# CHAPTER 10 by QdIe2NaD

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```									                                                                                         CHAPTER 9
TESTS OF HYPOTHESIS: SMALL SAMPLES

1.   a.      Reject Ho where t > 1.833
12  10
b.      t             2.108
(3 / 10 )
c.      Reject Ho, the mean is greater than 10.

2.   a.      Reject Ho if t < 3.106 or t > 3.106
407  400
b.      t               4.042
(6 / 12 )
c.      Reject Ho, the mean does not equal 400.

3.   Ho:   40       H1:  > 40     Reject Ho if t > 1.703
42  40
t               5.040
(2.1 / 28 )
Reject Ho and conclude that the mean number of calls is greater than 40 per week.

4.   Ho:   42.3 H1:  < 42.3 Reject Ho if t < 1.319
40.6  42.3
t               3.084
(2.7 / 24 )
Reject Ho. The mean assembly time is less than 42.3 minutes.

5.   Ho:   22,100          H1:  > 22,100            Reject Ho if t > 1.740
23,400  22,100
t                   3.680
(1500 / 18 )
Reject Ho and conclude that the mean life of the spark plugs is greater than 22,100 miles.

6.   Ho:   15      H1:  > 15      Reject Ho if t > 1.725
18  15
t            13.75
(1 / 21)
Reject Ho and conclude that the mean service time is greater than 15 minutes.

7.   a.      Reject Ho if t < 3.747
(85) 2
1495 
5  3536                  17  20
b.      X  17 and s                    .             t              190
.
51                            .
3536 / 5
c.      Do not reject Ho. We cannot conclude the population mean is less than 20.
d.      Between 0.05 and 0.10, about 0.065

85                                    Chapter 9
8.      a.      Reject Ho if t < 2.571 or t > 2.571
111667  100
.
b.       t                 4.72
6.055 / 6
c.      Reject Ho. The population mean is not equal to 100
d.      less than 0.01 (between 0.001 and 0.01)

9.      Ho:   4.35            H1:  > 4.35             Reject Ho if t > 2.821
4.368  4.35
t                  168
.
(0.0339 / 10 )
Do not reject Ho. The additive did not increase the mean weight of the chickens. The p-value is
between 0.10 and 0.05.

10.     Ho:   2160            H1:  > 2160             Reject Ho if t > 2.306
2172.44  2160
t                  3.98
(9.3823 / 9 )
Reject Ho. The mean chlorine shelf life has increased. The p-value is less than 0.005.

11.     Ho:   4.0              H1:  > 4.0           Reject Ho if t > 1.796
4.50  4.0
t                 0.65
(2.68 / 12 )
Do not reject Ho. Mean number of fish caught has not been shown to be greater than 4.0. The p-
value is greater than 0.10.

12.     Ho:   53              H1:  > 53           Reject Ho if t > 1.761
56.4  53.0
t                  352
.
(3.7378 / 15 )
Reject Ho. The mean number of surveys conducted is greater than 53. The p-value is less than
0.005.

13.     a.      Reject Ho if t > 2.120 or t < 2.120      df = 10 + 8 – 2 = 16
(10  1)(4)  (8  1)(5)
2            2
b.      s2                              19.9375
10  8  2
p

23  26
c.      t                       1416
.
F I
G J 1 1

19.9375
H K10 8
d.      Do not reject Ho.
e.      p-value is greater than 0.10 and less than 0.20

Chapter 9                                           86
14.   a.      Reject Ho if t > 1.697 or t < 1.697      df = 17 + 15 – 2 = 30
(15  1)(12)  (17  1)(15)
2              2
b.      s2                                 187.20
15  17  2
p

350  342
c.      t                       1651
.
F
G 1

1I
J
187.2
H15 17   K
d.      Do not reject Ho.
e.      p-value is greater than 0.10 and less than 0.20

15.   Ho: f  m              H1: f > m       df = 9 + 7 – 2 = 14       Reject Ho if t > 2.624
(7  1)(6.88)  (9  1)(9.49)
2                2
79  78
s2                                   71749
.                  t                      0.234
p
972                                                    F I
G J
71.749 
1 1
H K
7 9
Do not reject Ho. There is no difference in the mean grades.

16.   Ho: s  d               H1: s > d      df = 15 + 12 – 2 = 25 Reject Ho if t > 2.485
(15  1)(155) 2  (12  1)(181) 2
.                 .                               61  48.4
s2                                     278.69             t                     1.949
p
15  12  2                                              1F
G
1     I
J
278.69
H
15 12      K
Do not reject Ho. There is no difference in the mean amount of time spent watching television.

