Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
Solution Manual for Elementary Statistics
A Step by Step Approach 9th Edition by Bluman ISBN
1259199703
9781259199707
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Note: Graphs are not to scale and are intended to conveya general idea. Answers may varydue to rounding, TI-83's, or computer programs
EXERCISE SET 9-1
1. Testing a single mean involves comparinga
population mean to a specific value such as œ 100; whereas testing the difference between two means involves comparingthe means of two populations such as . " œ .2.
2
When both samples are greater than or equal to 30 the distribution will be approximately normal. The mean of the differences will be equal to zero. The standard deviation of the differences will be É5 5#
3 Both samples are random samples The populations must be independent of each other and they must be normallydistributed or approximatelynormallydistributed
5. continued
Do not reject the null hypothesis. There is not enough evidence to reject the claimthat the average lengths of the rivers is the same.
Do not reject the null hypothesis There is not enough evidence to support the claim that the average salaries are different.
164 É # # # #
6. H!: H": " œ # . " Á .# (claim)
C V. œ „ 1.65 z œ (64,510 ,900) œ 0.95 8200 7800 45 45
1.65 0 Å 0.95 1.65 n
" n#
7
165 4. H!: . " œ .# or H!: . " .# œ 0 H!: H": " œ # " Á # (claim) C V. œ „ 1.96 5 z œ (X" #) ( " #) œ (28 2) 5# 5# 7 2# 9 1# H!: H": . " œ .# " Á # (claim) Ê " # n" n# z œ 3.65 É 4! 40 C V. œ „ 2.58 X" œ 662.6111 X# œ 758.875 z œ (X #) ( #) œ (662 6111 875) 5# 5# 450# 474# Ê " # É 36 36 n" n# z œ 0.88 (TI83 answer is z œ 0.856) Å 1.96 0 1.96 3.65
the null hypothesis There is enough evidence to support the claim that commutingtimes are different in the winter. 2.58 Å 0 2.58 8 H!: H": " œ # " Á # (claim) 0.88 C. V. œ „ 1.96 z œ (123 2) œ 1.34 É98 120 6! 50
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
Reject
8. continued
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
10. continued
Reject the null hypothesis. There is enough evidence to reject the claim that the average costs are the same.
Do not reject the null hypothesis There is
not enough evidence to support the claim that there is a difference in heights
Reject the null hypothesis. There is enough evidence to support the claim that those who stayed have a higher GPA than those who left their profession
Reject the null hypothesis. There is enough evidence to support the claim that the average stay is longer for men than for
166
É É # # z œ
1.96 Å 0 1.96 11. H!: H": . " œ .# . " .# (claim) 1.34 C. V. œ 1.65 (X" #) ( " #) (3 28)
z œ 5# 5# œ 0 52# 0 46# œ 2.01 Ê " # É 103 225
n" n# 9 H!: H": " œ # " # (claim) C. V. œ 2.33 z œ (X" #) ( " #) œ (5 2) œ 3.75 Å 1.65 0 2.01 5# 5# 1 2# 1 5# Ê " # É 32 30 n" n#
0 2.33 Å 12 H!: H": . " œ .# " # (claim) 3.75
C. V. œ 1.65 X" œ 21.4 X# œ 20.8 s" œ 3 s# œ 3 (21 8) women 3# 3# 1000 500 œ 3.65 10 H!: H": . " œ .# " Á # (claim) C V. œ „ 2.58 z œ (93, ,043) œ 3.82 5602 4731 35 40 Å 2.58 0 2.58
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
Reject the null hypothesis. There is enough evidence to support the claim that ACT scores for Ohio students are belowthe national average. 13
10. continued
167
continued
8.
0 1.65 Å 3.65
3.82 H!: H": " œ # " Á # (claim)
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
13. continued 15.
support the claimthat there is a difference in scores.
Do not reject the null hypothesis. There is not enough evidence to support the claim that the average incomes are different.
Do not reject the null hypothesis There is
not enough evidence to support the claim
that the difference in average benefits is greater than 30
168
n n É # # " # ! n # # n C V. œ „ 1.96 z œ (X #) ( #)
P-value > 0.05,
not
There is not
to 5# 5s# Ê " # " # z œ (40, ,750) œ 0.66 É10,500# 12,500# 50 50
continued
Since
do
reject the null hypothesis
enough evidence
P-value œ
16 Residents Commuters X" œ 22.12 X# œ 22.76 s" œ 3.68 s# œ 4.70 n" œ 50 n# œ 50 1.96 0 Å 0.66 1.96 H!: H": " œ # . " Á .# (claim)
(TI:
0.3131)
14 z œ (22 76) œ 0.76 3 68 4 70 50 50 Area œ 0.2236 P-value œ 2(0.2236) œ 0.4472
P-value > 0.05, do not
the
hypothesis. There is
the claimthat
in H!: H": . " .# œ 30 . " .# 30 (claim) the ages 17 C V. œ 1.65 D œ 83.6 79.2 œ 4.4 z œ (960 50 89) œ 1.52 (X X ) z É5# 5# " # É98# 101# " # # " # # # 60 60 (X" X#) z! É5" 5# # n" n# 4.4 (1.65)É4 3# 3 8# 36 36 4.4 (1.65)É4 3# " # 3 8# 2.8 " # 6.0 36 36 0 Å 1.65 1.52 (TI: 2.83 . " .# 5.97) 18. D œ $9205 $6618 œ $2587
Since
reject
null
not enough evidence to reject
there is no difference
# #
(X" X#) z! É5" 5# " # # n" n# . .
15 (X" X#) z! É5" 5# # n" n# $2587 (1.96)É$1928# $1928# 35 35 " # H!: H": . " œ .# " Á # (claim) $2587 (1.96)É $1928# 35 $1928# 35 z œ (X" #) ( " #) œ Ð3 96)
169
13. continued 15. continued $1683.67 " # $3490.33 5# 5# 0 75# 0 75# Ê " # É 103 225 19. n" n# D œ 315 280 œ 35 # # z œ 1.01 (X" X#) z! É5" 5# . " .# Area œ 0.8438 # n" n# 5# 5# P-value œ 2(1 0.8438) œ 0.3124 (X" X#) z! É n " n # # " #
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
The interval gives evidence to reject the claimthat there is no difference in the means because 0 is not contained in the interval.
Reject the null hypothesis There is enough evidence to support the claim that women watch more televisionthan men
Since
> 0.01, do not reject the null hypothesis There is not enough evidence to support the claimthat there is a difference in
Since
< 0.05, reject the null hypothesis There is enough evidence to support the claimthat the average price of a home in Dallas is greater than the average price of a home in Orlando.
