Download exam ii review

MTH 265 – Statistics for Scientists and Engineers
EXAM II REVIEW
For this exam you may bring ONE 8.5 inch by 11 inch page of notes ONE SIDE ONLY. You may put any
formula on your note page. You may NOT put examples with solutions or any of our homework problems
with solutions on your page. Inappropriate items on your formula sheet will be removed before you take
your exam. Exam 2 will cover the following sections:
3.1
Measurement Error
 Be able to define and use the terms: systematic error, bias, random error, precision, accuracy, and
uncertainty. When can uncertainty be measured? When can accuracy be measured?
3.2
Linear Combinations of Measurements
 Be able to determine the mean, variance, and standard deviation of a constant multiple of a
random variable (given the mean and standard deviation of the random variable). See example
3.4.
 Be able to determine the mean, variance, and standard deviation of a linear combination of a set
of independent random variables (given the mean and standard deviation of the random
variables). See examples 3.5, 3.6, and 3.7.
 Be able to determine the mean, variance, and standard deviation of the mean of a random sample
from a population with known mean and standard deviation. See examples 3.8 and 3.9.
4.1
The Bernoulli Distribution
 Be able to find the distribution for a Bernoulli random variable. See examples 4.1, 4.2, and 4.3.
 Be able to calculate probabilities for a Bernoulli random variable.
 Be able to determine the mean, variance, and standard deviation for a Bernoulli random variable.
See example 4.4.
4.2
The Binomial Distribution
 Be able to find the distribution for a Binomial random variable. See example 4.5 and 4.6.
 Be able to calculate probabilities for a Binomial random variable. See examples 4.7, 4.8, 4.9, and
4.10.
 Be able to determine the mean, variance, and standard deviation for a Binomial random variable.
Formulas are at the top of page 208.
 Be able to calculate the sample proportion for a Binomial random variable and determine its
mean, variance, and standard deviation. See page 209 and example 4.12.
 Be able to find the size of a sample needed to guarantee a given uncertainty for the sample
proportion for a Binomial random variable. See example 4.13.
4.5
The Normal Distribution
 Be able to calculate the area under the normal curve (probabilities) for given values of the
standard normal variable Z. Use a table or your calculator. See example 4.41, 4.42, and 4.43.
 Be able to calculate percentiles for a standard normal random variable. See example 4.44.
 Be able to convert a normal random variable to a standard normal random variable. See example
4.45.
 Be able to calculate probabilities for any normal random variable given its mean and standard
deviation.
 Be able to calculate percentiles for a normal random variable.
 Be able determine the mean, variance, and standard deviation of a linear combination of
independent normal random variables. See top of page 248 and example 4.50.
 Be able calculate probabilities for a linear combination of independent normal random variables.
See example 4.51.
 Be able determine the mean, variance, and standard deviation for the sample mean of
independent and identically distributed normal random variables. See bottom of page 249.
4.11
The Central Limit Theorem
 Be able to use the Central Limit Theorem to determine the mean, variance, and standard
deviation for the sample mean of a simple random sample and be able to calculate probabilities
using them. See example 4.71.
5.1
Large-Sample Confidence Intervals for a Population Mean
 Be able to find two-sided and one-sided confidence intervals for the mean of a population using a
sample from a population with known mean and standard deviation. See examples 5.1, 5.2, 5.3,
and 5.9.
 Know how to interpret a confidence interval. Read page 328.
 Be able to find the level of a given confidence interval for the mean of a population. See example
5.4.
 Be able to find the size of the sample needed to obtain a given level of confidence for the mean of
a population. See example 5.8.
5.2
Confidence Intervals for Proportions
 Be able to find two-sided confidence intervals for the proportion of successes of a population
using a sample from independent Bernoulli trials. Use the formula that appears on page
339…NOT the one in the box on page 341. See example 5.12.
 Be able to find the level of a given confidence interval for the proportion of successes of a
population using a sample from independent Bernoulli trials.
 Be able to find the size of the sample needed to obtain a given level of confidence for the
proportion of successes of a population using a sample from independent Bernoulli trials. See
examples 5.13 and 5.14.
.
Small-Sample Confidence Intervals for a Population Mean
 Be able to probabilities involving the Student’s t distribution. See examples 5.15, 5.16, 5.17,
and 5.18.
 Be able to determine when the Student’s t distribution applies. Read page 344 and note the
summary at the top of page 345. Read page 348 and page 351.
 Be able to find two-sided confidence intervals and one-sided confidence bounds for the mean of a
population using a small sample. See the summary box on page 348. See example 5.19.
5.3
Any homework question would make a good test question. If you did not already practice the oddnumber problems that were assigned, then do so now. They are good practice for the exam.
Additionally the following supplementary exercises may be helpful.
Supplementary Exercises for Chapter 3 (p. 188) 3, 11, 15
Supplementary Exercises for Chapter 4 (p. 296) 3ab, 5, 7, 9ab
Supplementary Exercises for Chapter 5 (p. 364) 7, 9, 13, 15, 17