Answer:
The confidence interval for 90% confidence would be narrower than the 95% confidence
Step-by-step explanation:
From the question we are told that
The sample size is n = 41
For a 95% confidence the level of significance is ![\alpha = [100 - 95]\% = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%5B100%20-%2095%5D%5C%25%20%3D%20%200.05)
and
the critical value of 
is 
For a 90% confidence the level of significance is ![\alpha = [100 - 90]\% = 0.10](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%5B100%20-%2090%5D%5C%25%20%3D%20%200.10)
and
the critical value of is 
So we see with decreasing confidence level the critical value decrease
Now the margin of error is mathematically represented as
given that other values are constant and only 
is varying we have that
Hence for reducing confidence level the margin of error will be reducing
The confidence interval is mathematically represented as
Now looking at the above formula and information that we have deduced so far we can infer that as the confidence level reduces , the critical value reduces, the margin of error reduces and the confidence interval becomes narrower
Answer:
D. 10 square root 3 is your answer
Step-by-step explanation:
Here is what you do.
<em>square root 30 = 3 x 2 x 5 </em>
<em>square root 10 = 2 x 5</em>
Add them together.
<em>3 x 2 x 2 x 5 x 5 </em>
<em>3 x 4 x 25.</em>
4 and 25 can come out of the square root.
<em>2 x 5 = 10</em>
10 square root 3 is your answer.
Answer:
n=288
Step-by-step explanation:
Rewrite the equation as
√
n
=
18
√
8
−
8
√
18
.
√
n
=
18
√
8
−
8
√
18
To remove the radical on the left side of the equation, square both sides of the equation.
√n
2
=
(
18
√
8
−
8
√
18
)
2
Simplify each side of the equation.
Use
n
√
a
x
=
a
x
n
to rewrite
√
n as n
1
2
.
(
n
1
2
)
2
=
(
18
√
8
−
8
√
18
)
2
Simplify
(
n
1
2
)
2
.
Multiply the exponents in
(
n
1
2
)
2
.
Apply the power rule and multiply exponents,
(
a
m)n
=
a
m
n
.
n
1
2
⋅
2
=
(
18
√
8
−
8
√
18
)
2
Cancel the common factor of 2
Cancel the common factor.
n
1
2
⋅
2
=
(
18
√
8
−
8
√
18
)
2
Rewrite the expression.
n
1
=
(
18
√
8
−
8
√
18
)
2
Simplify.
n
=
(
18
√
8
−
8
√
18
)
2
Simplify
(
18
√
8
−
8
√
18
)
2
Simplify each term.
Rewrite
8 as 2
2
⋅
2
.
Factor
4 out of 8
n
=
(
18
√
4
(
2
)
−
8
√
18
)
2
Rewrite
4 as 2
2
n
=
(
18√
2
2
2
−
8
√
18
)
2
Pull terms out from under the radical.
n
=
(
18
(
2
√
2
)
−
8
√
18
)
2
Multiply
2 by 18
n
=
(
36
√
2
−
8
√
18
)
2
Rewrite
18
as
3
2
⋅
2
.
Factor
9
out of
18
.
n
=
(
36
√
2
−
8
√
9
(
2
)
)
2
Rewrite
9
as
3
2
.
n
=
(
36
√
2
−
8
√
3
2
⋅
2
)
2
Pull terms out from under the radical.
n
=
(
36
√
2
−
8
(
3
√
2
)
)
2
Multiply
3
by
−
8
.
n
=
(
36
√
2
−
24
√
2
)
2
Simplify terms.
Subtract
24
√
2
from
36
√
2
.
n
=
(
12
√
2
)
2
Simplify the expression.
Apply the product rule to
12
√
2
.
n
=
12
2
√
2
2
Raise
12
to the power of
2
.
n
=
144
√
2
2
Rewrite
√
2
2
as
2
.
Use
n
√
a
x
=
a
x
n
to rewrite
√
2
as
2
1
2
.
n
=
144
(
2
1
2
)
2
Apply the power rule and multiply exponents,
(
a
m
)
n
=
a
m
n
.
n
=
144
⋅
2
1
2
⋅
2
Combine
1
2
and
2
.
n
=
144
⋅
2
2
2
Cancel the common factor of
2
.
Cancel the common factor.
n
=
144
⋅
2
2
2
Rewrite the expression.
n
=
144
⋅
2
1
Evaluate the exponent.
n
=
144
⋅
2
Multiply
144
by
2
.
n
=
288
Craming last minute can lead to unecessary confusion however most examinars dont allow asking questions during exam
So if asking questions for clarification is allowed. A) is the odd one out
And these options are rather for test taking than learning
I believe the numbers are 22, 13, and 44.