170
n n É É 39 69 35 (1.96)É56 2# 52 1# Reject the null hypothesis There is enough 40 35 35 (1.96)É56 2# " # 52 1# evidence to
the
that
is a difference in commutingtimes. 10.5 " # 59.5 40 35 23
19. continued 22. continued
support
claim
there
H!: H": . " œ .# " Á # (claim) z œ (X #) ( #) 5# 5# 20. D œ 9.2 8.8 œ 0.4 Ê " # # 0.4 (1.96)É0 3# 0 1# z œ ($995 $1120) œ 2.47 27 30 " # 120# 250# 30 30 0.4 (1.96)É0 3# 0 1# Area œ 0.0068 27 30 0.281 " # 0.519 or 0.3 " # 0.5 21 P-value œ 2(0.0068) œ 0.0136
P-value
H!: H": " œ # . " .# (claim) sales. 24. C V œ 2.33 z œ (X #) ( #) œ (48 3) œ 3.43 H!: H": . " œ .# " # (claim) 5# 5# 5 6# 4 5# Ê " # É 40 40 n" n# z œ ($156, ,000) É$30,000# $32,500# 45 40 0 2.33 Å 3.43
z œ 2.13 Area œ
1 0.9834 œ 0.0166 P-value œ 0.0166
25 22 H!: " œ # H!: H":
# œ 8
" # 8 H": . " Á .#
C V œ 1.65 z œ (X" #) ( " #) œ (110 ) œ 0.73 5# 5# 15# 15# C V. œ „ 1.96 z œ (40 8) œ 3.16 67 24 35 30 Ê " # n" n# É 60 60
P-value
"
(claim)
(claim)
171
19. continued 22. continued 1.96 0 1.96 Å 3.16 Å 0.73 0 1.65
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
25. continued
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
Do not reject the null hypothesis There is not enough evidence to reject the claimthat
private school students have examscores that are at most 8 points higher than public school students
1. continued
Reject the null hypothesis. There is enough evidence to support the claim that the difference in the average sale prices is
Do not reject the null hypothesis There is not enough evidence to support the claim that there is a significant difference in the average number of weeks on the bestseller lists. 2.
Do not reject the null hypothesis There is not enough evidence to support the claim that the difference in income is not $30,000
Do not reject the null hypothesis. There is not enough evidence to support the claim that there is a difference in average values
(Note: Each data set contains a suspected outlier which may make the results suspect ) 3.
172
É # # É # #
C V. œ „ 1.761 d f œ 14 t œ (X" #) ( " #) s# s#
26. Ê # n" n# t œ (22 28) 0 œ 1.595 6 17 13 2 15 15 H!: H": . " .# œ $3400 " # $3400 (claim) C V. œ 1.65 z œ (261,500 ,200) 3400 œ 3.93 É10,500# 12,000# 40 40 1.761 Å 0 1.761 1.595 0 1.65 Å 3.93
H!: H": " œ # . " Á .# (claim)
than $3400 27. C. V. œ „ 2.131 d. f. œ 15 X" œ 24.75 s" œ 25.965 X# œ 42.94 s# œ 72.745 H!: H": " # œ $30,000 . " .# Á $30,000 (claim) t œ (24 94) 0 œ 0.942 25 965 72 745 16 16 C V. œ „ 2.58 z œ (90,200 ,800) ,000 œ 1.22 É15,000# 12,800# 100 100 2.131 Å ! 2.131 2.58 0 Å 1.22 2.58 0.942
greater
EXERCISE SET 9-2 1 H!: H": . " œ .# " Á #
H!: H":
(claim)
173
25. continued 1. continued " œ # " Á # (claim) C. V. œ „ 2.09 3 d f œ 19
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
Reject the null hypothesis There is enough evidence to support the claim that there is a difference in noise levels.
Do not reject the null hypothesis. There is not enough evidence to support the claim that there is a significant difference in the average number of grams of carbohydrates
Reject the null hypothesis There is enough evidence to support the claim that the average age of slot machine players is less than the average age of roulette players
Do not reject the null hypothesis. There is not enough evidence to support the claim that the means are different.
174
3. continued É # # É # # É t œ (X" #) ( " #) s# s# Ê " # n" n# t œ (63 3) 0 œ 3.811 4 1 7 5 20 24 1.812 Å 0 1.812 1.220 2.093 0 2.093 Å 3.811
6 H!: H": . " œ .# " Á # (claim) 4. H!: H": " œ # . " .# (claim) C V. œ „ 2.571 d f œ 5 X" œ 17.412 s" œ 2.451 X# œ 14.667 s# œ 4.761 C V. œ 1.711 d f œ 24 t œ (17 412 667) œ 1.351 t œ (48 7 55 3) 0 œ 4.509 6 8 3 2 25 35 2 451# 17 4 761# 6 Å 1.711 0 4.509 2.571 0 Å 1.351 1.812
7 5. H!: . " œ .# H!: H": " œ # " Á # (claim) H": " Á # (claim) X" œ 12.48 s" œ 1.477 X# œ 9.94 s# œ 0.666 C V. œ „ 1.812 d f œ 10 t œ (X" #) ( " #) s# s# X" œ 29.69 s" œ 6.499 Ê " # X# œ 34.36 s# œ 11.201 n" n# t œ (X #) ( #) t œ (12 94) 0 œ 5.103 É1 477# 0 666#
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
175
3. continued 5. continued É # # s# s# "! 15 Ê " # n" n# For t œ 5.103, the area is greater than t œ (29 36) 0 œ 1.220 6 499 11 201 13 11 0.9999. The P-value is 1 0.999 0.0001
7. continued
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
Since the P-value is less than ! œ 0.05, reject the null hypothesis There is enough evidence to support the claim that there is a difference in the weights of running
The
hypothesis since
is 0.05 There is enough evidence to support the claimthat the average salary for elementaryschool teachers is greater than the average salary for
Do not reject the null hypothesis There is enough evidence to support the claimthat there is no difference between the salaries.