17.   Ho: s  a              H1: s> a       df = 6 + 7 – 2 = 11     Reject Ho if t > 1.363
(6  1)(12.2)  (7  1)(158)
2
.  2
142.5  130.3
s2                                  20382
.                 t                    1536
.
p
672
20382 
F I
G J
1 1
.
H K
6 7
Reject Ho. The mean daily expenses are greater for the sales staff. The p-value is between 0.05
and 0.10.

18.   Ho: n  t                H1: n > t      df = 12 + 8 – 2 = 18  Reject Ho if t > 2.552
(12  1)(22.8) 2  (8  1)(34.4) 2                         5358  526.8
.
s2                                      777.88             t                   0.707
p
12  8  2
777.88 
F I
G J
1 1
H K
8 12
Do not reject Ho. There is no difference in the mean salary of nurses and elementary school
teachers. The p-value is greater than 0.10.

19.   a.      Reject Ho if t > 2.353
(12) 2
38 
12                                   4  0.816
b.       d       3.00           sd 
4                                 3
3.00
c.      t               7.35
0.816 / 4
d.      Reject the Ho. There are more defective parts produced on the day shift.
e.      p-value is less than 0.005, but greater than 0.0005

87                                     Chapter 9
20.     a.       Reject Ho if t < 2.776 or t > 2.776
(23) 2
115 
23                                   5  152
b.       d        4.6            sd                  .
5                                4
4.6
c.       t              6.767
.
152 / 5
d.       Reject the Ho. There is a difference in the mean number of citations given by the two
officers.
e.       p-value is less than 0.01, but greater than 0.001

21.     Ho: d  0             H1: d > 0      Reject Ho if t > 2.764
d = 7.3636             sd = 8.3699
7.3636
t               2.92         Reject Ho. The weights have increased
8.3699 / 11

22.     Ho: d  0             H1: d > 0        Reject Ho if t > 1.796
d = 25.917              sd = 40.791
25.917
t               2.20
40.791 / 12
Reject Ho. The incentive plan resulted in an increase in daily income. The p-value is about
0.025.

23.     Ho: d  0                H1: d > 0      Reject Ho if t > 2.821
d = 0.10                  sd = 4.28
.
010
t             0.07              Fail to reject Ho. There has been no reduction.
4.28 / 10

24.     Ho: d  0     H1: d < 0         Reject Ho if t < 2.998
d = 3.625     sd = 4.8385
3.625
t              2.12            Do not reject Ho. The p-value is about 0.035
4.8385 / 8

25.     Ho:   87       H1:  < 87       Reject Ho if t < 1.895
664                                 55,244  (664) 2 / 8
X    83.0                   s                          4.3425
8                                        81
83  87
t               2.61           Reject Ho. The mileage is less than advertised.
4.3425 / 8

26.     Ho:   42       H1:  > 42    Reject Ho if t > 1.796
51  42
t           3.90
8 / 12
Reject Ho. The mean time for delivery is more than 42 days. The p-value is less than 0.005

Chapter 9                                               88
27.   Ho:   9        H1:  > 9     Reject Ho if t > 2.998
X = 9.488       s = 0.467
9.488  9.00
t                2.95
0.467 / 8
Do not reject Ho. The mean prime rate for small banks is 9.0 percent. The p-value is less than
0.025.

28.   Ho:  =2.25     H1:   2.25 Reject Ho if t < 2.201 or t > 2.201
X = 2.087       sd = 0.4048
2.087  2.25
t                1395
.
0.4048 / 12
Do not reject Ho. There is not a difference in the mean amount of coffee consumed at
Northwestern State.

29.   Ho:   25      H1:  > 25    Reject Ho if t > 2.624
X = 26.07       s = 1.5337
26.07  25.00
t                 2.702
.
15337 / 15
Reject Ho. The mean number of patients per day is more than 25. The p-value is less than 0.01.

30.   Ho:   6.5     H1:  < 6.5     Reject Ho if t < 2.718
X = 5.1667      s = 3.1575
51667  6.5
.
t                 1463
.
.
31575 / 12
Do not reject Ho.

31.   Ho:   3.5     H1:  < 3.5   Reject Ho if t < 1.746
2.9553  35 .
X  2.9553     s= 0.5596       t                4.013
0.5596 / 17
Reject Ho. The mean time to complete a game is less than 3.5 hours.

32.   Ho:  =0        H1:   0      Reject Ho if t < 2.110 or t > 2.110
X = 0.2322 s = 0.3120
0.2322  0
t                3158
.
0.3120 / 18
Reject Ho. The mean gain or loss does not equal 0. The p-value is less than 0.01, but greater than
0.001.

