Download Math 12 Elementary Statistics Marcella Laddon, Instructor

Math 12 Elementary Statistics
Marcella Laddon, Instructor
Review for Exam 3: Ch. 7 – 8
Reminder: You will be provided the “Formulas and Tables” handout as at the first exam. In addition,
you may bring a 3”x5” index card with any notes you like (both sides). As always, your calculator can
help you with many of the calculations.
Chapter 7 – Estimates and Sample Sizes
7-2
Vocabulary: point estimate, confidence interval, confidence level, critical value.
• Know that pˆ = x / n and x= n ⋅ pˆ . Round x to a whole number when using the calculator.
• Be able to interpret a confidence interval correctly (“We are 95% confident that…”). When
two confidence intervals overlap we cannot conclude equality of the population parameters
(proportion or mean). When two confidence intervals do not overlap, we can then reasonably
conclude that the population parameters are different.
• The confidence level (90%, 95%, etc) is one way of stating how much area we want in the center
part of our distribution (.90, .95, etc). The critical values will then force the remaining area to be
equally divided between the two tails, thus the notation zα 2 .
•
•
•
Find a margin of error using the formula or your calculator.
Use the formulas for sample size (and to know when to use each of the two formulas – it
depends on whether we have a sample proportion p or not). Sample sizes are always rounded up
to the next whole number.
Calculator: 1-PropZInt, possibly in combination with invNorm (or Table A-2).
•
•
•
This section is similar to 7.2, only here we discuss estimating a population mean instead of a
proportion. In this section we must be given the population standard deviation ( σ ). Other
assumptions: 1) the sample is a simple random sample and 2) either the population is normally
distributed and/or n > 30.
We use the normal distribution in this section.
Be able to find the sample size using the formula.
Calculator: Z-Interval, possibly in combination with invNorm (or Table A-2).
7-3
7-4
•
•
7-5
In this section we are again estimating a population mean, only now we do not know σ .
Assumptions: 1) the sample is a simple random sample and 2) either the population is normally
distributed and/or n > 30.
We must use the t distribution – either on your calculator, or from table A-3. Notice in
calculating with the t distribution, we must know the degrees of freedom = n – 1. It is dependent
on the sample size! Study the chart [p.367] for determining which distribution to use (we will not
address the nonparametric/bootstrapping methods).
Calculator: T-Interval, possibly in combination with PGRM  TINVRS83 (or Table A-3).
Here we estimate a population SD, using yet another distribution (the chi-square or χ 2 distribution). Assumptions: 1) sample is simple random, 2) the population is normally
distributed. Notice again we use the “degrees of freedom”, which is again n – 1.
Calculator: No quick interval function – use the formula, along with PGRM  CHINV83 (or
Table A-4). Be sure to use
when estimating σ (instead of σ 2 ).
“Chapter Review” p.388: Read, then try “Statistical Literacy and Critical Thinking” # 1 – 4 and
“Review Exercises” # 1 – 7.
Chapter 8 Hypothesis Testing – be sure to see the handout about how to show your work.
8-2
See the list of objectives near the beginning of this section and the example that follows. It is
an excellent summary of the section and much of the chapter. Note that the “Formulas and
Tables” handout has a useful page about p-values and wording conclusions!
Also in this section: Type I and Type II errors. Be able to state these errors in terms of a given
claim (I have a video that may help with this).
8-3
Be able to show the five steps in the handout (in Instructor Notes) when testing a claim about a
proportion using one of the methods: traditional or p-value. Notice the assumptions that are
made (similar to those in Ch.7).
Calculator: 1-PropZTest, possibly in combination with invNorm (or Table A-2).
8-4
Be able to test a claim about a mean when the population SD ( σ ) is known – note we use a zstatistic here. Again, know one of the methods as in 8.3 (traditional or p-value).
Calculator: Z-Test, possibly in combination with invNorm (or Table A-2).
8-5
Be able to test a claim about a mean when the population SD is not known – note we use a tstatistic here (review 7.4 about the t-distribution) – though again be careful with the assumptions.
Choose a method here, too! I see a pattern!
Calculator: T-Test, possibly in combination with PGRM  TINVRS83 (or Table A-3).
8-6
Be able to test a claim about a standard deviation or variance. Although the calculator will
not do quite as much for you here, you can easily find the test statistic from the formula. Use this
as needed in the testing process. Review 7.5 about the χ 2 -distribution.
Calculator: No quick test function – use the formula, along with PGRM  CHINV83 (or Table
A-4). It is possible to find the p-value using 2nd VARS  χ 2 cdf, but it is not necessary.
Again – I will be picky about how you show your work for a hypothesis test – study the handout
and practice!
“Chapter Review”: Read (Note the nice chart summarizing hypothesis testing so far!), then try “Review
Exercises” # 1 – 6, 9 – 12.
Be sure to get your lab activities done!