Answer:
The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Apartment:
38 out of 78, so:
[tex]p_A = \frac{38}{78} = 0.4872[/tex]
[tex]s_A = \sqrt{\frac{0.4872*0.5128}{78}} = 0.0566[/tex]
Home:
46 out of 84, so:
[tex]p_H = \frac{46}{84} = 0.5476[/tex]
[tex]s_H = \sqrt{\frac{0.5476*0.4524}{84}} = 0.0543[/tex]
Test if the there a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees:
At the null hypothesis, we test if there is no difference, that is, the subtraction of the proportions is equal to 0, so:
[tex]H_0: p_A - p_H = 0[/tex]
At the alternative hypothesis, we test if there is a difference, that is, the subtraction of the proportions is different of 0, so:
[tex]H_1: p_A - p_H \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the samples:
[tex]X = p_A - p_H = 0.4872 - 0.5476 = -0.0604[/tex]
[tex]s = \sqrt{s_A^2 + s_H^2} = \sqrt{0.0566^2 + 0.0543^2} = 0.0784[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-0.0604 - 0}{0.0784}[/tex]
[tex]z = -0.77[/tex]
P-value of the test and decision:
The p-value of the test is the probability of the difference being of at least 0.0604, to either side, plus or minus, which is P(|z| > 0.77), given by 2 multiplied by the p-value of z = -0.77.
Looking at the z-table, z = -0.77 has a p-value of 0.2207.
2*0.2207 = 0.4414
The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.
Please Help! I will give you the brainiest and a lot of points!
Which inequality represents all values of x which the product below is defined Square root 4x Square root x+2
Answer:
Option (D) x≥ 0 is absolutely correct
Step-by-step explanation:
The reason is that the square root function is defined for only non negative numbers.
Answer: x is greater than or equal to 0
Step-by-step explanation:
The cost of three pants and four shirts is $68.45 if a pant costs $6.85 more than a shirt find the cost of a pant and a shirt estimate to the nearest whole number.
Answer:
3 pants are $20.55
4 shirts are $47.9
Step-by-step explanation:
a pant is $6.85 × 3= $20.55
68.45 - 20.55 = $47.9
$47.9 ÷ 4 = $11.98 a shirt
the
Calculate the consumer Surplus, if the
demand function is given as pdf=Q²-3q-4 at
the equilbrum
Price of
6.00
Answer:
2
Step-by-step explanation:
33
Please help me with this someone
9514 1404 393
Answer:
79 23/24 yards
Step-by-step explanation:
10 5/8 +24 5/6 +44 1/2 = (10 +24 +44) +(5/8 +5/6 +1/2)
= 78 +(15/24 +20/24 +12/24) = 78 +47/24 = 79 23/24 . . . yards
_____
Express the fractions over a common denominator, add, and convert back to a mixed number. Here, the fraction cannot be reduced.
47/24 = 1 23/24
(2√8)(√2) =
Select one:
a. 128
b. none of these
c. 6√10
d. 32
e. 8√16
Describe what is the most difficult part of solving equations, for you personally.
What do you personaly feel like is most dificult.
For me its rembering minus signs
Solve for x.
2(3x - 7) = 16
Simplify your answer as much as possible.
X =
Answer:
x = 5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
2(3x - 7) = 16
Step 2: Solve for x
[Division Property of Equality] Divide 2 on both sides: 3x - 7 = 8[Addition Property of Equality] Add 7 on both sides: 3x = 15[Division Property of Equality] Divide 3 on both sides: x = 5Answer:
X=5
Step-by-step explanation:
divide by 2 on both sides first then you have
3x-7 = 8
take 7 to the other side so that you have an X factor on one side, thus
3x =15
then divide by 3 to remain with X
X = 5
Convert the following numbers into scientific notation. ( i did them but I feel like they wrong can y’all correct them if they are?)
Answer:
only 4 is incorrect...
1,450,000 = 1.45 x [tex]10^{6}[/tex] NOT
1,450,000 = 1.45 x [tex]10^{7\\}[/tex]
Step-by-step explanation:
William sold tooth pick for €2 a pack.On Selling 60% of his ware he still had 200 left.How much money did he collect from his entire sales?