176
É # # É É t œ œ 2.601 t œ
11. continued
there
TV
and teens 12 8 H!: " œ # H!: H": " œ # " Á # (claim) H": " # (claim) C V. œ „ 2.145 t œ ($48, ,633) œ 1.921 $3912 40 $5533 26 24
shoes that
is a difference in
viewing times between children
P-value
P-valu
d. f. œ 14 t œ (501, ,360) 0 œ 1.70 É20,000# 18,000# 15 15
school teachers 2.145 Å 0 2.145 9 For the 95% Confidence Interval: 6.8 2.093(1.784) " # 6.8 2.093(1.784) 3.07 " # 10.53 (TI:3.18 " # 10.42) 1.70
is 0.025
0.05 (0.031). The decision is to reject the null
P-value
secondary
13 10. For the 95% Confidence Interval: H!: H": . " œ .# . " .# (claim) 2.745 2.571(2.0325) . " .# 2.745 2.571(2.0325) 2.48 " # 7.97 X" œ 39.6667 s" œ 18.3703 X# œ 28.8333 s# œ 17.1279 C. V. œ 3.365 d. f. œ 5 (39 6667 28 8333) 0 (TI: 2.24 . " .# 7.73) 11 18 3703# 17 1279# 6 6 œ 1.057 H!: H": . " œ .# " Á # (claim) C. V. œ „ 2.977 d. f. œ 14 (22 45 5) 16 4 18 2 15 15 0 Å 3.365 1.057 2.977
2.977 2.601 Do not reject the null hypothesis
There is not enough evidence to support the claim that the average number of students attending cyber schools in Allegheny County is greater than those who attend cyber schools outside Alleghen yCounty One reason why caution should be used is that
Do not reject the null hypothesis There is not enough evidence to support the claim
cyber charter schools are a relativelynew concept.
177
! Å
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances 7. continued 11. continued
Chapter 9
-
Testing the Difference Between Two Means, Two Proportions, and Two Variances
Do not reject the null hypothesis There is not enought evidence to support the claim that the average scores are different.
Since P-value > 0.01, do not reject the null hypothesis There is not enough evidence to
reject the claimthat the mean hospital stay is the same. (TI: P-value œ 0.026)
" #
P-value < 0.005 (0.00005) which is !
For t œ 6.22, the area is less than 0.0001 Since the P-value is less than ! œ 0.01, reject the null hypothesis There is enough evidence to support the claim that the average gasoline price in 2005 was less than
the average price in 2011
178
É # # # # 17 16 17 16 6 7 É É # # t œ 14 H!: H": . " œ .# " Á # (claim) 17. Research: X" œ 596.2353 s" œ 163.2362 PrimaryCare: X# œ 481.5 s# œ 179.3957 C V. œ „ 2.306 d f œ 8 X" œ 65.727 s" œ 9.122 X# œ 60.222 s# œ 11.389 t œ (65 222) œ 1.174 9 122 11 389 11 9 90% Confidence Interval: 114.7353 1.753É163 2363# 179 3957# " # 114.7353 1.753É 163 2363 179 3957 114.7353 104.8 . " .# 114.7353 104.87 9.865 . " .# 219.6053 (TI: 13.23 . " .# 216.24) 2.306 ! Å 2.306 1.174 18. Private: X œ $16,147.5 s œ 4023.7 Public: X œ $9039.9 s œ 3325.5
15 95% Confidence Interval: 7107.6 2.571É4023 7# 3325 5# " # H!: H": " œ # " Á # (claim) 7107.6 2.571É 4023 7# 6 3325 5# 7 P-value: 0.02 P-valu 0.05 (0.026) d f œ 15 t œ (2 9) œ 2.385 É0 6# 0 3# $1789.70 " # $12,425.41 (TI: $2484. " # $11,731) 19 16 16
H!: H": " œ # " # (claim)
X" œ 2.563 s" œ 0.361 X# œ 3.767 s# œ 0.332 (X" #) ( " #) 99% Confidence Interval: t œ s# s# 0.4 2.947(0.1677)
0.4 2.947(0.1677) 0.1 " # 0.9 (TI: 0.07
# 0.87) Ê " # n" n# (2 563 767) 0 361# 0 332# 6 7 œ 6.22
!:
.
œ .#
"
16 H
H":
"
" # (claim)
C V. œ 1.729
f œ
œ (62 6) 0 œ 4.364 5 4 3 9 20 20
d
19 t
20
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
(TI: P-value œ 0.000055)
Reject the null hypothesis There is enough evidence to support the claim that houses in
179
H!: H": " œ # . " Á .# (claim) Whiting are older X" œ 55 s" œ 7.01 X# œ 49.57 s# œ 6.73
20. continued
Chapter 9
-
Testing the Difference Between Two Means, Two Proportions, and Two Variances
0.20 (0.1506) Since the P-value is greater than ! œ 0.05, do not reject the null hypothesis There is not enough evidence to support the claimthat there is a difference in the scores.
Do not reject the null hypothesis There is not enought evidence to support the claim that the means of the batting averages are
different. EXERCISE SET 9-3
Reject the null hypothesis. There is enough evidence to support the claim that the means are different. This is the expected conclusion because, since randomnumbers are different, one would expect the means to be different.
180
90 85 5 25 80 72 8 64 90 80 10 100 75 80 -5 25 80 70 10 100 90 75 15 225 84 80 4 16 !D œ 47 !D# œ 555 É # # É # # n 7 É # # t œ ( 57) œ 1.529 7 01 6 73 8 7
P-valu
21 2.571 ! Å 2.571 1.701 H!: H": " œ # . " Á .#
0.10
(claim)
C. V. œ „ 1.761 d. f. œ 14 X" œ 33.53 s" œ 20.791 X# œ 52.33 s# œ 35.187 t œ (X #) ( #) s# s# Ê " # n" n# t œ (33 33) œ 1.782 20 791 35 187 15 15
1
Dependent
Independent d Dependent
Independent 2 Book DVD D D# Å 1.761 ! 1.782 1.761
a. Dependent b.
c.
e.
H!: H": .D œ ! D 0 (claim) 22. H!: H": " œ # " Á # (claim) C V. œ 1.943 d f œ 6 D œ !D œ 47 œ 6.714 sD œ Én D D) œ É7(555) 47 œ 6.317 ! # ! # # C V. œ „ 2.571 d f œ 5 D n(n 7(6) 6 X" œ 0.438 s" œ 0.168 X# œ 0.321 s# œ 0.013 t œ (0 438 321) œ 1.701 0 168 0 013 6 6 t œ SD Èn œ 6È317 7 œ 2.812 0 1.943 Å
181 Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances 20. continued 22. continued 2.812
2. continued
Chapter 9
-
Testing the Difference Between Two Means, Two Proportions, and Two Variances
Reject the null hypothesis There is enough
evidence to support the claim that book scores are higher than DVD scores
4. continued
Reject the null hypothesis There is enough
evidence to support the claim that the seminar increased the number of hours students studied
Reject the null hypothesis There is enough evidence to support the claim that students
did better the second time. Possible reasons include familiaritywith the course, warmed up, etc.
