MTH 265 – Statistics for Scientists and Engineers
Exam 3 Review
6.1
Large Sample Tests for a Population Mean
 Be able to define the null and alternative hypothesis for testing a population mean using
a large sample.
 Be able to calculate the test statistic, which is a z-value in this case.
 Be able to compute the P-value and be able to write out the probability statement for
the P-value that involves the test statistic.
 Be able to determine whether or not the null hypothesis should be rejected.
6.2
Drawing Conclusions from the Results of Hypothesis Tests READ THIS SECTION
 Be able to answer questions related to P-values, the plausibility of the null hypothesis,
and whether the null hypothesis is rejected or not rejected.
 Be able to answer questions about the connection between P-values and confidence
intervals. Read pages 404 and 405.
 Know what it means for a result to be statistically significant. Read page 401
 Read the paragraph on page 402 where it says, “The P-value is NOT the Probability
That Ho is True.”
 Read page 403 and look over the examples that show how to set up the hypothesis
statements so that rejecting Ho actually means something.
6.3
Tests for a Population Proportion
 Know what conditions must be checked in order to run the hypothesis test for a
population proportion.
 Be able to define the null and alternative hypothesis for testing a population proportion
using a large sample.
 Be able to calculate the test statistic, which is a z-value in this case.
 Be able to compute the P-value and be able to write out the probability statement for
the P-value that involves the test statistic.
 Be able to determine whether or not the null hypothesis should be rejected.
6.4
Small-Sample Test for a Population Mean
 Know what conditions must be fulfilled before a hypothesis test using the Student’s t
statistic can be done.
 Be able to define the null and alternative hypothesis for testing a population mean using
a small sample.
 Be able to determine the degrees of freedom for the t statistic.
 Be able to calculate the test statistic, which is a t-value in this case.
 Be able to compute the P-value and be able to write out the probability statement for
the P-value that involves the test statistic.
 Be able to determine whether or not the null hypothesis should be rejected.
6.5
Large-Sample Tests for the Difference Between Two Means
 Be able to define the null and alternative hypothesis for testing the difference between
two means using large samples from two populations.
 Be able to calculate the test statistic, which is a z-value in this case.
 Be able to compute the P-value and be able to write out the probability statement for
the P-value that involves the test statistic.
 Be able to determine whether or not the null hypothesis should be rejected.
6.6
Tests for the Difference Between Two Proportions
 Be able to define the null and alternative hypothesis for testing the difference between
two proportions using large samples from two binomial populations.
 Be able to calculate the test statistic, which is a z-value in this case.
 Be able to compute the P-value and be able to write out the probability statement for
the P-value that involves the test statistic.
 Be able to determine whether or not the null hypothesis should be rejected.
6.7
Small-Sample Tests for the Difference Between Two Means
 Know under what conditions you can use the Student’s t distribution to run the
hypothesis test.
 Be able to define the null and alternative hypothesis for testing the difference between
two means using small samples from two populations.
 There is a formula for the degrees of freedom that you can calculate by hand but it is
fine if you let your calculator do it. Find it under the 2 sample T-Test.
 Be able to calculate the test statistic, which is a t-value in this case.
 Be able to compute the P-value and be able to write out the probability statement for
the P-value that involves the test statistic.
 Know when to pool the sample standard deviations.
 Be able to determine whether or not the null hypothesis should be rejected.
6.10
The Chi-Square Test
 Be able to define the null and alternative hypothesis for testing the probabilities in a
multinomial experiment…you will either test whether observed results fit some
theoretical probability model or whether two variables are independent.
 Be able to compute the expected values.
 Be able to calculate the value of the chi-square test statistic. Be sure you can show the
formula and how the first few calculations would look even if you get the value of the
chi-square test statistic from your calculator.
 Be able to compute the P-value and be able to write out the probability statement for
the P-value that involves the test statistic.
 Be able to determine whether or not the null hypothesis should be rejected.
6.11
The F Test for Equality of Variance
 Know when the F Test is used…see the middle of page 467.
 Know under what conditions you can run a hypothesis test using the F statistic.
 Read the paragraph on page 467 where it says, “The F Test Cannot Prove That Two
Variances Are Equal.”
 Be able to define the null and alternative hypothesis for testing the equality of variance
for two populations.
 Be able to calculate the value of the F test statistic.
 Be able to compute the P-value and be able to write out the probability statement for
the P-value that involves the test statistic.
 Be able to determine whether or not the null hypothesis should be rejected.
7.1 Correlation
 What is the correlation coefficient? Read pages 500 and 501.
 Study equation 7.1 on page 502 so you have a good feel for HOW the correlation
coefficient measures the linear relationship between two variables.
 What does it mean if the correlation coefficient is 1, 1, 0, positive, or negative? Page
503
 Are there units associated with the correlation coefficient? Page 503
 Is the correlation coefficient affected by outliers?
 What is confounding? Read page 509and examples 7.1 and 7.2.
7.2 The Least-Squares Line
 Be able to calculate the Least-Squares line.
 Know what a residual is. page 519
 The Least-Squares line fits the data the “best” but what does that mean? page 519
 Be able to use the Least-Squares line to make predictions and answer other questions as
you did in problem like 2 and 5.
 Know what the coefficient of determination is and how it is calculated. page 526
 Use a scatterplot to show an example of the error sum of squares, the total sum of
squares, and the regression sum of squares to help you explain how the coefficient of
determination works. See figure 7.12
NOTES: You may have two sides of an 8.5 inch by 11 inch paper for notes. As always do not
show examples.
Chapter 6 Supplementary Exercises (page 495-499): 1, 3, 4, 5, 9, 19, 21, 23
To practice for the material from sections 7.1 and 7.2, work on the assigned odd numbered
problems.