If X is Lognormal (ln), what type of distribution does it follow?
What is an easy way of remebering this?
Normal Distibution.
Log is normal (Lognormal)
What is used (multiplied by) to scale up volatility?
Square root of time.
What is the difference between Bootstrapping and Monte Carlo Simulation?
One is data driven and one is model driven.
- Bootstrapping resamples historical data to create new scenarios.
- Monte Carlo simulation generates outcomes using random numbers based on assumed probability distributions.
How is a Lognormal Distibution Skewed? and what is it bounded by?
A lognormal distribution is positively skewed and is bounded below by zero.
Are partial datasets used when bootstrap resampling?
No, the full data set is used.
What is a hypothesis in statistics?
A statement about the value of a population parameter, developed for testing a theory or belief.
What is the null hypothesis (H0)?
The hypothesis that the researcher wants to reject. It always includes ‘equal to’ and is tested directly.
What is the alternative hypothesis (Ha)?
The hypothesis concluded if H0 is rejected. It is usually what we are trying to prove.
What does it mean that H0 and Ha are mutually exclusive and exhaustive?
They cover all possible outcomes (exhaustive) and cannot both be true at the same time (mutually exclusive).
List the 7 steps of the hypothesis testing procedure.
1) State H0 and Ha
2) Select test statistic
3) Specify significance level
4) State decision rule
5) Collect sample and calculate statistic
6) Make decision vs. critical value or p-value
7) Conclude.
What is the rejection rule for a two-tailed z-test at α=0.05?
Reject H0 if test statistic < -1.96 or > +1.96.
What are the critical z-values for common significance levels?
±1.65 (10% two-tailed or 5% one-tailed), ±1.96 (5% two-tailed), ±2.33 (1% one-tailed), ±2.58 (1% two-tailed).
Formula for a test statistic when testing a mean?
(Sample statistic – Hypothesized value) / Standard error of sample statistic.
How is the standard error of the mean computed when σ is known?
σ / √n.
How is the standard error of the mean computed when σ is unknown?
s / √n, where s is the sample standard deviation.
What is a Type I error?
Rejecting H0 when it is actually true.
What is a Type II error?
Failing to reject H0 when it is actually false.
What does the significance level (α) represent?
The probability of making a Type I error.
What is the power of a test?
The probability of correctly rejecting a false null hypothesis. Power = 1 – P(Type II error).
How does lowering α affect Type II error and power?
Lower α reduces Type I error but increases Type II error and reduces power.
How can you increase the power of a test (holding α constant)?
Increase the sample size.
What are the possible decisions in hypothesis testing?
Reject H0 or Fail to reject H0 (never ‘accept H0’).
What is a p-value?
The probability of obtaining a test statistic that would lead to rejection of H0, assuming H0 is true. It is the smallest significance level at which H0 can be rejected.
When do you use a z-test instead of a t-test?
Use a z-test when the population variance (σ²) is known and the sample is large (n > 30). Use a t-test when σ² is unknown and the sample is small (n ≤ 30).
