Answer:
A) 95% confidence interval for the population mean PEF for children in biomass households = (3.314, 3.486)
95% confidence interval for the population mean PEF for children in LPG households
= (4.195, 4.365)
Simultaneous confidence interval for both = (3.314, 4.365)
B) The result of the hypothesis test is significant, hence, the true average PEF is lower for children in biomass households than it is for children in LPG households.
C) 95% confidence interval for the population mean FEY for children in biomass households = (2.264, 2.336)
Simultaneous confidence interval for both = (2.264, 4.365)
This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).
Step-by-step explanation:
A) Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the z-distribution. This is because although, there is no information provided for the population standard deviation, the sample sizes are large enough for the sample properties to approximate the population properties.
Finding the critical value from the z-tables,
z-critical value for 95% confidence level = 1.960 (from the z-tables)
For the children in the biomass households
Sample mean = 3.40
Standard error of the mean = σₓ = (σ/√N)
σ = standard deviation of the sample = 1.20
N = sample size = 756
σₓ = (1.20/√756) = 0.04364
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 3.40 ± (1.960 × 0.04364)
CI = 3.40 ± 0.08554
95% CI = (3.31446, 3.48554)
95% Confidence interval = (3.314, 3.486)
For the children in the LPG households
Sample mean = 4.28
Standard error of the mean = σₓ = (σ/√N)
σ = standard deviation of the sample = 1.19
N = sample size = 752
σₓ = (1.19/√752) = 0.043395
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 4.28 ± (1.960 × 0.043395)
CI = 4.28 ± 0.085054
95% CI = (4.1949, 4.3651)
95% Confidence interval = (4.195, 4.365)
Simultaneous confidence interval for both = (3.214, 4.375)
B) The null hypothesis usually goes against the claim we are trying to test and would be that the true average PEF for children in biomass households is not lower than that of children in LPG households.
The alternative hypothesis confirms the claim we are testing and is that the true average PEF is lower for children in biomass households than it is for children in LPG households.
Mathematically, if the true average PEF for children in biomass households is μ₁, the true average PEF for children in LPG households is μ₂ and the difference is μ = μ₁ - μ₂
The null hypothesis is
H₀: μ ≥ 0 or μ₁ ≥ μ₂
The alternative hypothesis is
Hₐ: μ < 0 or μ₁ < μ₂
Test statistic for 2 sample mean data is given as
Test statistic = (μ₂ - μ₁)/σ
σ = √[(s₂²/n₂) + (s₁²/n₁)]
μ₁ = 3.40
n₁ = 756
s₁ = 1.20
μ₂ = 4.28
n₂ = 752
s₂ = 1.19
σ = √[(1.20²/756) + (1.19²/752)] = 0.061546
z = (3.40 - 4.28) ÷ 0.061546 = -14.30
checking the tables for the p-value of this z-statistic
Significance level = 0.01
The hypothesis test uses a one-tailed condition because we're testing in only one direction.
p-value (for z = -14.30, at 0.01 significance level, with a one tailed condition) = 0.000000001
The interpretation of p-values is that
When the p-value > significance level, we fail to reject the null hypothesis and when the p-value < significance level, we reject the null hypothesis and accept the alternative hypothesis.
Significance level = 0.01
p-value = 0.000000001
0.000000001 < 0.01
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that true average PEF is lower for children in biomass households than it is for children in LPG households.
C) For FEY for biomass households,
Sample mean = 2.3 L/s
Standard error of the mean = σₓ = (σ/√N)
σ = standard deviation = 0.5
N = sample size = 756
σₓ = (0.5/√756) = 0.018185
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 2.30 ± (1.960 × 0.018185)
CI = 2.30 ± 0.03564
95% CI = (2.264, 2.336)
Simultaneous confidence interval for both = (2.264, 4.365)
This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).
Hope this Helps!!!
Want Brainliest? Get this correct Which of the following is the quotient of the rational expressions shown below? Make sure your answer is in reduced form.
Answer:
B.
Step-by-step explanation:
First, notice that we can cancel out an x in the second term. Thus:
[tex]\displaystyle \frac{3x^2}{x^2+x} =\frac{3x^2}{x(x+1)} =\frac{3x}{x+1}[/tex]
As with the last question, change the sign to multiplication and "flip" the second term:
[tex]\displaystyle \frac{2x-1}{x+1}\cdot \frac{x+1}{3x}[/tex]
Multiply straight across:
[tex]\displaystyle =\frac{(2x-1)(x+1)}{(x+1)(3x)}[/tex]
We can cancel the (x + 1) term:
[tex]\displaystyle =\frac{2x-1}{3x}[/tex]
This cannot be simplified further. Hence, our answer is B.
Answer:
It is B)
Step-by-step explanation:
Ap3x Approved
Find equations for the tangent lines and the normal lines to the hyperbola for the given value of x. (The normal line at a point is perpendicular to the tangent line at the point.)
