CAS MA 113 Study Guide - Final Guide: Dennis Wrong, Test Statistic, Statistical Hypothesis Testing
9 May 2018
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Study Guide for MA113 Final
This study guide covers chapters 10.1, 10.2, and 10.3 for the MA 113 final. Remember that the
final is cumulative, meaning that questions from previous chapters could appear on the exam.
This study guide is meant as a supplement to homework and textbook readings, as well as
previous study guides.
Part 1) Hypothesis Testing
Hypothesis Testing is the method we use to test theories about population parameters. We design
experiments such that the null hypothesis, , represents the theoretical parameter value we
want to prove/disprove, and the alternative hypothesis, , is some value that contradicts the
null hypothesis.
You can run 3 types of hypothesis tests:
Two-sided/Two-tailed
(for some constant c)
(we reject if our sample result it significantly higher or lower)
Right-tailed
(we reject if our sample result it significantly higher)
Left-tailed
(we reject if our sample result it significantly lower)
To test our hypothesis, we first assume the null hypothesis is correct. We then take a sample and
compute our corresponding parameter estimator from the sample. If the sample estimate is
significantly far from our hypothesized mean, we reject the null hypothesis. If the sample
estimate is NOT significantly far from the hypothesized mean, we fail to reject the null
hypothesis.
Formulas:
Hypothesis test for μ:
If we meet the conditions:
(a) Population is normally distributed or
(b) n ≥ 30
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Hypothesis test for p:
If we meet the condition:
(a) np(1-p) 10
Hypothesis test for :
If we meet the condition:
(a) Population is normally distributed
We can carry out hypothesis tests using either the Classical Approach or the p-value
Approach.
Classical Approach:
Step 1) Look up the critical value(s) for the test from the corresponding table
Note: The critical value(s) are the values that separate out the top α% of outliers. (see above
graphs)
Step 2) Compute the test statistic using the corresponding formula from above.
Step 3) Compare the critical value and the test statistic. The rejection rule changes based on what
kind of test you are running:
For a left-tailed test, you reject when the test statistic is less than the critical value.
For right-tailed test, you reject when the test statistic is greater than the critical value.
*Left-Tailed Test
*Right-Tailed Test
*Two-Tailed Test
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
This study guide covers chapters 10. 1, 10. 2, and 10. 3 for the ma 113 final. Remember that the final is cumulative, meaning that questions from previous chapters could appear on the exam. This study guide is meant as a supplement to homework and textbook readings, as well as previous study guides. Hypothesis testing is the method we use to test theories about population parameters. We design experiments such that the null hypothesis, (cid:2868), represents the theoretical parameter value we want to prove/disprove, and the alternative hypothesis, (cid:2869), is some value that contradicts the null hypothesis. You can run 3 types of hypothesis tests: Left-tailed (cid:2868):= (cid:2869):< (for some constant c) (we reject if our sample result it significantly higher or lower) (we reject if our sample result it significantly higher) (we reject if our sample result it significantly lower) To test our hypothesis, we first assume the null hypothesis is correct.
