Chapter 10: Introduction to Inference

Key Vocabulary:

 §         confidence interval §         margin of error §         interval §         confidence level §         a level C confidence interval §         upper p critical value §         test of significance §         null hypothesis §         alternative hypothesis §         p-value §         statistically significant §         test statistic §         significance level §         z test statistic §         Hawthorne effect     §         Type I Error §         Type II Error §         acceptance sampling §         power (of a test)

Calculator Skills:

§         ZInterval

§         Z-Test

10.1  Estimating with Confidence (pp.536-559)

1.      In statistics, what is meant by a 95% confidence interval?

2.      Sketch and label a 95% confidence interval for the standard normal curve.

3.      In a sampling distribution of , why is the interval of numbers between  called a 95% confidence interval?

4.      Define a level C confidence interval.

5.      Sketch and label a 90% confidence interval for the standard normal curve.

6.      What does z* represent?

7.      What is the value of z* for a 95% confidence interval?  Include a sketch.

8.      What is the value of z* for a 90% confidence interval?  Include a sketch.

9.      What is the value of z* for a 99% confidence interval?  Include a sketch.

10.  What is meant by the upper p critical value of the standard normal distribution?

11.  Explain how to find a level C confidence interval for an SRS of size n having unknown mean m and known standard deviation s.

12.  What is meant by a margin of error?

13.  Why is it best to have high confidence and a small margin of error?

14.  What happens to the margin of error as z* decreases?  Does this result in a higher or lower confidence level?

15.  What happens to the margin of error as s decreases?

16.  What happens to the margin of error as n increases?  By how many times must the sample size n increase in order to cut the margin of error in half?

17.  The formula used to determine the sample size n that will yield a confidence interval for a population mean with a specified margin of error m is .  Solve for n.

10.2  Tests of Significance (pp.559-585)

1.      What is a null hypothesis?

2.      What is an alternative hypothesis?

3.      In statistics, what is meant by the P-value?

4.      If a P-value is small, what do we conclude about the null hypothesis?

5.      If a P-value is large, what do we conclude about the null hypothesis?

6.      How small should the P-value be in order to claim that a result is statistically significant?

7.      Explain the difference between a one-sided alternative hypothesis and a two-sided alternative hypothesis.

8.      What does a test statistic estimate?

9.      What is meant by a significance level?

10.3  Using Significance Tests (pp.560-566)

10.4  Inference as Decision (pp. 567-577)

1.      Significance tests are not always valid.

What are some factors that can invalidate a test?

2.      Explain the difference between a Type I Error and a Type II Error.

3.      What is the relationship between the significance level a and the probability of Type I Error?

4.      Describe how to calculate the power of a significance test.