Math 113: Study Guide - Chapters 7 - 8

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Problems 1 - 11 are matching definition 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
• Level of Confidence
• Probability Value
• Type I Error
• Type II Error
• Critical Region
• Critical Value
• Test Statistic
• Independent Samples
• Dependent Samples

Problem 12 - Know the assumption fundamental to all hypothesis testing.

Problem 13 is to complete the conclusion to a test. There is (sufficient/insufficient) evidence to (reject/support) the claim.

Problems 14 - 22 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 23 and 24 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 25 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 26 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 27 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.

Problems 28-30 are hypothesis tests that are to be worked out on Statdisk. Identify which test on Statdisk you selected. Also write the claim, the critical value(s), test statistic, p-value, decision, and conclusion.

#	1	2	3	4	5	6	7	8	9	10
Pts	2	2	2	2	2	2	2	2	2	2
#	11	12	13	14	15	16	17	18	19	20
Pts	2	3	4	2	2	2	2	2	2	2
#	21	22	23	24	25	26	27	28	29	30
Pts	2	2	2	2	10	10	4	7	9	9