Math 113: Study Guide - Chapters 5-6
- Know which distributions (uniform, binomial, normal, t) are symmetric about their mean
- Know which distributions require degrees of freedom
- Know the best point estimate for the population mean
- Know the best point estimate for the population proportion.
- Know which distribution is appropriate in the described situation: Example: A small sample
from a normal population with the population standard deviation unknown would be the
Student's t distribution.
- Know the effect of increasing or decreasing the sample size on the maximum error of the
- Know the effect of increasing or decreasing the level of confidence on the maximum error of
- Know the relationship between the confidence level and the area in the tails.
- Know properties of the standard normal distribution (multiple choice)
- Know properties of the Student's t distribution (multiple choice)
- Know properties of the chi-square distribution (multiple choice)
- Know properties of the sampling distribution of the sample means (multiple choice)
- Know why statistics are calculated and parameters are estimated
- Know what a confidence interval means. See section on "Interpreting a confidence interval"
on page 296, especially the line "it is correct to say ..."
- Know the difference between a standard normal a non-standard normal distribution.
- Application problem from Internet. Identify the type of sampling (random, systematic,
convenience, cluster, or stratified - choices aren't given on test) used. Does the problem
satisfy the conditions of a binomial experiment? Find the confidence interval (the sample
proportion and maximum error of the estimate are given). Know what conditions must be
satisfied to approximate the binomial using the normal.
- Given a confidence interval, find the sample mean and the maximum error of the estimate.
- Identify the distribution from the graph. Need to know what an uniform, binomial, normal,
and Student's t distribution looks like.
- Competitive Test problem. Given the mean and standard deviation of test scores, find the
probability of receiving a certain grade if grades are assigned competitively. Only one letter
grade is given. Very similar to problem 5.4.18.
- Application problem using a non-standard normal distribution. Straight from the text in 5.3.
Looking through your lecture notes would be wise.
- Application problem using a non-standard normal distribution. One part is a single value, the
other part is involving the mean. Straight from the text in 5.5.
- Look up a z, t, and chi-square critical from the tables using the alpha notation. Z0.05 means the
z-score with 0.05 area to the right which is 1.645. Three parts.
- Given a confidence level and a critical value from the t-table, find the sample size.
Remember that the t-table gives degrees of freedom, you will need to add 1 to get the sample
- Determine the degrees of freedom for the described situation. Two parts.
- Use a standard normal distribution to find probabilities. There are seven parts. You must
draw the picture and find the probability. There is a normal graph given, you just need to
shade the proper portion. Two points for finding the correct probability and one point for
shading the proper region. This problem accounts for slightly over 1/5th of the points on the
test, but it is very important!