Answer:
.......................
Functions f and g are defined for all real
numbers. The function f has zeros at -2, 3, and 7:
and the function g has zeros at -3, -1, 4, and 7.
How many distinct zeros does the product
function f g have?
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Answer:
6
Step-by-step explanation:
The number of distinct zeros in the product will be the union of the sets of zeros. Duplicated values are not distinct, so show in the union of sets only once.
F = {-2, 3, 7}
G = {-3, -1, 4, 7}
F∪G = {-3, -2, -1, 3, 4, 7} . . . . . . a 6-element set
The product has 6 distinct zeros.
_____
As you may notice in the graph, the duplicated zero has a multiplicity of 2 in the product.
How do I solve this?
The question is somewhat poorly posed because the equation doesn't involve θ at all. I assume the author meant to use x.
sec(x) = csc(x)
By definition of secant and cosecant,
1/cos(x) = 1/sin(x)
Multiply both sides by sin(x) :
sin(x)/cos(x) = sin(x)/sin(x)
As long as sin(x) ≠ 0, this reduces to
sin(x)/cos(x) = 1
By definition of tangent,
tan(x) = 1
Solve for x :
x = arctan(1) + nπ
x = π/4 + nπ
(where n is any integer)
In the interval 0 ≤ x ≤ 2π, you get 2 solutions when n = 0 and n = 1 of
x = π/4 or x = 5π/4
I need you guy’s help answer thanks so much
Answer:
(c) (f-g ) (x) = 6x*3 -2x*2 +4x -8
write
the following numbers using Roman numerals 20
Step-by-step explanation:
xx is the Roman number of 20
I really need the help please and thank you
Answer:
Answer is D.
Step-by-step explanation:
Let the inverse be m:
[tex]{ \sf{m = \sqrt{x} - 8 }} \\ { \sf{m + 8 = \sqrt{x} }} \\ { \sf{x = {(m + 8)}^{2} }} \\ { \bf{f {}^{ - 1} (x) = {(x + 8)}^{2} }}[/tex]
Domain:
[tex]{ \sf{x \geqslant - 8}}[/tex]
There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.08 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.04 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm.
1. What is the probability that the first machine produces an acceptable cork?
2. What is the probability that the second machine produces an acceptable cork?
3. Which machine is more likely to produce an acceptable cork?
Answer:
Step-by-step explanation:
Determine whether the following polygons are similar. If yes, type 'yes' in the Similar box and type in the similarity statement and scale factor. If no, type 'None' in the blanks. For the scale factor, please enter a fraction. Use the forward dash (i.e. /) to create a fraction (e.g. 1/2 is the same as 12
1
2
).
Answer:
Step-by-step explanation:
a swimming pool is 130 feet long and the length is 3 times the width plus 10 feet. Let x be the width of the pool. how wide is the pool?
Answer:Perimeter of a rectangle is 2*the length plus 2*the width
P = 2L + 2W and P = 130, so
L + W = 65
Three times the length is equal to 10 times the width, giving
3L = 10W
Substituting into the above for L = 65 – W,
3(65 – W) = 10W
195 – 3W = 10W
195 = 13W
W = 195/13 = 15
W = 15 yards,
And L = (10/3)W = (10/3)*15 = 50
L = 50 yards
Step-by-step explanation:
f(x)=|x| to the graph of g(x)=∣∣4+x∣∣?
Help only #31,33, please thank you
Answer:
31) 4d + 28 33) 10 + 5
Step-by-step explanation:
31) 4 ( d + 7) = 4 x 7 = 28 = 4d + 28
33) 5 ( 2m + 1 ) = 5. 2m + 5 . 1: 10m + 5
If the nominal rate of interest is 10% per annum and there is quarterly compounding, the effective rate of interest will be: a) 10% per annum b) 10.10 per annum c) 10.25%per annum d) 10.38% per annum
9514 1404 393
Answer:
d) 10.38%
Step-by-step explanation:
The multiplier for four quarters of quarterly compounding is ...
(1 +10%/4)^4 = 1.025^4 = 1.103812890625
This is about 1 + 10.38%.
The effective rate of interest is about 10.38% per annum.
