Study Guide for Exam 1 ~ STAT 110



Study Guide for Exam 2 ~ STAT 210

Chapter 8 & 11 ~ Normal Distribution and Central Limit Theorems

(Note: Book refers to these as

The Law of Averages)

• Given X ~ N([pic]) be able to find probabilities and quantiles associated with X.

Practice Problems: 8.11, 8.13

• Normal approximation to the Binomial Distribution.

Practice Problems: 8.29, 8.43, 8.49

[pic] provided n is sufficiently large ([pic]).

• Know what the central limit theorem for the sample proportion says and how to apply it.

Practice Problem: 11.37

[pic] provided n is sufficiently large ([pic]).

• Know what the central limit theorem for the SUM says and how to apply it.

Practice Problems: 11.40, 11.41, 11.43

[pic] provided X is normal to begin with or n is “large”[pic].

• Know what the central limit theorem for the sample means says and how to apply it.

Practice Problems: 12.5

[pic] provided X is normal to begin with or n is “large”[pic].

Chapter 12 – z and t Tests of Hypotheses

• Be able to conduct a z-test “by hand”. Specifically be able to set up the hypotheses to be tested, compute the test statistic, find the associated p-value and state your conclusions correctly using both in statistical and non-statistical terms.

Practice Problems: 12.5, 12.17

• Be able to answer the question: “What the hell is a p-value anyway?”

• Be able to interpret output from a t-test conducted in JMP and interpret output from the t-Probability calculator. This includes being able to read a normal quantile plot.

Chapter 13 – Estimation with Confidence (Confidence Intervals)

• Be able to construct and interpret a 100(1-2α)% CI for a population mean ([pic]) using the t-table in your text to find the appropriate

t-quantile, e.g. [pic].

[pic] (two-sided)

[pic] (one-sided upper)

[pic] (one-sided lower)

Practice Problems:

13.11, 13.13, 13.15 (a.) [pic], 13.41,

13.51. 13.53

• Be able to construct and interpret a 100(1-2α)% CI for a population proportion ([pic]). You only need to know the large sample case:

[pic] (two-sided)

[pic] (one-sided upper)

[pic] (one-sided lower)

Practice Problems: 13.29, 13.49

• Given an estimate of [pic] you should be able to determine the sample size needed to have a given margin of error when estimating the mean with a 100(1-2α)% CI. (see pages 367-368)

Required sample size [pic]

Practice Problems: 13.19, 13.21

• You should be able to determine the sample size needed to have a given margin of error when estimating the population proportion with a 100(1-2α)% CI. (see pages 371-372)

Required sample size [pic] (conservative)

Required sample size [pic] (prior knowledge for π)

Practice Problem: 13.27

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