AP Statistics
Test 7 Syllabus
AP Statistics: Test 7 Syllabus1
(8.1)
Null and
Alternative
8.8 , 8.9, 8.11, 8.12, 8.13–8.16.
Hypotheses
(8.2)
Large-Sample
Hypotheses
8.17–8.20, 8.22, 8.23, 8.25, 8.26 .
Testing
about the Mean
(8.3)
The Meaning of
8.30–8.33, 8.34 , 8.35–8.37, 8.38 –8.40, 8.43, 8.44.
Significance
(8.4)
Small-Sample
Hypothesis
8.45– 8.48 , 8.49–8.51, 8.54, 8.55, 8.58 .
Testing
about the Mean
(8.5)
Large-Sample
Hypothesis
Testing
8.61–8.63, 8.64 –8.66, 8.67, 8.68 , 8.70, 8.73, 8.75.
about a
Population
Proportion
1 The exercises in this batch continue to come from our primary textbook, Statistics, by James T. McClave and
Terry Sinich, Ninth Edition, Freeman, 2003, ISBN 0-13-065598-8.
AP Statistics—Mr. S
Examples of Types I and II Errors Compiled from AP Practice
Examinations
PE 4, #33 In leaving for school on an overcast April morning you make a judgement
on the null hypothesis: The weather will remain dry. What would the results be
of Type I and Type II errors?
(A)
Type I error: get drenched
Type II error: needlessly carry around an umbrella
(B)
Type I error: needlessly carry around an umbrella
Type II error: get drenched
(C)
Type I error: carry an umbrella, and it rains
Type II error: carry no umbrella, but weather remains dry
(D)
Type I error: get drenched
Type II error: carry no umbrella, but weather remains dry
(E)
Type I error: get drenched
Type II error: carry an umbrella, and it rains
PE 5, #37 An assembly-line machine is supposed to turn out ball bearings with a
diameter of 1.25 centimeters. Each morning the first 30 bearings produced are
pulled and measured. If their mean diameter is under 1.23 centimeters or over
1.27 centimeters, the machinery is stopped and an engineer is called to make
adjustments before production is resumed. The quality control procedure may
be viewed as a hypothesis test with the null hypothesis H0 : µ = 1.25 and
the alternative hypothesis is Ha : µ 6= 1.25. The engineer is asked to make
adjustments when the null hypothesis is rejected. In test terminology, what
would be the result of a Type II error?
(A) A warranted halt in production to adjust the machinery
(B) An unnecessary stoppage of the production process
(C) Continued production of wrong size ball bearings
(D) Continued production of proper size ball bearings
(E) Continued production of ball bearings that randomly are the right or wrong
size
PE 6, #36 A piece of medical equipment is not functioning properly, however, in
running operational checks, a lab technician does not find evidence of the malfunction. The lab technician has committed
(A) a Type I error
(B) a Type II error
(C) both a Type I and a Type II error
(D) neither a Type I nor a Type II error
(E) a random sampling error
Here’s one of my own. Mr. Surowski’s grading policies have come under attack
by the Central Administration as well as by the Board of Directors of SAS. To
analyze the situation, a null hypothesis together with an alternative hypothesis
have been formulated:
H0 : Mr. Surowski’s grading policies are fair
Ha : Mr. Surowski plays favorites in awarding grades.
The Board of Directors finds no irregularities, and therefore takes no actions
against him, but the rumors among the students is that it is advantageous for
Mr. Surowski’s students to regularly give him chocolate-covered expresso coffee
beans. It is conceivable that
(A) a Type I error has been made
(B) a Type II error has been made
(C) a Type I and a Type II error have been made
(D) neither type of error was made
(E) the null and alternative hypotheses were incorrectly formed.