33.   Ho:   4.5%            H1:  > 4.5%           Reject Ho if t > 1.796
X = 4.5717      s = 0.2405
4.5717  4.50
t                 1033
.
0.2405 / 12
Do not reject Ho. The mean number rate of return is not more than 4.5%.

89                                    Chapter 9
34.     Ho: 1 = 2               H1: 1  2            Reject Ho if t < 2.060 or t > 2.060
(15  1)(2.6)  (12  1)(3.3) 2
2
17.6  16.2
s2                                   8.5772                      t                     123
.
p
15  12  2                                                        F
G
1

1      I
J
8.5772
H
15 12        K
Do not reject Ho. There is no difference in the mean percent of salaries spent by employees on
the two health packages.

35.     Ho: e  b               H1: e > b           Reject Ho if t > 1.701
(20  1)(584)  (10  1)(5.67)
.    2               2
24.80  20.25
s2                                    33.4767                   t                               2.031
p
20  10  2                                                       F 1I
33.4767G  J
1
H 20K
10
Ho is rejected. The mean weight of the packages at the end of the month is larger.

36.     Ho: n = s               H1: n  s              Reject Ho if t < 2.086 or t > 2.086
(10  1)(10.5)  (12  1)(14.25)
2                  2
8355  78.8
.
s2                                      1612969
.            t                          0.874
p
10  12  2                                                1F
G  
1   I
J
.
1612969
H
10 12      K
Do not reject Ho. There is no difference in the mean number of hamburgers sold at the two
locations.

37.     Ho: 1  2               H1: 1 > 2              Reject Ho if t > 2.567
(8  1)(2.2638)  (11  1)(2.4606)
2                   2
10.375  5.636
s2                                         5.672         t                    4.28
p
8  11  2                                           F I
G J
1 1
5.672 
H K
8 11
Reject Ho. The mean number of transaction by the young adults is more than for the senior
citizens.

38.     Ho: 1 = 2               H1: 1  2                Reject Ho if t > 2.086 or t < 2.086
X 1 =12.17        s1 = 1.0563     X 2 = 14.875       s2 = 2.2079
(10  1)(10563) 2  (12  1)(2.2079) 2
.                                                           12.17  14.875
s2                                            31832
.                    t                       3541
.
p
10  12  2                                                   F 1I
31832G  J
1
.
H 12 K
10
Reject Ho. There is a difference in the mean race times.

39.     Ho: 1  2               H1: 1 > 2           Reject Ho if t > 2.650
X 1 =125.125      s1 = 15.094     X 2 = 117.714         s2 = 19.914
(8  1)(15.094) 2  (7  1)(19.914) 2                               125125  117.714
.
s2                                           305.708                t                       0.819
p
872                                                          F 1I
305.708G J
1
H 7K
8
Ho is not rejected. There is no difference in the mean number sold at the regular price and the
mean number sold at reduced price.

Chapter 9                                               90
40.   Ho: 1 = 2              H1: 1  2             Reject Ho if t > 1.717 or t < 1.717
(10  1)(13.68)  (14  1)(6.71) 2
2
838  79.29
.
s2                                      10316
.           t                        1.07
p
10  14  2                                           F
G 1

1 I
J
.
10316
H10 14    K
Do not reject Ho. There is no difference in the mean number of hours for the two treatments.

41.   Ho: 1 = 2              H1: 1  2             Reject Ho if t > 2.819 or t < 2.819
(10  1)(2.33)  (14  1)(2.55) 2
2
1587  18.29
.
s2                                     6.06            t                      2.374
p
10  14  2                                        F
G  1

1    I
J
H
6.06
10 14      K
Do not reject Ho. There is no difference in the mean amount purchased.

42.   Ho: d  0              H1: d < 0    Reject Ho if t < 2.998
d = 2.5        sd = 2.928
2.5
t              2.415
2.928 / 8
Do not reject Ho. There mean number of accidents has not been reduced.

43.   Ho: d  0              H1: d > 0       Reject Ho if t > 1.895
d = 1.75       sd = 2.9155
.
175
t              1698
.
2.9155 / 8
Do not reject Ho. There is no difference in the mean number of absences. The p-value is greater
than 0.05.

44.   Ho: d  0              H1: d > 0     Reject Ho if t > 1.796
d = 0.1908      sd = 0.3260
.
01908
t                2.027
0.3260 / 12
Reject Ho. The chip reduced the mean processing time. The p-value is greater than 0.025.

45.   Ho: d  0               H1: d > 0   Reject Ho if t > 1.833
d = 0.027       sd = 0.2661
0.027
t                0.321
0.2661 / 10
Do not reject Ho. We have not shown a decline in grades.

