypothesis.

The alternative hypothesis exhausts all potential parameter values not accounted for by the null hypothesis.

Who has fatter tails? Z distribution or T

T distribution has fatter tails

T/F The null hypothesis is considered true unless the sample we use to conduct the hypothesis test gives convincing evidence that the null is false

TRUE

T/F if it is a non-normal distribution, even with variance know you cannot complete problem

TRUE

p-value

The probability level which forms basis for deciding if results are statistically significant (not due to chance).

In which of the following situations would a non-parametric test of a hypothesis most likely be used? The sample data are ranked according to magnitude. The sample data come from a normally distributed population. The test validity depends on many assumptions about the nature of the population.

The sample data are ranked according to magnitude.

Which of the following characteristics of an investment study most likely indicates time-period bias? The study is based on a short time-series. Information not available on the test date is used. A structural change occurred prior to the start of the study's time series.

The study is based on a short time-series. A short time series is likely to give period-specific results that may not reflect a longer time period.

Central Limit Theorem

The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.

A population has a non-normal distribution with mean µ and variance σ2. The sampling distribution of the sample mean computed from samples of large size from that population will have: the same distribution as the population distribution. its mean approximately equal to the population mean. its variance approximately equal to the population variance.

its mean approximately equal to the population mean. distribution doesn't matter.

t or Z? normal distribution with variance KNOWN

Z

An analyst is examining the monthly returns for two funds over one year. Both funds' returns are non-normally distributed. To test whether the mean return of one fund is greater than the mean return of the other fund, the analyst can use: a parametric test only. a nonparametric test only. both parametric and nonparametric tests.

a nonparametric test only.

In generating an estimate of a population parameter, a larger sample size is most likely to improve the estimator's: consistency. unbiasedness. efficiency.

consistency.

A pooled estimator is used when testing a hypothesis concerning the: equality of the variances of two normally distributed populations. difference between the means of two at least approximately normally distributed populations with unknown but assumed equal variances. difference between the means of two at least approximately normally distributed populations with unknown and assumed unequal variances.

difference between the means of two at least approximately normally distributed populations with unknown but assumed equal variances.

The sampling error is best described as the: sample standard deviation divided by the square root of the sample size. difference between the observed value of a statistic and the quantity it is intended to estimate. sum of squared deviations from the mean divided by the sample size minus one.

difference between the observed value of a statistic and the quantity it is intended to estimate.

When making a decision in investments involving a statistically significant result, the: economic result should be presumed meaningful. statistical result should take priority over economic considerations. economic logic for the future relevance of the result should be further explored.

economic logic for the future relevance of the result should be further explored.

Simple Random Sampling

every member of the population has an equal probability of being selected for the sample

When flipping three coins simultaneously, the number of outcomes that contain at least two heads is most likely: eight. four. three.

four.

data mining bias

from repeatedly doing tests on the same data sample

In contrast to normal distributions, lognormal distributions: are skewed to the left. have outcomes that cannot be negative. are more suitable for describing asset returns than asset prices.

have outcomes that cannot be negative.

The alterantive hypothesis is the one you write as the A. hoped for condition B. not hoped for condition

hoped for condition

A limitation of Monte Carlo simulation is: its failure to do "what if" analysis. that it requires historical records of returns its inability to independently specify cause-and-effect relationships.

its inability to independently specify cause-and-effect relationships.

Look ahead bias

occurs when a study tests a relationship using sample data that was not available on the test date.

Unbiased estimator

one whose expected value equals the parameter it is intended to estimate

Best way to investigate data mining?

out of sample test

When evaluating mean differences between two dependent samples, the most appropriate test is a: chi-square test. paired comparisons test. z-test.

paired comparisons test.

Confidence interval formula

point estimate +/- reliability factor * standard of error or point estimate +/- margin of error

Time period bias

relationship exists only during the time period of sample data

Stratified Random Sampling

separation of the target population into different groups, called strata, and the selection of samples from each stratum

Standard error calculation

std deviation / sqroot(n)

t or Z? normal distribution with variance UNKNOWN

t

A Monte Carlo simulation can be used to: directly provide precise valuations of call options. simulate a process from historical records of returns. test the sensitivity of a model to changes in assumptions.

test the sensitivity of a model to changes in assumptions.

Type 1 error is also known as

the level of significance or alpha

Power of the test

the probability of rejecting the null when it is false correctly rejecting the null

standard error

the standard deviation of a sampling distribution