182
3 Before After D D # 9 9 0 0 12 17 -5 25 6 9 -3 9 15 20 -5 25 3 2 1 1 18 21 -3 9 10 15 -5 25 13 22 -9 81 7 6 1 1 !D œ -28 !D# œ 176 5 S - Th F - S D D # 8 4 4 16 5.5 7 -1.5 2.25 7.5 10.5 -3 9 8 12 -4 16 7 11 -4 16 6 9 -3 9 6 6 0 0 8 9 -1 1 !D œ -12.5 !D# œ 69.25 67 68 -1 1 72 70 2 4 80 76 4 16 70 65 5 25 78 75 3 9 82 78 4 16 69 65 4 16 75 68 7 49 !D œ 28 !D# œ 136 # 8 2 33 n 3 33 sD œ É œ É œ 3.3 n 8 2 665
C V. œ 1.895 d f œ 7
D œ 28 œ 3.5 sD 8( (28) 2.33 œ É 8(7) œ t œ 3 œ 4.249 È8 H!: H": .D œ 0 .D 0 (claim) 0 1.895 Å 4.249
C. V. œ 1.397 d. f. œ 8 D œ !D œ 3.11
! # ! # # n D ( D) 9( (-28) n(n 9(8) t œ 11 0 œ 2.802 È9 Å 1.397 0 2.802
H!: H": .D œ 0 D Á 0 (claim)
C. V. œ „ 2.365 d. f. œ 7 D œ !D œ 5 œ 1.5625 ! # ! # sD n D ( D) œ É n(n # 4 sD 8(69 (-12 5) 2.665 Before After D D # œ É 8(7) œ t œ 562 œ 1.658 È8
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
183
2. continued H!: D œ 0 2.365 Å 0 2.365 H": D 0 (claim) 1.658
Chapter 9 - Testing the Difference Between Two Means,
Two Proportions, and Two Variances
5. continued 7. continued
Do not reject the null hypothesis There is
not enough evidence to support the claim that there is a difference in the mean number of hours slept.
Reject the null hypothesis. There is enough evidence to support the claim that there is a difference in the scores
Do not reject the null hypothesis. There is not enough evidence to support the claim that the errors have been reduced
Reject the null hypothesis. There is enough evidence to support the claim that the dogs lost weight.
184
6 Thursday Friday D D # 67 68 -1 1 65 70 -5 25 68 69 -1 1 68 71 -3 9 68 72 -4 16 70 69 1 1 69 70 -1 1 70 70 0 0 !D œ -14 !D# œ 54 7 Before After D D # 12 9 3 9 9 6 3 9 0 1 -1 1 5 3 2 4 4 2 2 4 3 3 0 0 !D œ 9 !D# œ 27 1 643 # 8 2 053 6 3 869
sD œ Én D ( D) œ É6(27) 9 œ 1.643 ! # ! # #
n(n 6(5) t œ 1 5 0 œ 2.236 È6 0 Å 2.571 H!: H": .D œ 0 D Á 0 (claim) 2.236
8 C V. œ „ 2.365 d f œ 7 Before After D D # D œ œ 1.75 sD 8(54) (-14) 2.053 42 39 3 9 53 45 8 64 œ É 8(7) œ t œ 75 0 œ 2.411 È8 48 40 8 64 65 58 7 49 40 42 -2 4 52 47 5 25 H!: D œ 0 !D œ 29 !D# œ 215 H": D 0 (claim) C V. œ 2.015 d f œ 5 D œ 29 œ 4.833 6(215) (29)# Å 2.365 0 2.365 2.411 sD œ É 6(5) œ 3.869
t œ 4 833 0 œ 3.060 È6 0 2.015 Å 3.060
!: H": D œ 0 D 0 (claim)
H
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
185
5. continued 7. continued n 6 C V. œ 2.571 d f œ 5 D œ !D œ 9 œ 1.5
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
10. continued 0.01 < P-value < 0.025 (0.012). Do not reject the null hypothesis since P-value > 0.01 There is not enough evidence to support the claimthat learning has occurred
P-value > 0.20 (0.361) Do not reject the null hypothesis since P-value > 0.01 There is not enough evidence to support the claim that there is a difference in the pulse rates.
Do not reject the null hypothesis There is not enough evidence to support the claim that the mean scores of the two rounds are
different.
186
A B D D # 87 83 4 16 92 95 -3 9 78 79 -1 1 83 83 0 0 88 86 2 4 90 93 -3 9 84 80 4 16 93 86 7 49 !D œ 10 !D# œ 104 È8 D # 1 100 90 10 100 2 150 130 20 400 3 150 150 0 0 4 110 90 20 400 5 130 105 25 625 6 120 110 10 100 7 118 120 -2 4 !D œ 83 !D# œ 1629 È D È n 8 3 62 n(n 8(7) 8 2 696 n 7 sD œ É œ É 9.
Confidence Interval: 11.857 3.707 ˆ10 367‰ 7 11.857 3.707 ˆ10 367‰ 7 H!: H": .D œ 0 .D Á 0 (claim) 2.7 < D < 26.4 11 Golfer Round 1 Round 2 D D # d f œ 7 D œ !D œ 10 œ 1.25 1 72 72 0 0 2 73 69 4 16 3 72 75 -3 9 ! # ! # # sD œ Én D ( D) œ É8(104) 10 œ 3.62 t œ 1 25 0 œ 0.978 È8 4 72 76 -4 16 5 72 75 -3 9 6 70 73 -3 9 7 73 75 -2 4 8 70 74 -4 16
H!: H": .D œ 0 D Á 0 (claim) !D œ -15 !D# œ 79 Confidence Interval: 1.25 3.499 ˆ$Þ'#‰ .D C V. œ „ 2.365 d f œ 7 D œ œ 1.875 # È) sD 8( (-15) 2.696 1.25 3.499 ˆ$Þ'# ‰ È) œ É 8(7) œ 3.2 < .D < 5.7 10 Child 1 2 D t œ 875 0 œ 1.967 2.365 Å 0 2.365 H!: H": D œ 0 D 0 (claim) 1.967
d. f. œ 6 D œ !D œ 83 œ 11.857
! # ! # # n D ( D) 7( 83 n(n 7(6) sD œ 10.367
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
187
10 367 t œ 11 857 0 œ 3.026 È7
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
Reject the null hypothesis There is enough evidence to support the claim that the average number of mistakes has decreased.
