Answer:
H0: μ ≤ 1.30
H1: μ > 1.30
|Test statistic | > 1.833 ; Reject H0
Test statistic = 3.11
Yes
Pvalue = 0.006
Step-by-step explanation:
H0: μ ≤ 1.30
H1: μ > 1.30
Samples, X ; 1.36,1.35,1.33, 1.66, 1.58, 1.32, 1.38, 1.42, 1.90, 1.54
Xbar = 14.84 / 10 = 1.484
Standard deviation, s = 0.187 (calculator)
Decison rule :
|Test statistic | > TCritical ; reject H0
df = n - 1 = 10 - 1 = 9
Tcritical(0.05; 9) = 1.833
|Test statistic | > 1.833 ; Reject H0
Test statistic :
(xbar - μ) ÷ (s/√(n))
(1.484 - 1.30) ÷ (0.187/√(10))
0.184 / 0.0591345
Test statistic = 3.11
Since ;
|Test statistic | > TCritical ; We reject H0 and conclude that water consumption has increased
Pvalue estimate using the Pvalue calculator :
Pvalue = 0.006
12x > 18x - 27 - 15
12x > 18x - 42
12x - 18x > -42
-6x > -42
x < -42/-6
two negatives make a positive so now its x < 42/6
Lastly divide 42/6 so it can equal 7
Answer: X < 7.
Answer:
a) False
b) False
c) True
d) False
e) False
Step-by-step explanation:
a. A single vector by itself is linearly dependent. False
If v = 0 then the only scalar c such that cv = 0 is c = 0. Hence, 1vl is linearly independent. A set consisting of a single vector v is linearly dependent if and only if v = 0. Therefore, only a single zero vector is linearly dependent, while any set consisting of a single nonzero vector is linearly independent.
b. If H= Span{b1,....bp}, then {b1,...bp} is a basis for H. False
A sets forms a basis for vector space, only if it is linearly independent and spans the space. The fact that it is a spanning set alone is not sufficient enough to form a basis.
c. The columns of an invertible n × n matrix form a basis for Rⁿ. True
If a matrix is invertible, then its columns are linearly independent and every row has a pivot element. The columns, can therefore, form a basis for Rⁿ.
d. In some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix. False
Row operations can not affect linear dependence among the columns of a matrix.
e. A basis is a spanning set that is as large as possible. False
A basis is not a large spanning set. A basis is the smallest spanning set.
the answer for x is 1 because 1/3 should be multiplied by x and x is one