What is the solution to the equation fraction 1 over 3x = 6?
x = 18
x = 2
x = fraction 1 over 2
x =
Hi there!
[tex]\large\boxed{\frac{1}{18}}[/tex]
1/3x = 6
Begin by multiplying both sides by 3 to cancel the fraction:
1/x = 18
Take the reciprocal of both sides:
x = 1/18
Answer:
1/18
Step-by-step explanation:
I N E E D P O I N T S :O)
Write an equation in slope-intercept form for the line with slope -3/2
and y-intercept 5.
Answer: y = -3/2x + 5
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = slope = -3/2b = y-intercept = 5y = -3/2x + 5
Answer:
y = -3/2x + 5 totally
Step-by-step explanation:
This is Some next level Geometry
Step-by-step explanation:
Measure of Angle 1 is 115 due to corresponding angles postulate
Measure of Angle 2 is 65 is linear pair postulate.
Find the product:
1 -1 2
12 1 0] -1 -2 1 [a b c
0 1 1
a
12
b=0
Answer:
[tex][1, -4 ,5][/tex]
Step-by-step explanation:
In this question we are multiplying together two matrices. When we multiply a (1 x 3) matrix with a (3 x 3) matrix, we get a (1 x 3) matrix.
To compute each value, all you need to do is take the each value in each row in the first matrix, and multiply it by each value in each column of the second matrix and add up the result. So let's do that.
[tex]a = (2 * 1) + (1 * -1) + (0 * 0) = 2 - 1 + 0 = 1[/tex]
[tex]b = (2 * -1) + (1 * -2) + (0 * 1) = -2 -2 = -4[/tex]
[tex]c = (2 * 2) + (1 * 1) + (0 * 1) = 4 + 1 + 0 = 5[/tex]
A bag of 31 tulip bulbs contains 13 red tulip bulbs, 9 yellow tulip bulbs, and 9 purple tulip bulbs. Suppose two tulip bulbs are randomly selected without replacement from the bag. (a) What is the probability that the two randomly selected tulip bulbs are both red? (b) What is the probability that the first bulb selected is red and the second yellow? (c) What is the probability that the first bulb selected is yellow and the second red? (d) What is the probability that one bulb is red and the other yellow?
Answer:
36% on first
Step-by-step explanation:
Supervisor: "I need you to increase the number of customers you talk to daily by
20%."
Employee: "I talk to an average of 8 customers per hour during an 8 hour shift so
now I'll need to talk to customers per day."
68
77
85
97
160
NEXT
Answer:
77
Step-by-step explanation:
Currently:
Talk to 8 customers per hour, work 8 hours, so:
Talk to 8*8 = 64 customers.
With the increase:
Has to increase by 20%, so 64 is multiplied by 1 + 0.2 = 1.2. Then
64*1.2 = 76.8
Rounding up, 77 is the answer.
Help? Thanks!!!!!!!! If possible show work please!
Answer:
[tex]B =102[/tex]
[tex]Y = 32[/tex]
Step-by-step explanation:
Solving (47):
To solve for B, we have:
[tex]B + 50 + 28 = 180[/tex] --- sum of angles in a triangle
This gives
[tex]B + 78 = 180[/tex]
Collect like terms
[tex]B =- 78 + 180[/tex]
[tex]B =102[/tex]
Solving (48):
To solve for Y, we have:
[tex]X + Y+ Z = 180[/tex] --- sum of angles in a triangle
This gives
[tex]Y = 180 - X - Z[/tex]
Where
[tex]W+ X=180[/tex] -- angle on a straight line
Solve for X
[tex]X=180 -W[/tex]
[tex]X=180 -100 = 80[/tex]
So, we have:
[tex]Y = 180 - X - Z[/tex]
[tex]Y = 180 - 80 - 68[/tex]
[tex]Y = 32[/tex]
the point a(2,-5) is reflected over the origin and its image is point b. what are the coordinates of point b
Answer:
b(-2,-5)
Step-by-step explanation:
Find the distance across the lake, assume the triangles are similar
Answer:
C
Step-by-step explanation:
Since the triangles are similar, the scale factor is 100/5=20. So L/15=20, L=300