a. x œ 0.16(100) œ 16
b x œ 0.08(50) œ 4
c. x œ 0.06(800) œ 48
d. x œ 0.52(200) œ 104
e. x œ 0.20(150) œ 30
a. x œ 0.24(300) œ 72
b x œ 0.09(200) œ 18
c. x œ 0.88(500) œ 440
d x œ 0.4(480) œ 192
e. x œ 0.32(700) œ 224
For each part, use the formulas p œ X X# #
and q œ 1 p
a. p œ 60 40 œ 0.5 q œ 1 0.5 œ 0.5
b p œ 22 18 œ 0.5
q œ 1 0.5 œ 0.5
c. p œ 18 20 œ 0.27
q œ 1 0.27 œ 0.73
d p œ 12 œ 0.2125
q œ 1 0.2125 œ 0.7875
188
12 Student Before After D 2 D # Use ^ p œ X and q ^ œ 1 ^ A 10 4 6 36 n B 6 2 4 16 C 8 2 6 36 36 36 D 8 7 1 1 2 881 n n 8 8 8 8 8 8 8 8 8 8 " # 80 100 n E 13 8 5 25 a. ^ p œ 20 b ^ p œ 35 p q ^ œ 16 q ^ œ 15 F 8 9 -1 1 50 50 !D œ 21 !D# œ 115 c. ^ p œ 16 q ^ œ 48 H!: D œ 0 64 64 H": D 0 (claim) d ^ p œ 200 q ^ œ 200 175 25 C. V. œ 2.015 d. f. œ 5 e. ^ p œ 16 q ^ œ 132 D œ 3.5 sD œ 2.881 148 148 3 t œ 3 5 0 œ 2.976 È6 0 2.881 Å 2.976
4
5
13. \" \# œ !\" \# ! \" \# œ !Ð\" \# Ñ !Ð\" \# Ñ œ ! \" !\# ! \" !\# œ \ \ EXERCISE SET 9-4 1 Use ^ p œ X and q ^ œ 1 ^ p
a. ^ p œ 34 q ^ œ 14 e. p œ
œ
48 48 50
œ
b ^ p œ 28 q ^ œ 47 75 75 6.
12 15
0.216
q
1 0.216 œ 0.784
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
189
c. ^ p œ 50 q ^ œ 50 For each part, use the formulas p œ X X# 100 100 and q œ 1 p n" n# d ^ p œ 6 q ^ œ 18 24 24 a. p œ 9 œ 0.5 e. ^ p œ 12 q ^ œ 132 q œ 1 0.5 œ 0.5 144 144
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
(Using the TI83, the 95% confidence
Do not reject the null hypothesis There is not enough evidence to support the claim
that the proportions are different. A researcher might want to find out why people feel that they have less leisure time nowas opposed to 10 years ago Are they working more? Raising a family? etc.
Do not reject the null hypothesis There is not enough evidence to reject the claimthat
the proportions are equal.
190
50 50 100 " # " # É 6. continued b p œ 21 43 œ 0.256 8. ^ p" œ 44 œ 0.88 ^ p# œ 48 œ 0.96 100 150 q œ 1 0.256 œ 0.744 50 50 p œ X" X# œ 44 48 œ 0.92 n" n# c. p œ 20 65 œ 0.425 q œ 1 0.425 œ 0.575 q œ 1 0.92 œ 0.08 H!: p" œ p# d. p œ 15 3 œ 0.290 q œ 1 0.290 œ 0.710 H": p" Á p# (claim) e. p œ 24 18 œ 0.553 C. V. œ „ 1.65 z œ (0 96) œ 1.47 É(0 92)(0 08)( 1 1 ) q œ 1 0.553 œ 0.447 7 ^ p" œ 0.83 ^ p# œ 0.75 X" œ 0.83(100) œ 83 X# œ 0.75(100) œ 75 p œ 83 75 œ 0.79 q œ 1 0.79 œ 0.21 1.65 Å 0 1.65 H!
H": p" Á p#
: p" œ p#
(claim) 1.47
C V. œ „ 1.96 ! œ 0.05 interval
0.168 p
z œ (p ^ ^ p (p p ) œ (0 75)
is:
" p# 0.008).
É( p )( q ) ( 1 1 ) É(0 79)(0 21)( 1 1 ) z œ 1.39 n" n# 100 100
9. ^ p" œ 44 œ 0.55 ^ p# œ 41 œ 0.4556 1.96 0 Å 1.96 80 90 p œ X" X# œ 44 41 œ 0.5 1.39 n" n#
q œ 1 p œ 1 0.5 œ 0.5 H!: p" œ p
H": p" Á p# (claim) p ^ q ^ p ^ q ^ C V. œ „ 2.58 ! œ 0.01 (^ p" ^ p#) z! É " " # # p" p# ^ ^ 2 n" n# z œ (p" p#) (p" p#) œ (0 4556)
#
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
191
(^ p ^ p ) z! Ép"q p q 80 90 "!! "!! ^ ^ " " # ^ ^# # ( p )( q ) ( 1 1 ) n" n# É(0 5)(0 5)( 1 1 ) 2 n" n# z œ 1.23 !Þ!) "Þ*'É!Þ)$Ð!Þ"(Ñ !Þ(&Ð!Þ#&Ñ "!! "!! p" p# !Þ!) "Þ*'É!Þ)$Ð!Þ"(Ñ !Þ(&Ð!Þ#&Ñ !Þ!$# p" p# !Þ"*# 2.58 0 Å 1.23 2.58
9. continued
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
Do not reject the null hypothesis. There is not enough evidence to support the claim that the proportions are different.
10.
Do not reject the null hypothesis There is not enough evidence to support the claim that there is a difference in the proportions.
Do not reject the null hypothesis There is not enough evidence to support the claim that the proportin of dog owners has changed.
