CHAPTER 12
Section 12.1
1. a. Stem and Leaf display of temp: 17 0 17 23 17 445 17 67 17 18 0000011 18 2222 18 445 18 6 18 8
stem = tens leaf = ones
180 appears to be a typical value for this data. The distribution is reasonably symmetric in appearance and
CHAPTER 13
Section 13.1
1. a.
2 ^i is 10 1 - 1 - (x i - 15 ) = = 250 , so s.d. of Yi - Y 5 250
x = 15
and
(x
j
- x)
2
6.32, 8.37, 8.94, 8.37, and 6.32 for i = 1, 2, 3, 4, 5. b. Now
x = 20 and
(x
i
- x ) = 1250 , giving standard deviations 7.87, 8.49, 8.
CHAPTER 14
Section 14.1
1. a. We reject Ho if the calculated
2 value is greater than or equal to the tabled value of
2 , k -1 from Table A.7. Since 12.25 .2 , 4 = 9.488 , we would reject Ho . 05
b. c. d.
Since 8.54 is not Since 4.36 is not
.2 , 3 = 11.3
CHAPTER 15
Section 15.1
1.
H 0 : = 100 vs. H a : 100 . The test statistic is s + = sum of the ranks associated with the positive values of ( xi - 100) , and we reject Ho at significance level .05 if s + 64 . (from Table A.13, n = 12, with / 2 = .026 , whi
CHAPTER 16
Section 16.1
1. All ten values of the quality statistic are between the two control limits, so no out-of-control signal is generated.
2.
All ten values are between the two control limits. However, it is readily verified that all but one plotted
CHAPTER 9
Section 9.1
1. a.
E (X - Y ) = E( X ) - E (Y ) = 4.1 - 4.5 = -.4 , irrespective of sample sizes.
V ( X - Y ) = V (X ) + V (Y ) =
of
2 12 2 (1 .8) (2.0) = .0724 , and the s.d. + = + m n 100 100 2 2
b.
X - Y = .0724 = .2691 .
c.
A normal curve wit
CHAPTER 11
Section 11.1
1. a.
30.6 59.2 7.65 = 7.65 , MSE = = 4.93 , f A = = 1.55 . Since 1.55 is 4 12 4.93 not F. 05, 4 ,12 = 3.26 , don't reject HoA . There is no difference in true average tire MSA =
lifetime due to different makes of cars.
b.
44.1 14.
CHAPTER 10
Section 10.1
1. a. Ho will be rejected if
f F.05, 4,15 = 3.06 (since I 1 = 4, and I ( J 1 ) = (5)(3) = 15 ).
The computed value of F is
f =
3.06 , Ho is not rejected. The data does not indicate a difference in the mean tensile strengths of the
CHAPTER 8
Section 8.1
1. a. b. c. d. Yes. It is an assertion about the value of a parameter. No. The sample median
~ X is not a parameter.
No. The sample standard deviation s is not a parameter. Yes. The assertion is that the standard deviation of populat
CHAPTER 7
Section 7.1
1. a.
z 2 = 2.81 implies that 2 = 1 - (2.81) = .0025 , so = .005 and the confidence
level is 100 1 -
(
)% = 99.5% .
b. c.
z 2 = 1.44 for = 2[1 - (1.44)] = .15 , and 100(1 - )% = 85% .
99.7% implies that
= .003 , 2 = .0015 , and z .0
CHAPTER 2
Section 2.1
1.
a. S = cfw_ 1324, 1342, 1423, 1432, 2314, 2341, 2413, 2431, 3124, 3142, 4123, 4132, 3214, 3241, 4213, 4231 Event A contains the outcomes where 1 is first in the list: A = cfw_ 1324, 1342, 1423, 1432 Event B contains the outcomes
CHAPTER 5
Section 5.1
1. a. b. c. P(X = 1, Y = 1) = p(1,1) = .20 P(X 1 and Y 1) = p(0,0) + p(0,1) + p(1,0) + p(1,1) = .42 At least one hose is in use at both islands. P(X 0 and Y 0) = p(1,1) + p(1,2) + p(2,1) + p(2,2) = .70 By summing row probabilities, p
CHAPTER 3
Section 3.1
1. S: X: FFF 0 SFF 1 FSF 1 FFS 1 FSS 2 SFS 2 SSF 2 SSS 3
2.
X = 1 if a randomly selected book is non-fiction and X = 0 otherwise X = 1 if a randomly selected executive is a female and X = 0 otherwise X = 1 if a randomly selected driv
CHAPTER 6
Section 6.1
1. a. We use the sample mean,
x to estimate the population mean .
^ =x=
b.
xi 219.80 = = 8.1407 n 27
We use the sample median, ascending order).
~ = 7.7 (the middle observation when arranged in x
1860.94 - ( 219.8) 27 s = = 1.660 26
Chapter 1: Overview and Descriptive Statistics
CHAPTER 1
Section 1.1
1. a. b. c. d. Houston Chronicle, Des Moines Register, Chicago Tribune, Washington Post Capital One, Campbell Soup, Merrill Lynch, Pulitzer Bill Jasper, Kay Reinke, Helen Ford, David Men
Chapter 4
Continuous
Random Variables
and Probability
Distributions
4.1
Continuous Random
Variables and
Probability
Distributions
Continuous Random Variables
A random variable X is continuous if its
set of possible values is an entire
interval of numbers
Chapter 3
Discrete Random
Variables and
Probability
Distributions
3.1
Random
Variables
Random Variable
For a given sample spaceS of some
experiment, a random variable is any
rule that associates a number with
each outcome in S .
Bernoulli Random Variable