Hypothesis Testing Flashcards
When Would the T-Distribution be Used?
When the population Standard Deviation is unknown.
Use N-1 degrees of freedom
What May or May not Effect Our Decision Rule?
1) sample size is very big, does not make much difference if t or z is used.
2) sample size < 100, population must follow normal distribution for test to be valid.
When Should H0 be Accepted?
Decision Rule: accept H0 if sample value < critical value.
There is not enough evidence to disprove it at relevant significance level.
How to find the Sample t-Value:
(x̄ - μ) / SE(x̄ )
SE(x̄) = S / √𝑁
What is Type 1 Error?
When H0 is rejected, even though it is true.
What is Type 2 Error?
To accept H0 when H1 is true.
How can the Chance of a Type 2 Error be Reduce Without Increasing the Chance of a Type 1 Error?
Increase N, so SE(x̄) decreases and value of the sample t-value increases.
OR
Use a 1-tail instead of 2-tail test. More likely to reject H0 is H1 is true.
What is the Decision Rule when Working with Confidence Intervals?
Reject H0 if sample value is outside the confidence interval for the mean.
What is the Main Disadvantage of Using the Confidence Interval?
Cannot easily be applied to 1-tail test.
How does Confidence Interval Relate to Classical Approach for 2-Tail Tests?
95% CI = 5% sig fig (CA)
90% CI = 10% sig fig (CA)
What is the P-Value Approach?
P-value gives lowest possible significance level at which you would reject H0.
For a positive sample t-value, p-value is the total probability to the right of the sample value.
If 2-tail test, p-value x 2.
P-value < sig fig, reject H0.
How to Know Whether Power Increases or Decreases
If probability of a type 1 error increases, probability of a type 2 error decreases and power of test increases.
Power = 1 - probability of type 2 error.
How Does Using a 1-tail or 2-tail test effect the Power?
2-tail rejection area smaller, so less likely to reject H0 when H1 is true. Decreases power.