192
)! *! 1 1 # " # 75 60 73 80 (^ p ^ p ) z! Ép"q p q
!Þ!' !Þ"# p" p# !Þ!' !Þ"# !Þ") p" p# !Þ!' 11 p ^ q ^ p ^ q ^ ^ 26 ^ 26 (^ p" ^ p#) z! É " # # p" p# p" œ 75 œ 0.3467 p2 œ 60 œ 0.4333 2 n" n# ^ p q ^ p ^ q ^ (^ p" ^ p#) z! É " " # # p œ X" X# œ 26 26 œ 0.3852 2 n" n# n" n# !Þ!*%% #Þ&)É!Þ&&Ð!Þ%&&'Ñ !Þ%&&'Ð!Þ&&Ñ q œ 1 p œ 1 0.3852 œ 0.6148 p" p# H : p œ p ! " # !Þ!*%% #Þ&)É !Þ&&Ð!Þ%&&'Ñ !Þ%&&'Ð!Þ&&Ñ H : p Á p (claim) )! *! " " # !Þ"!% p" p# !Þ#*$ C V. œ „ 1.96 ! œ 0.05 (TI: 0.103 p" p# 0.291) z œ (^ p" p ^ (p p ) œ (0 4333) 10 É( p )( q ) ( n" n# ) É(0 3852)(0 6148)( 1 1 ) ^ p" œ 10 œ 0.14 ^ p# œ 16 œ 0.20 z œ 1.03 73 80 p œ 10 16 œ 0.17 q œ 1 0.17 œ 0.83 H!: p" œ p# H": p" Á p# (claim) 1.96 Å 0 1.96 C V. œ „ 1.96 z œ (0 14 0 20) 0 œ 0.99 É(0 17)(0 83)( 1 1 ) (TI: z œ 1.04) 1.03
continued
12 ^ p" œ X œ 130 œ 0.65 n" 200 ^ p2 œ X2 œ 63 œ 0.21 1.96 Å 0 1.96 n2 300 0.99 p œ X" X# œ 130 63 œ 0.386 n" n# 200
q œ 1 p œ 1 0.386 œ 0.614 H!: p" œ p# ^ ^ " " # ^ ^# # p" p# H": p" p# (claim)
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
Since
193
($ )! 2 n n# p ^ q ^ p ^ q ^ z œ (0 21) œ 9.90 (^ p" ^ p#) z! É " " # # É(0 386)(0 614)( 1 1 ) 2 n" n# Ð!Þ"% !Þ#Ñ "Þ*'É!Þ"%Ð!Þ)'Ñ !Þ#Ð!Þ)Ñ 200 300 P-value < 0001
P-value < 0.01, reject the null hypothesis There is enough evidence to p" p# !Þ"%Ð!Þ)'Ñ !Þ#Ð!Þ)Ñ Ð!Þ"% !Þ#Ñ "Þ*'É ($ )! support the claimthat men are more safetyconscious than women
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
Do not reject the null hypothesis. There is
not enough evidence to support the claim that the proportions are different.
194
" # " # (^ p ^ p ) z! Ép"q p q (^ p ^ p ) z! Ép"q p q 150 200 200 300 150 13. ^ p" œ X" œ 50 œ 0.25 14. continued n" 200 ^ p# œ œ $ œ 0.31 X2 93 n2 00 p œ X" X# œ 50 93 œ 0.286 n" n# 200 q œ 1 p œ 1 0.286 œ 0.714 H!: p" œ p# 1.645 Å 0 H": p" Á p# (claim) 1.12 C V. œ „ 2.58 ! œ !Þ!" Do not reject the null hypothesis There is z œ (p ^ ^ p (p p ) œ (0 31) not enough evidence to support the claim É( p )( q ) ( 1 1 ) n" n# z œ 1.45 É(0 286)(0 714)( 1 1 ) 200 300 that a higher percentage of women have high blood pressure. 2.58 Å 1.45 0 2.58 15 ! œ 0.01 ^ p" œ 0.8 q ^ " œ 0.2 ^ p# œ 0.6 q ^ # œ 0.4 ^ p" ^ p# œ 0.8 0.6 œ 0.2 ^ ^ " " # ^ ^# # p" p#
2 n" n# p ^ q ^ p ^ q ^
(^ p" ^ p#) z! É " " # # 2 n" n# 0.2 2.58É(0 8)(0 2) (0 6)(0 4) p p ^ ^ " " # ^ ^# # p" p# 150 200 " # 2 n" n# p ^ q ^ p ^ q ^ 0.2 2.58É(0 8)(0 2) (0 6)(0 4) (^ p" ^ p#) z! É " " # # 0.077 p" p# 0.323 2 n" n# 0.06 2.58É 0 25Ð0 75Ñ 0 31Ð0 69Ñ 16 200 300 ^ p" œ 50 180 œ 0.278q ^ " œ 0.722 p" p# 0.06 2.58É 0 25Ð0 75Ñ 0 31Ð0 69Ñ 0.165 p" p# 0.045 ^ p# œ 39 œ 0.26 q ^ # œ 0.74 ^ p" ^ p# œ 0.278 0.26 œ 0.018 14 0.018 2.326É (0.278)(0.722) (0.26)(0.74) p p
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
The interval does not support the claimthat there is a difference. The interval contains 0
which allows for the possibilitythat no difference exists
195
200 200 ^ p" œ 43 œ 0.287 ^ p# œ 52 œ 0.347 180 150 " # (0.278)(0.722) (0.26)(0.74) 150 150 p œ 43 52 œ 0.317 0.018 2.326É 180 150 150 150 q œ 1 p œ 0.683 H!: p" œ p# 0.096 p" p# 0.132
H": p" p# (claim)
C V. œ 1.65 z œ (0 287 0 347) 0 œ 1.12 17 É(0 317)(0 683)( 1 1 ) 150 150 p ^ " œ 80 œ 0.4 ^ p# œ 59 œ 0.295 p œ X" X# œ 80 59 œ 0.3475 n" n# 200
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
Do not reject the null hypothesis. There is
not enough evidence to support the claim that the proportions are different.
The interval does agree with the Almanac statistics stating a difference of 0.042 since 0.042 is contained in the interval.
Reject the null hypothesis There is enough evidence to support the claim that the proportionof married men is greater than the proportionof married women.
196
continued
continued (^ p ^ p ) z! Ép"q p q " # " # 300 300 œ œ œ 0.528 300 250 p œ q œ 1 p œ 1 0.3475 œ 0.6525 H!: p" œ p# ^ p" ^ p# œ 0.0018 (^ p" ^ p#) z! É " # # p" p# H": p" Á p# (claim) q ^ 2 n" p ^ q ^ n# ^ ^ " " # ^ ^# # C V. œ „ 2.58 2 n" n# z œ (p ^ ^ p (p p ) œ (0 4 0 0 (0.2857)(0.7143) (0.2875)(0.7125) É( p )( q ) ( 1 1 ) É(0 3475)(0 6525)( 1 1 ) 0.0018 1.96É 350 400 n" n# 200 200 p" p# (0.2857)(0.7143) (0.2875)(0.7125) z œ 2.21 0.0018 1.96É 350 400 0.066 p" p# 0.0631
17.
