MTH 265 Statistics for Scientists and Engineers

MTH 265 – Statistics for Scientists and Engineers

Exam 3 Review

6.1Large 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 compute the P-value and be able to write out the probability statement for the P-value that involves the test statistic.

6.2Drawing 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.

6.3Tests 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.

6.4Small-Sample Test for a Population Mean

Know what conditions must be fulfilled before a hypothesis test using the Student’st 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.

6.5Large-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.

6.6Tests 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 compute the P-value and be able to write out the probability statement for the P-value that involves the test statistic.

6.7Small-Sample Tests for the Difference Between Two Means

Know under what conditions you can use the Student’stdistribution 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 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.

6.10The 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.

6.11The 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 Ftest 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.

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.