46.   Ho: d = 0              H1: d  0       Reject Ho if t < 1.761 or t > 1.761
d = 247.67             sd = 548.04
247.67
t                175
.
548.04 / 15
Do not reject Ho. There is no difference in the mean insurance price.

91                                  Chapter 9
47.     Ho: d  0              H1: d > 0       Reject Ho if t > 2.764
d = 4.02        sd = 6.41
4.02
t             2.080
6.41 / 11
Do not reject Ho. Stock prices have not significantly increased.

48.     Answers will vary. Answer developed February 10, 1998
Ho: d  0             H1: d > 0       Reject Ho if t > 1.860
d = 2.99               sd = 3.38
2.99
t            2.654
3.38 / 9
Reject Ho. The mean price of the stock increased.

49.     a.      1 = without pool        2 = with pool
Ho: 1 = 2              H1: 1  2             Reject Ho if t > 2.000 or t < 2.000
X 1 = 202.79    s1 = 33.71       n = 38
X 2 = 231.48    s2 = 50.48       n = 67
(38  1)(33.71)  (67  1)(50.48) 2
2
s2                                        204105
.
38  67  2
p

202.79  231.48
t                          312
.
F
G1

1I
J
2041.05
H38 67   K
Reject Ho. There is a difference in mean selling price for homes with and without a pool.
b.      1 = without garage       2 = with garage
Ho: 1 = 2               H1: 1  2             Reject Ho if t > 2.000 or t < 2.000
 = 0.05                  df = 34 + 71 – 2 = 103
X 1 = 185.44      s1 = 28.01       X 2 = 238.18 s2 = 44.88
(34  1)(28.01) 2  (71  1)(44.88) 2
s2 
p                                          1620.25
103
185.44  238.18
t                         6.28
F
G1

1 I
J
1620.25
H
34 71    K
Reject Ho. There is a difference in mean selling price for homes with and without a
garage.

Chapter 9                                           92
c.   Ho: 1 = 2                H1: 1  2            Reject Ho if t > 2.036 or t < 2.036
X 1 = 196.92       s1 = 35.79      n = 15
X 2 = 227.45       s2 = 44.2      n = 20
(15  1)(35.79)  (20  1)(44.2) 2
2
s2                                      1668.24
15  20  2
p

196.92  227.45
t                        2.188
1F
G
1    I
J
1668.24
H
15 20     K
Reject Ho. There is a difference in mean selling price for homes in Township 1 and
Township 2.

50.   a.   Ho: n = a                    H1: n  a               Reject Ho if t > 2.048 or t < 2.048
(16  1)(34.3) 2  (14  1)(40.7) 2
s2                                          1399.3471
16  14  2
p

160.3  178.5             18.2
t                                        1329
.
F
G    1

1I
J     13.69
1399.3471
H   16 14     K
Do not reject Ho. There is no difference in mean number of home runs hit per team in the
American League and the National League.
b.   Ho: n = a                    H1: n  a               Reject Ho if t > 2.048 or t < 2.048
(16  1)(0.0125)  (14  1)(0.0095)
2                    2
s2                                               0.0001256
16  14  2
p

0.262  0.271             0.090
t                                         2.194
F
G     1

1I
J     0.0041
0.0001256
H    16 14    K
Reject Ho. There mean team batting average is different for the American and national
League teams..
c.   Ho: n = a                    H1: n  a               Reject Ho if t > 2.048 or t < 2.048
(16  1)(0.826)  (14  1)(0.833)
2                   2
s2                                            0.6877
16  14  2
p

2.402  2.299             .
0103
t                                     0.339
F
G1

1I
J     0.3035
0.6877
H
16 14      K
Do not reject Ho. There is no difference in the mean attendance between National and
American League teams.
d.   Ho: T = G                    H1: T  G               Reject Ho if t > 2.048 or t < 2.048
(21  1)(318)  (9  1)(47.0)
.    2                 2
s2                                        1353.46
21  9  2
p

1761  1517
.        .            24.4
t                                      1.665
F I
G J
1 1

14.6572
1353.46
H K
21 9
Do not reject Ho. There is no difference between the mean number of home runs hit by
teams with artificial turf stadiums and those with grass fields

93                                   Chapter 9
51.     Ho: 1 = 2               H1: 1  2            Reject Ho if t > 2.052 or t < 2.052
(22  1)(354)  (7  1)(150)
.   2
. 2
s2                                   10.2468
22  7  2
p

12.89  14.59       17000
.
t                                  1224
.
F I
G J 1 1

.
13891
10.2468
H K
22 7
Do not reject Ho. There is no difference in the mean percent of the population over 65 years of
age for G7 countries and non G7 countries.

Chapter 9                                          94

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