19.
2.58 0 Å 2.58 2.21 20 ^ p" œ 178 œ 0.593^ p# œ 139 œ 0.463
X" X# n" n# 178 139 317 300 600
q œ 1 p œ 1 0.5283 œ 0.472 H!: p" œ p# 18 ^ p" œ X" œ 213 œ 0.71 ^ p# œ 185 œ 0.74 H": p" p# (claim) n" 300 250 C. V. œ 1.65 (0 593 0 0 p œ X" X# œ 213 185 œ 0.724 z œ œ 3.19 É(0 528)(0 472)( 1 1 ) n" n# 300 300 300 q œ 1 p œ 1 0.7236 œ 0.276 H!: p" œ p# H": p" Á p# (claim) C V. œ „ 2.58 z œ (0 71 0 74) 0 œ 0.78 É(0 724)(0 276)( 1 1 ) 0 1.65 Å 3.19 2.58 Å 0 2.58
21. 0.78 ^ p" œ X" œ 180 œ 0.6 ^ p# œ 200 œ 0.8
Chapter
9
-
Testing the Difference Between Two Means, Two Proportions, and Two Variances
197
continued 19. continued 350 n" 300 250
not reject the null hypothesis There is p œ X" X# œ 180 200 œ 0.691 not enough evidence to support the claim n" n# 300 that there is a difference in the proportions 19 q œ 1 p œ 1 0.691 œ 0.309 H!: p" œ p# ^ p1 œ 100 œ 0.2857 q ^ 1 œ 0.7143 ^ p2 œ 115 œ 0.2875 q ^ 2 œ 0.7125 H": p" Á p# (claim) 400 C V. œ „ 2.58
17.
Do
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
Reject the null hypothesis. There is enough evidence to support the claim that the
Do not reject the null hypothesis There is not enough evidence to support the claim that the proportions are different between
Reject the null hypothesis There is enough evidence to support the claim that the proportions are different.
198
21. continued 23. continued " # " # # " # 1200 200 œ œ 0.485 # " # p œ z œ (p ^ ^ p (p p ) œ (0 6 0 0 H!: p" œ p# É( p )( q ) ( 1 1 ) É(0 691)(0 309)( 1 1 ) n" n# 300 250 H": p" Á p# (claim) z œ 5.05 C V. œ „ 2.58 z œ (^ p" p ^ (p p ) œ (0 6 0 0 É( p )( q ) ( 1 1 ) É(0 563)(0 437)( 1 1 ) z œ 1.10 n" n# 120 150 Å 2.58 0 2.58 5.05
2.58 0 Å 2.58
students receiving
22 ^ p" œ X" œ 980 œ 0.8167 1.10
proportionof
aid has changed
n" 1200 ^ p# œ 940 œ 0.7833 p œ X" X# œ 980 940 œ 0.8 male interviewees and female interviewees 24 n" n# 1200 ^ p" œ X" œ 114 œ 0.57 q œ 1 p œ 1 0.8 œ 0.2 n" 200 H!: p" œ p# ^ p# œ 80 œ 0.4 H": p" Á p# (claim) X" X# n" n# 114 80 200 C. V. œ „ 1.96 z œ (0 8167 0 7833) 0 œ 2.045 q œ 1 p œ 1 0.485 œ 0.515 H!: p" œ p# É(0 8)(0 2)( 1 1 ) H : p Á p (claim) (TI œ 2.041) 1200 1200 " " # C. V. œ „ 1.96 z œ (^ p" p ^ (p p ) œ (0 57 0 0 É( p )( q ) ( 1 1 ) É(0 485)(0 515)( 1 1 ) z œ 3.402 n" n# 200 200 1.96 0 1.96 Å 2.045
23 1.96 0 1.96
199
Two Means,
Proportions,
Variances 21. continued 23. continued 150 Å 3.402 ^ p" œ X" œ 72 œ 0.6 Reject the null hypothesis There is enough n" 120 ^ p# œ 80 œ 0.533 p œ X" X# œ 72 80 œ 0.563 evidence to support the claim that the proportions are different. n" n# 120 q œ 1 p œ 1 0.563 œ 0.437
Chapter 9 - Testing the Difference Between
Two
and Two
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
27. continued
2.952 (TI: z œ 2.9589; P-value œ 0.00154)
< 0.002 (0.0015).
Since P-value < !, reject the null hypothesis. There is enough evidence to support the claimthat the proportionof women who use coupons is greater than the proportionof men who use coupons
Do not reject the null hypothesis. There is not enough evidence to support the claim that there is a difference in the proportions
28. No, because p" could equal p3.
1
The variance in the numerator should be the larger of the two variances
2.
Since the larger variance is placed in the numerator of the formula, F € 1.
3.
One degree of freedomis used for the
variance associated with the numerator, and one is used for the variance associated with the denominator
P-value œ 0.3050.
Since P-value > !, do not reject the null hypothesis There is not enough evidence to support the claimthat the proportionof men who have never married is greater than the proportionof women who have never married.
27.
4.
The characteristicsof the F-distributionare:
a. The values of F cannot be negative.
b The distributionis positivelyskewed
c. The mean value of F is approximately equal to 1.
d. The F distributionis a familyof curves based upon the degrees of freedom
200
25.
