AP Statistics / Mr. Hansen

Name: _________________________________

Test #5 SAMPLE (2/24/1999)

General Instructions: Show all work and all answers in the spaces provided. If you need more room, write OVER and continue on the reverse side. Unless otherwise stated, all numeric answers are to be rounded to 3 places after the decimal point.

Part I: Fill-In (25 points)

Fill in each blank with the word, symbol, or phrase that best fits. Although most of the choices will come from the list below, you may need to make slight adjustments in some cases.

alternative hypothesis
confidence intervals
critical value (upper p critical value) for z and t tests
degrees of freedom
distribution-free procedure
matched pairs procedure
nonparametric procedure
null hypothesis
one-sided alternative / one-sided tests
power
P-value

robust procedure
sign test
significance
significance level
standard error
t distribution
t test for significance
two-sided alternative / two-sided tests
Type I error
Type II error
z test for significance

1-2.

The ______________ is an example of a nonparametric procedure. It may also be called "______________" because it requires essentially no assumptions about the underlying distribution.

3-4.

The ______________ for computing confidence intervals, like the similar z procedures, are not very ______________ in the presence of outliers in a small sample, because the sample mean is not a resistant measure of central tendency.

5-6.

If our SRS has 28 data points, then the ______________ for the t test equals ______________.

7-8.

The t procedures for calculating confidence intervals are similar to the z procedures, except that the margin of error equals a critical value times ______________ , as opposed to the critical value times s /Ö n.

9-10.

If a particular value of the ______________ is specified, the probability of making a Type II error equals ______________.

11.

A one-sided significance test for the purposes of making decisions may use a fixed value of a , perhaps a = 0.10. A normalized test statistic whose absolute value is less than the critical value for p=0.10 in the t table corresponds to a finding that is ______________ .

12.

A 95% confidence interval for a sample mean drawn from an SRS represents a belief that ________________________________________________________________________

________________________________________________________________________

Part II: Quick Response (25 points)

Fill in each answer blank. For full credit, you must show the formula or technique you are using. In some cases, your justification will consist of only 2 words: "by calculator" or "from table." However, you must provide it.

13.

In a sample of size 72 drawn from an SRS having mean 13.2 and s=2.54, a 95% confidence interval for the true mean is ______________ to ______________ .
   
   

14.

The z score corresponding to the 95th percentile of a standard normal distribution can be found from the ______________ line of Table E or by calculator. The answer is ______________ .
   
   
   
   
   

15.

Assume that our statistical consultant has told us that in our study, any t score of 3.0 or above (when measured to the nearest tenth) will establish 2-sided significance at the 0.02 level. We can deduce that there are ______________ subjects in our SRS.
   
   
   
   
   

16.

Determine the skewness, if any, of the following data points: 15, 18, 20, 21, 23, 23, 24, 27, 29. Support your answer with a normal quantile plot or a stemplot (your choice).
   
   
   
   
   

17.

A z statistic of 2 corresponds to a one-sided P value of between ______________ and ______________ (or if you prefer, give the exact value here: ______________). Does this correspond to statistical significance under the usual cutoff criterion? ______________ What if this were a 2-sided test with the same z score? Would we have statistical significance or not?

 

 

 

 

Part III: Problem Solving (30 points)

Show everything: setup, definitions of variables (if any), assumptions, computations, conclusions, and discussions of shortcomings (if any) in the experimental design.

18.

Twenty patients with inoperable knee injuries are given a drug that is supposed to reduce pain and improve freedom of movement. Their overall knee health is measured before and after treatment in an effort to see if the drug is effective. (There is an elaborate, statistically valid method for "scoring" knee health.) The coded scores are given below.
   

bef.

after

32

34

31

31

29

35

10

16

30

33

33

36

22

24

25

28

32

26

20

26

30

36

20

26

24

27

24

24

31

32

30

31

15

15

32

34

23

26

23

26

Is there evidence that the drug is effective for patients in this condition?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Part IV: In-Depth Understanding (20 points)

Write thoughtful answers using complete sentences. Brevity is preferred to padding, however.

19.

Explain what is meant by the statement "statistical significance is different from practical significance." An example would be very helpful.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

20.

Describe what happens to the P-value of a test, when H0 is false and all facts about the population remain unchanged, but n increases. Diagram(s) would be very helpful.