MTH 265 – Exam 3 Review
Your exam is Friday, March 4. You may bring in one 8.5 inch by 11 inch page of notes, both sides,
hand-written. I will provide a t-table in case you don’t have the invt button on your calculator and I’ll
provide the tolerance interval critical value table.
5.4
Small-Sample Confidence Intervals for the Population Mean
 Recognize when you have the conditions to use the Student-t distribution to make a
confidence interval.
 Be able to calculate the test statistic, which is a t-value in this case.
 If you know nothing about the population, then you should check the sample for outliers.
 Reasonable test questions would be like exercises 5, 7, and 8.
5.5
Prediction Intervals and Tolerance Intervals
 Remember prediction and tolerance intervals require the population be normally
distributed.
 Be able to construct a prediction interval and be able to discuss when you would want to
construct a prediction interval.
 Why are prediction intervals always wider than confidence intervals?
 Be able to construct a tolerance interval and be able to discuss when you would want to
construct a tolerance interval. I will provide the table you would need to find the critical
value for the interval.
 Reasonable test questions would be like exercises 1, 3, and 5. Expect discussion questions
about all three types of intervals.
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.
 Be able to determine whether or not the null hypothesis should be rejected and always write
a meaningful conclusion.
 Be sure to read this section carefully. It is in this section where the theory of hypothesis
testing is laid out for you.
 Reasonable test questions would be like exercises 1, 3, 5, 7, 11, 12, 13. Expect discussion
questions from this section also.
6.2
Drawing Conclusions from the Results of Hypothesis Tests
 Be able to answer questions related to P-values, what they mean, the plausibility of the null
hypothesis, and whether the null hypothesis is rejected or not rejected. Read this section
carefully.
 Be able to answer questions about the connection between P-values and confidence
intervals. Read pages 225 and 226.
 Know what it means for a result to be statistically significant. Read page 222.
 Read the paragraph on page 402 where it says, “The P-value is NOT the Probability
That Ho is True.”
 Reasonable test questions would be like exercises 1, 2, 3, 4, 5, 7, 9, and 11. Expect
discussion questions from this section also.
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.
 Be able to calculate the test statistic, which is a z-value in this case and the p-value.
 Be able to determine whether or not the null hypothesis should be rejected. Always state a
meaningful conclusion.
 Reasonable test questions would be like exercises 1, 3, 5, 7, and 9.
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, and the p-value.
 Be able to determine whether or not the null hypothesis should be rejected. State a
meaningful conclusion.
 Reasonable test questions would be like exercises 3, 5, and 9. Remember that if the
problem states, “Can you conclude that…” then you should conduct a hypothesis test.
6.5
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 chisquare test statistic from your calculator. Be able to get the p-value.
 Be able to determine whether or not the null hypothesis should be rejected. Write a
meaningful conclusion.
 Reasonable test questions would be like exercises 1, 3, 4, and 7.
7.1
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.
 Be able to determine whether or not the null hypothesis should be rejected and state a
meaningful conclusion.
 Reasonable test questions would be like exercises 1, 3, 13, and 15.
7.5
The F Test for Equality of Variance
 Know when the F Test is used. You must have normal populations.
 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 calculate the F test statistic, the p-value, and state a conclusion.
 Reasonable test questions are like exercises 3, 4, and 5.