Hypothesis Testing Flashcards
The six-step process of Hypothesis Testing
- state the hypothesis
- identify the appropriate test statistic and its probability distribution
- specify the significance level
- state the decision rule
- collect data and calculate the test statistic
- make a decision
Null hypothesis
- Ho
- what the researcher wants to reject
- contains the = component, <=, >=, =
Alternative hypothesis
- Ha
- what the researcher wants to prove
- if Ho is rejected, the Ha is considered valid
What is the Ho and Ha for:
Supposed you are a researcher and believe that the average return on all Asian stocks was greater than 2%.
- Ho: mue <= 2%
- Ha: mue > 2%
How to tell if a test will be left-sided or right-sided:
It comes down the the direction () of the Ha
- Right-side, “mue is greater than 2%” (>)
- Left-side, “mue is less than 2%” (
Left-side test symbol
- Ha less than symbol
Ha = Mue < x.
Right-side test symbol
- greater than
- Ha = Mue > x
Test statistic def
- the test stat is calculated from sample data and compared to a critical value to decide whether or not we can reject the null hypotheses
Test stat of a population formula:
test stat = sample stat - value of the parameter under Ho / std error
= ^x - mue / std/squrt n
What is the test stat formula for:
Draw 36 observations from a population and get a sample mean of 4. we are told that the std of the population is 4. if the hypothesized value of the pop mean is 2, the test stat is:
test stat = ^x - mue / std error
4 - 2 / (4 / sq rt of 36) = 6
Level of Significance
- reflects how much sample evidence is required to reject the null hypothesis
- ie. a=5%, there is a 5% chance of rejecting a true null hypothesis
Type I error
- we may reject a true null hypothesis
probability, significance level, a
Type I error
- we may reject a true null hypothesis
probability, significance level, a
Type II error
- we fail to reject a false null hypothesis
- denoted as (B)
- represents the probability of correctly rejecting the null when it is false
- P test, 1 - P, ie 1 - B
If we decrease the probability of a Type I error by using a smaller significance level (ie use a=1% vs a=5%), we increase the probability of a Type II error.
The only way to reduce both types of errors is by increasing the sample size, n
The critical value is also known as the …
- the rejection point for the test statistic
- a=5%, rejection point at z=1.645 on the bell curve
p-value
- “probability value”
- the smallest level of significance at which the null hypothesis can be rejected
If the p-value is lower than our specified level of significance, we…
p-value < significance level
- we reject the Ho, accept Ha
If p-value is greater than our specified level of significance, we…
p-value > level of significance
we do not reject the null
The power of test
- correctly accepting Ha when Ho is false
- calculated as (1-B)
The probability of a Type II error:
- denoted as B (beta)
Given a small sample (n<30) and Normal Distribution, which test is used when the variance is known?
- z test when variance is known
Given a small sample (n<30) and Normal Distribution, which test is used when the variance is unknown?
- t-test when the variance is unknown
Given a large sample (n>=30) and Normal Distribution, which test is used when the variance is known?
- z test when variance is known
Given a large sample (n>=30) and Normal Distribution, which test is used when the variance is unknown?
- either a t-test or z-test will work with a large sample and unknown variance
Given a small sample (n<30) and Non-Normal Distribution, which test is used when the variance is unknown?
- NA
Given a small sample (n<30) and Non-Normal Distribution, which test is used when the variance is known?
- NA
Given a large sample (n>30) and Non-Normal Distribution, which test is used when the variance is unknown?
- t-test or z-test when the sample is large and variance is unknown for a non-normal distribution
Given a large sample (n>=30) and Non-Normal Distribution, which test is used when the variance is known?
- z-test when the sample is large and variance is known for a non-normal distribution
A Chi-square test is used for:
- tests concerning the variance of a normally distributed population
- the graph is bound at zero
A F-Test is used for:
- testing the equality of two variances
- graph is bound at zero
assumes:
- samples must be independent
- the populations from which the samples are taken are normally distributed
