Download Chapter 22 Group Quiz

CHAPTER 22 GROUP QUIZ
1. TWO CONFIDENCE INTERVAL ESTIMATES
FROM THE SAME SAMPLE ARE (16.4, 29.8) AND
(14.3,31.9). WHAT IS THE SAMPLE MEAN, AND
IF ONE ESTIMATE IS AT THE 95% LEVEL WHILE
THE OTHER IS AT THE 99% LEVEL, WHICH IS
WHICH?
A
A. = 23.1; (16.4, 29.8) is the 95% level.
B. = 23.1; (16.4, 29.8) is the 99% level.
C. It is impossible to completely answer this question without
knowing the sample size.
D. It is impossible to completely answer this question without
knowing the sample standard deviation.
E. It is impossible to completely answer this question without
knowing the sample size and standard deviation.
2. HOSPITAL ADMINISTRATORS WISH TO LEARN THE AVERAGE
LENGTH OF STAY OF ALL SURGICAL PATIENTS. A STATISTICIAN
DETERMINES THAT, FOR A 95% CONFIDENCE LEVEL ESTIMATE
OF THE AVERAGE LENGTH OF STAY TO WITHIN +0.5 DAYS, 50
SURGICAL PATIENTS’ RECORDS WILL HAVE TO BE
EXAMINED. HOW MANY RECORDS SHOULD BE LOOKED AT TO
OBTAIN A 95% CONFIDENCE LEVEL ESTIMATE TO WITHIN +0.25
DAYS?
A. 25
B. 50
C. 100
D. 150
E. 200
E
3. THE NUMBER OF ACCIDENTS PER DAY
AT A LARGE FACTORY IS NOTED FOR EACH
OF 64 DAYS. ASSUME Σ = 1.52. WITH
WHAT DEGREE OF CONFIDENCE CAN WE
ASSERT THAT THE MEAN NUMBER
ACCIDENTS PER DAY AT THE FACTORY IS
BETWEEN 3.2 AND 3.96?
A. 48% B. 63% C. 90% D. 95% E. 99%
D
4. A MANUFACTURER WISHES TO DETERMINE THE LIST
PRICE FOR A SMOKE DETECTOR. A SURVEY OF THE
LIST PRICE OF SIMILAR SMOKE DETECTORS SOLD BY
NINE OTHER COMPETING COMPANIES SHOWED AN
AVERAGE LIST PRICE OF $10.95 WITH A STANDARD
DEVIATION OF $1.49. FIND A 95% CONFIDENCE
INTERVAL FOR THE AVERAGE LIST PRICE FOR A SMOKE
DETECTOR. (ASSUME ALL CONDITIONS ARE MET)
A. Between $9.98 and $11.92
B. Between $9.80 and $12.10
C. Between $9.98 and $12.07
D. None of these
B
5. A SURVEY OF THE HOSPITAL RECORDS OF 25
RANDOMLY SELECTED PATIENTS SUFFERING FROM A
PARTICULAR DISEASE INDICATED THAT THE AVERAGE
LENGTH OF STAY IN THE HOSPITAL IS 10 DAYS. THE
STANDARD DEVIATION IS ESTIMATED TO BE 2.1
DAYS. THE CRITICAL VALUE NEEDED FOR FINDING A
95% CONFIDENCE INTERVAL WOULD BE WHICH OF THE
FOLLOWING:
A. t* = 2.064
C. z* = 1.960
B. t* = 2.060
D. none of these
A
6. IT IS BELIEVED THAT USING A NEW FERTILIZER WILL
RESULT IN A YIELD OF 1.6 TONS PER ACRE. A
BOTANIST CARRIES OUT A TWO-TAILED TEST ON A
FIELD OF 64 ACRES. DETERMINE THE P-VALUE IF THE
MEAN YIELD PER ACRE IN THE SAMPLE IS 1.72 TONS
WITH A STANDARD DEVIATION OF 0.4. WHAT IS THE
CONCLUSION?
A. P = .0097, so the claim should be rejected at
1%, 5%, and 10% significance levels.
B. P = .0193, so the claim should be rejected at
the 10% and 5% levels but not at the 1% level.
C. P = .0097, so the claim should be rejected at
the 10% level but not at the 5% and 1% levels.
D. P = .0193, so the claim should be rejected at
the 1% level but not at the 10% and 5% levels.
E. P = .0097, and so there is not enough evidence
to reject the claim at any of the three levels.
B
7. AN AUTHOR OF A NEW BOOK CLAIMS THAT ANYONE FOLLOWING
HIS SUGGESTED DIET PROGRAM WILL LOSE AN AVERAGE OF 2.8
POUNDS PER WEEK. A RESEARCHER BELIEVES THAT THE TRUE
FIGURE WILL BE LOWER AND PLANS A TEST INVOLVING A RANDOM
SAMPLE OF 36 OVERWEIGHT PEOPLE. SHE WILL REJECT THE
AUTHOR’S CLAIM IF THE MEAN WEIGHT LOSS IN THE VOLUNTEER
GROUP IS LESS THAN 2.5 PER WEEK. ASSUME THAT THE STANDARD
DEVIATION AMONG ALL INDIVIDUALS IS 1.2 POUNDS PER WEEK. IF
THE TRUE MEAN VALUE IS 2.4 POUNDS PER WEEK, WHAT IS THE
POWER OF THE TEST?
A
B
C
D
E
B
8) The Clements HS website claims that the average SAT math
score is 617. We believe that the average score is higher. We
plan to survey 200 students and intend to speak up if their
average score is at least 630. Suppose the true average score is
620 with a standard deviation of 75. What is the probability of
making a Type II error?
Power
630  620 

