11.1: Hypothesis Tests and Types of Errors Flashcards
What is a hypothesis?
A hypothesis is a statement about the value of a population parameter developed for the purpose of testing a theory or belief.
What is the hypothesis testing procedure? State the hypothesis testing procedure (7).
Hypothesis testing procedures is based on sample statistics and probability theory and are used to determine whether a hypothesis is a reasonable statement and should not be rejected or if it is an unreasonable statement and should be rejected.
- State the hypothesis
- Select the appropriate test statistic
- Specify the level of significance
- State the decision rule regarding the hypothesis
- Collect the sample and calculate the sample statistics
- Make a decision regarding the hypothesis
- Make a decision based on the results of the test
What is the null hypothesis?
The null hypothesis, designated as H0, is the hypothesis that the researcher wants to reject that is actually tested.
Null hypothesis is always the “equal to” condition.
Which type of hypothesis always includes the “equal to” condition?
Null hypothesis
What is alternative hypothesis? What is a one-tailed test? Two-tailed?
Alternative hypothesis is what is concluded if there is sufficient evidence to reject the null hypothesis. It can be one-sided or two-sided.
One-sided test is a one-tailed test.
Two-sided test is a two-tailed test, which uses two critical values (rejection points).
What is the general decision rule for a two-tailed hypothesis test?
Reject the null hypothesis if:
test statistic > upper critical value
test statistic < lower critical value
What is the general decision rule for a one-tailed hypothesis test?
Opposite of what the null hypothesis purposes.
How is the test statistic computed?
Test statistic = sample statistic - hypothesized value over the standard error of the sample statistic.
What is a Type I error?
Type I error is rejecting the null hypothesis when it is true.
What is a Type II error?
Type II error is the failure to reject the null hypothesis when it is actually false.
What is significance level? Explain with a significance level of 5%.
What happens when the significance level is decreased?
Significance level is the probability of making a Type I error (rejecting null hypothesis when it is actually true).
A significance level of 5% means that there is a 5% chance of rejecting a true null hypothesis.
When significance level is decreased, the probability of Type II error will increase and therefore reduce the p
What is the decision rule?
The decision rule for rejecting or failing to reject the null hypothesis is based on the distribution of the test statistic. It is specific and quantitative, which states that if the test statistic is greater or less than the value X, reject the null.
What is the power of a test?
Power of a test is the probability of correctly rejecting the null hypothesis when it is false, which is stated as 1 - Type II error such that the probability of rejecting the null when it is false equals to one minus the probability of not rejecting the null when it is false.
What determines the probability of a Type II error?
Sample size and the choice of significance level will together determine the probability of a Type II error.
What happens when sample size is increased for a given significance level?
Type II error is decreased and the power of a test is increased.
