Chapter 7 - Hypothesis Testing Flashcards
What is the null hypothesis?
✯ What we assume to be correct is the null hypothesis.
What is the alternative hypothesis?
✯ The alternative hypothesis is what we are trying to test. It tells us about the parameter when our assumption is shown to be wrong.
What is the test statistic?
✯ The statistic calculated from a sample taken from the population is called the test statistic. It is used to test a hypothesis.
What is a hypothesis?
✯ A hypothesis is a statement made about the value of a population parameter.
What is a hypothesis test?
✯ A hypothesis test uses a sample or an experiment to determine whether or not to reject the hypothesis.
What assumption is made for test statistic?
✯ An assumption is made that the test statistic can be modelled by a binomial distribution
What is a Critical Region?
✯ Critical Region – A critical region is a region of the probability distribution which, if the test statistic falls within it, would cause you to reject the null hypothesis.
What is a Critical Value?
✯ Critical Value – The critical value is the first value to fall inside of the critical region.
What is an Acceptance Region?
✯ Acceptance region – The region where we accept the null hypothesis, the range of values outside of the critical region.
What should we look out for in terms of significance level in two tailed tests?
✯ In a two-tailed test we must take the significance level and divide it by 2.
To find the overall critical region of a two-tailed test, what must we do?
✯ Lower critical values (where p<…) and upper critical values (where p>…) must be calculated to find the overall critical region of a two-tailed test.
How can we find the actual significance level?
✯ Actual significance level = P (critical region)
✯ Do not forget to multiply by 100 to give the final answer of the actual significance level!
What is the definition of the actual significance level?
✯ The actual significance level of a hypothesis test is the probability of incorrectly rejecting the null hypothesis.
What are the five steps that must be taken for one tailed tests?
- State the test statistic
- State the distribution for X
- State the null and alternative hypotheses.
- Find the probability and compare it with the significance level.
- State the conclusion in context.
What is the differnece between two tailed and one tailed tests?
✯ A one-tailed test is used when it is claimed that the probability has either gone up or gone down, in other words, whether we are certain we know it is going in a certain direction.
✯ However, a two-tailed test is used when it is thought that the probability has changed in either direction, and thus we are uncertain of the direction.
What is the expected value?
E(x)
In X~B (n,p), a binomial distribution model.
✯ n multiplied by p (np) = E(x)
If X~B (n,p) is the observed value, then, what two different scenarios would occur?
- If x< E(x), find P (X ≤ x)
or..
- If x > E(x), find P (X ≥x)