P( x  630)  P  z 
  0.03
75 / 200 

TypeII
0.97
630  620 

P( x  630)  P  z 
  0.97
75 / 200 

9. GIVEN:
WITH A SAMPLE
SIZE OF 21 AND A KNOWN POPULATION
STANDARD DEVIATION. IF THE TEST STATISTIC =
1.9. WHAT IS THE P-VALUE?
A. 0.03597
C. 0.05743
B. 0.0287
D. 0.0719
C
10. GIVEN:
WITH A
SAMPLE SIZE OF 28 AND AN UNKNOWN Σ.
IF THE TEST STATISTIC = 1. WHAT IS THE PVALUE?
A. 0.1629
C. 0.1587
B. 0.3262
D. 0.1631
D
11. THE LABEL ON THE PACKAGE OF CORDS CLAIMS THAT THE
BREAKING STRENGTH OF A CORD IS 3.5 LBS, BUT A HARDWARE
STORE OWNER BELIEVES THE REAL VALUE IS LESS. SHE PLANS
TO TEST 36 SUCH CORDS; IF THE MEAN BREAKING STRENGTH IS
LESS THAN 3.25 LBS, SHE WILL REJECT THE CLAIM ON THE
LABEL. IF THE STANDARD DEVIATION FOR THE BREAKING
STRENGTHS OF ALL SUCH CORDS IS 0.9 LBS, WHAT IS THE
PROBABILITY OF MISTAKENLY REJECTING A TRUE CLAIM?
A. 0.05
C. 0.15
B. 0.10
D. 0.45
E. 0.94
A
12) City planners are trying to decide among various parking
plan options. Before making a decision they wish to test the
claim that shoppers park for an average of 47 minutes in
the downtown area. The planners have decided to tabulate
parking durations for 225 shoppers and reject the claim if
the sample mean exceeds 50 minutes. If the claim is
actually wrong and the true mean is 51 minutes, what is the
probability that planners will mistakenly fail to reject the
false claim? Assume the standard deviation in parking
durations
is 27



 min.


50

47
A. P  z 

27 



225 



D.  50  51 
P z 

27




225


B.
E.


 50  47 
Pt 

27




225 



 50  51 
Pt 

27




225



50  51 
C. P  z  27 




225

