## Math 113: Study Guide - Chapters 7 - 8

Problems 1 - 8 are definition / description problems. Some answers may be repeated. Some answers are not used. You should know the definitions / descriptions of:

• Null Hypothesis
• Alternative Hypothesis
• Level of Significance / Significance Level
• Type I Error
• Type II Error
• Critical Value
• Test Statistic
• Independent Samples
• Dependent Samples

Problems 9 - 15 are fill in the blank. You should know:

• What the probability-value means.
• How to make a decision based on the probability value.
• How to tell which type of test (left, right, or two-tailed) you have.
• The default value used for the level of significance.
• What you're rejecting or failing to reject in the decision (null or alternative hypothesis)?
• What rejecting or failing to reject the null hypothesis means in terms of the conclusion (sufficient or insufficient evidence).
• What the original claim means in term of the conclusion (reject the claim or support the claim).

• Know what assumption is central to hypothesis testing.

Problems 17 - 25 are true / false. Concentrate on:

• Using the probability value with new tests that you've never seen before (like the F-test was in class). That is - can you make a decision without knowing anything about the distribution?
• What two things are compared to reach a decision when using the classical approach to hypothesis testing?
• What are the definitions of level of significance and probability-value in terms of area under the curve. That is, what are the values that define the starting point for each.
• Know the relationship between the probability value for a one-tail test and a two-tail test.
• Know the general form of test statistics = ( observed - expected ) / standard error
• The mean of the distributions.
• When the binomial can be approximated using the normal.
• Know what the ratio of two independent chi-square variables divided by their respective degrees of freedom is.
• Know that a sample must be from an essentially normal distribution to use the student's t (page 378, item 3b), chi-square (page 396 - assumption in blue box), and F (page 436, item 2) distributions

Problems 26 and 27 are to use the normal and or student's t table to look up a probability-value when the test statistic is known (read section on p-values on pages 382-383, especially the first example) and finding the critical value.

Problem 28 is to write the null and alternative hypotheses for the given claim. The claim could be about one or two means, proportions, variances or standard deviations. Also identify whether the test is a left-tailed, right-tailed, or two-tailed test (based on the alternative hypothesis). Five parts.

Problem 29 is to write the decision (Reject the null hypothesis or Fail to reject the null hypothesis). Also identify whether the test is left-tailed, right-tailed, or two-tailed if possible - it won't be possible from just a p-value. You can tell the type of test by looking at the critical value and it's relationship to the mean for that distribution. If the critical value is less than the mean, it's a left tail test; if it's greater than the mean, it's a right tail test; if there are two critical values, it's a two-tailed test. You should know the means of all the distributions. Five parts.

Problem 30 is to write the distribution that the test statistic would have. This is where you need to know when to use Z as opposed to T (is sigma known? is n large?). Also know that chi-square is used for a single variance and F for two variances.

Problem 31 is to take the output from a statistical test you've never seen before and determine if the results are significant or not. Basically, do you understand p-values?

Problem 32 is a normal probability plot. We called it a Q-Q Plot with the calculator program. Basically, the data is approximately normal if the q-q plot doesn't deviate too much from a line.

Problem 33 is to take the output from Excel and answer the questions about the hypothesis test based on the output. Concentrate on the difference of the means with small sample sizes (the ones where you have to do an F-test first) and how to use p-values.