Math 217, Fall 2008
Final Exam Information
Our final exam is scheduled for Thursday 12/11, 2 pm, in CFA 107. To prepare for the exam, you should read, and work to understand, the following sections: 6.1, 6.2, 6.3, 7.1. Also review the relevant homework exercises and related class work. Some of the key concepts are shown in the outline below.
Section 6.1: Introduction to Confidence Intervals for a Mean What is the purpose of a confidence interval?
What is the exact meaning of the confidence level?
What is the basic form of a confidence interval?
How is the margin of error of a confidence interval affected by the confidence level? by the sample size? by the population standard deviation? See cautions p.393.
Section 6.2: Introduction to Significance Testing for a Mean What is the purpose of a test of significance?
What is the exact meaning of the P-value?
How do you use the STAT > TESTS menu for Z-intervals and Z-tests? [optional] What should you conclude from a significance test? Note:
The null hypothesis is never established or proven; when P is large we simply fail to refute the null hypothesis. The alternative hypothesis is never proven false or refuted; when P is large we simply do not have enough evidence to convince us the alternative is true.
Section 6.3: Use and Abuse of Statistical Tests
Under what circumstances are the Z procedures in chapter 6 valid and appropriate? Consider the context when choosing a level of significance. Note that .05 is not a magical or sacred cut-off for significance: P = .0501 is about as significant as P = .0499. Formal statistical inference cannot correct basic flaws in experimental design and data collection. You cannot legitimately test a hypothesis on the same data that first suggested that hypothesis – you have to design a study specifically to test for the effect you now believe exists. Statistical significance is different than practical significance (importance). If you perform repeated testing and occasionally find significance (say, P < .05 about 5% of the time or less) then those tests probably show significance just due to luck! We expect P to come out small now and then just due to random sampling error, even when the null hypothesis is true.
Section 7.1: Inference for the Mean of a Population
Standard error of the sample mean is SE = , which estimates the standard deviation of the sampling distribution of the sample mean (know the SE formula). The t distributions: How do you determine the degrees of freedom? How do the t distributions compare with the standard normal? How do you use Table D to find critical values (t*) and P values? When is it correct to use the one-sample t confidence interval for a population mean? What is the margin of error? How does it compare with the Z interval from chapter 6? The one-sample t test: How does it compare with the Z test from 6.2? When is it correct to use this procedure? How do you use the STAT > TESTS menu for t-intervals and t-tests? [optional] How are the t procedures used to analyze data from matched pairs?
p.396, #1-31 ODDS ONLY (formula sheet)
p.416, #33-49, 55, 57, 61-71 ODDS ONLY (formula sheet)
p.428, #72-84 (evens & odds)
n/a (study for exam)
p.471, #6abc, 7abc, 10bce, 11, 12, 13, 16, 17, 20, 21, 29, 34, 35, 37b (SEE GRAPHS AND TABLES) (formula sheet) Fri 12-5-08
1. In a study of possible iron deficiency in infants, researchers compared several groups of infants who were following different feeding patterns. One group of 26 infants was being breast-fed. At 6 months of age, these children had a mean hemoglobin level of grams per 100 milliliters of blood and a standard deviation of 1.6 grams per 100 milliliters of blood. (a) Give a 95% confidence interval for the mean hemoglobin level of breast-fed infants. (b) What assumptions are required for the...
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