" # " # 250 200 " # " # 200 200 ^ p" œ 132 œ 0.733^ p# œ 56 œ 0.56 z œ (0 065 0 0 œ 0.58 180 100 É(0 0725)(0 9275)( 1 1 ) p œ X" X# œ 132 56 œ 188 œ 0.671 200 200 n" n# 180 280 q œ 1 p œ 1 0.671 œ 0.329 H!: p" œ p# H": p" p# (claim) z œ (p ^ ^ p (p p ) œ (0 733 0 0 1.96 Å 0 1.96 É( p )( q ) ( 1 1 ) É(0 671)(0 329)( 1 1 ) n" n# 180 100 0.58
œ
P-value
z
26 ^ p" œ 78 œ 0.312^ p# œ 58 œ 0.29 p œ X" X# œ 78 58 œ 0.302
EXERCISE
9-5
SET
n" n# 250 q œ 1 p œ 1 0.302 œ 0.698 H!: p" œ p#
": p" p#
H
(claim)
z œ (p ^ ^ p (p p ) œ (0 312 0 0
É( p )( q ) ( 1 1 ) n" n# z œ 0.505 or 0.51 É(0 302)(0 698)( 1 1 ) 250 200
^ p" œ 13 œ 0.065 ^ p2 œ 16 œ 0.08 5
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
201
25. 27. continued p œ œ 0.0725 a. d. f. N œ 15, d. f. D œ 22; C. V. œ 3.36 13 16 200 200 q œ 1 p œ 1 0.0725 œ 0.9275 H!: p" œ p# b. d. f. N œ 24, d. f. D œ 13; C. V. œ 3.59 c. d. f. N œ 45, d. f. D œ 29; C. V. œ 2.03 6 H": p" Á p# (claim) a. d. f. N œ 8, d. f. D œ 4, C. V. œ 14.80 b. d. f. N œ 20, d. f. D œ 16; C. V. œ 2.28 C. V. œ „ 1.96 c. d f. N œ 10, d f. D œ 10; C V. œ 2.98
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
Note: Specific P-values are in parentheses
c. P-value œ 0.05 d
< P-value < 0.01 (0.006)
standard deviations are different. 1.00
Do not reject the null hypothesis There is not enough evidence to support the claim that the variances are different.
!: H": 5# œ 5# 5# Á 5# (claim)
2.08 C V. œ 4.36 ! œ 0 05
10. H!: H"
: 5
202
10.
8 a. P-value œ
P > 0.10
d 0.01 < P-value
9 " # " # 2 s " # " # 2 # s " " # 2 3 232# 2 F œ (7 5) œ 3.35 # #
7.
continued
0.05 b.
(0.112) c. 0.05 < P-value < 0.10 (0.068)
< 0.02 (0.015)
11.
0.005
H!: H": 5# œ 5# 5# Á 5# (claim) s" œ 33.99 s# œ 33.99 C. V. œ 4.99 ! œ 0 05 d f. N œ 7 d f. D œ 7 F œ s" œ (33 99) œ 1 # # # (33 99)# H!: H": 5# œ 5# 5# Á 5# (claim) s" œ 2.290 s# œ 1.586 C V. œ 3.43 ! œ 0 05 0 Å 4.99
a. 0.025 < P-value < 0.05 (0.033) b. 0.05 < P-value < 0.10 (0.072) f. N œ 12 d f. D œ 11 F œ s" œ 2 290# œ 2.08 # 1 586#
d
0 Å 3.43 s" œ 8.039 s# œ
12.
H
3.232
" œ
5" Á
C. V. œ 2.51 ! œ 0
0 4.36 Å d f. N œ 23 d f. D œ
# (4 1)# 6.19
Do not reject the null hypothesis. There is not enough evidence to support the claim that the variances are different.
d. f. N œ 9 d. f. D œ 8 F œ 8 039# œ 6.19
5#
5# (claim)
05
19
Reject the null hypothesis. There is enough evidence to support the claim that there is a difference in the variances
Reject the null hypothesis There is enough evidence to support the claim that the
203 r 9 - Testing the Difference Between ns, Two Proportions,
Variances
continued " # " # 0 2.51 Å 13 H!: H": 5# œ 5# 5# 5# (claim) 3.35
and Two
10.
s" œ 111.211 s# œ 35.523 n" œ 7 n# œ 6 d f. N œ 6 d f. D œ 5 C. V. œ 4.950 at ! œ 0.05
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
14. continued
Reject the null hypothesis at ! œ 0.05. There is enough evidence to support the claimthat the variance in area is greater for Eastern cities
Do not reject the null hypothesis at !
0.01 There is not enough evidence to support the claimthat the variance in area is greater for Eastern cities.
Do not reject the null hypothesis. There is not enough evidence to support the claim that there is a difference between the variances in tuition costs
204
s " # " # 2 s " # " # " # F œ (118 4) œ 1.45 2 F œ œ 2.97 # # 13.
C. V. œ 10.67 at ! œ 0.01
continued
# # F œ s œ (111 211) œ 9.80 are not the same. # (35 523)# 15. H!: 5# œ 5# H": 5# Á 5# (claim) 0 4.95 Å 9.80 Research: s" œ 5501.118 PrimaryCare: s# œ 5238.809 C V. œ 4.03 ! œ 0 05
chocolate candyand non-chocolate candy
d. f. N œ 9 d. f. D œ 9 # # F œ s" œ (5501 118) œ 1.10 # (5238 809)# Å 9.801 10.67 0 Å 1.10 4.03
œ
16 14. H!: 5# œ 5# # # H!: H": 5# œ 5# 5# 5# (claim) H": 5" Á 5# (claim) s œ 98.2 s œ 118.4 " # Chocolate: s œ 6.4985 C. V. œ 3.15 ! œ 0.01 Non-chocolate: s œ 11.2006 d f. N œ 19 d f. D œ 19 # (98 2)# C. V. œ 2.75 ! œ 0 10 d. f. N œ 10 d. f. D œ 12 11 2006# 6 4985# 0 Å 1.45 3.15
Do not reject the null hypothesis. There is not enough evidence to support the claim that the variance of the areas in Indiana is less than the variance of the areas in Iowa.
Reject the null hypothesis There is enough evidence to support the claim that the variances in carbohydrate grams of
205
-
0 2.75 Å 2.97
Chapter 9
Testing the Difference Between Two Means, Two Proportions, and Two Variances
Chapter 9 - Testing the Difference Between Two Means,
Two Proportions, and Two Variances
Do not reject the null hypothesis. There is not enough evidence to reject the claimthat the variances of the heights are equal.
Reject the null hypothesis There is enough evidence to support the claim that the variances of the two teams are different.
Since
reject the null hypothesis There is enough evidence to
Since
hypothesis. There is enough evidence to support the claimthat the variation in the salaries of the elementaryschool teachers is greater than the variation in salaries of the secondaryteachers
Reject the null hypothesis. There is enough evidence to support the claim that the variances are different.
206
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P-valu !,
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reject the claimthat the variances in weights
are equal.
P-valu !,
reject the null
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Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
207
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continued
Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances
24. continued
Do not reject the null hypothesis. There is not enough evidence to support the claim that there is a difference in the variances REVIEW
Do not reject the null hypothesis. There is not enough evidence to support the claim that there is a difference in the variances.
Reject the null hypothesis There is enough evidence to support the claim that there is a difference in the variances
Do not reject the null hypothesis There is not enough evidence to support the claim that single people do more pleasure driving than married people.
208
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EXERCISES
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- CHAPTER 9
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