Answer:
P (7, 28)
Step-by-step explanation:
The Marine Corps is ordering hats for all the new recruits for the entire next year. Since they do not know the exact hat sizes they will use statistics to calculate the necessary numbers. This is the data from a sample of the previous recruits: 7.2, 6.8, 6, 6.9, 7.8, 6.2, 6.4, 7.2, 7.4, 6.8, 6.7, 6, 6.4, 7, 7, 7.6, 7.6, 6, 6.8, 6.4 a. Display the data in a line plot and stem-and-leaf plot. (These plots don’t need to be pretty; just make sure I can make sense of your plots.) Describe what the plots tell you about the data. b. Find the mean, median, mode, and range. c. Is it appropriate to use a normal distribution to model this data? d. Suppose that the Marine Corps does know that the heights of new recruits are approximately normally distributed with a mean of 70.5 inches and a standard deviation of 1.5 inches. Use the mean and standard deviation to fit the new recruit heights to a normal distribution and estimate the following percentages. d1. What percent of new recruits would be taller than 72 inches? d2. What percent of new recruits would be shorter than 67.5 inches? d3. What percent of new recruits would be between 69 and 72 inches? d4. Between what two heights would capture 95% of new recruits?? By using statistics are the numbers changed to whole numbers?
Answer:
60-|||
61-
62-||
62
64-|||
65
66
67-|
68-|||
69-|
70-||
71
72-||
73
74-||
75
76-||
77
78-|
This is a stem and leaf plot.
mean is 138.2/20=6.91
median of 20 is half way between 10th and 11th or an ordered plot. The 10th and the 11th are both 6.8, so that is the median.
6.4 and 6.8 are modes, but they are so minimal I would say there isn't a clear mode.
The range is 1.8, the largest-the smallest
This is not a normal distribution.
z=(x-mean) sd
a.(72-70.5)/1.5=1 so z>1 is the probability or 0.1587.
b.shorter than 67.5 inches is (67.5-70.5)/1.5 or z < = -2, and probability is 0.0228.
c.Between 69 and 72 inches is +/- 1 sd or 0.6826.
95% is 1.96 sd s on either side or +/- 1.96*1.5=+/- 2.94 interval on either side of 70.5
(67.56, 73.44)units in inches
Step-by-step explanation:
Carlos mixed 3 1⁄2 cups of red paint with 4 1⁄2 cups of yellow paint to make an orange paint. How many cups of red paint and how many cups of yellow paint will Carlos need to make 12 cups of the same shade of orange paint? Solve in at least three different ways.
Answer:
The answer is " red cups is "5.25""
Step-by-step explanation:
Given:
red paint= [tex]3\frac{1}{2}= \frac{7}{2} =3.5[/tex]
yellow paint= [tex]4\frac{1}{2}= \frac{9}{2} =4.5[/tex]
total cups=12
i) The Ratio of red and yellow is= 3.5 : 4.5
If the red cups are= [tex]\frac{3.5}{8}[/tex]
number of red cups:
[tex]\to \frac{3.5}{8}\times 12\\\\\to \frac{3.5}{2}\times 3\\\\\to 3.5\times 1.5\\\\\to 5.25[/tex]
ii)
[tex]\to 3.5x+4.5x=12......(a)\\\\\to 8x=12\\\to x=\frac{12}{8}\\\\\to x=\frac{3}{2}\\\\[/tex]
put the value of x in equation (a):
[tex]\to 3.5 \times \frac{3}{2}+4.5\times \frac{3}{2}=12\\\\\to 35 \times \frac{3}{20}+45\times \frac{3}{20}=12\\\\\to 5.25+6.75=12[/tex]
iii)
if [tex]\frac{4.5}{8} \times 12= 6.75[/tex] yellow cups used in making orange paint
so, red paint +yellow paint = total cups
let, red paint cups =x
⇒x+6.75=12
⇒x=12-6.75
⇒x=5.25
The value of red cups is 5.25.
4. Average daily demand for a product is normally distributed with a mean of 40 units and a standard deviation of 8 units. Lead time is fixed at 30 days. What reorder point provides for a service level of 95 percent (z=1.65)? (2 points)
Answer:
1236.15
Step-by-step explanation:
Data provided
Daily demand (d) = 40 units
Standard deviation = 8 units
Lead time (L) = 30 days
The Service level of 95 percent z value = 1.65
The computation of the reorder point is shown below:-
Reorder point = demand during lead time + safety stock
[tex]= daily\ demand \times Lead\ time + z\times \sigma\times \sqrt{L}[/tex]
[tex]= 40 \times 30 + 1.65\times 4\times \sqrt{30}[/tex]
= 1236.149689
or
= 1236.15
Therefore the correct answer is 1236.15
hey guys please help me
Answer:
5/6
Step-by-step explanation:
The probability of the 10th roll will be 6 is 1 out 6 because there's only one side with 6 (we spouse the dice is not biased) so the probability of the roll not to be 6 is 5/6
what is the solution of x^y=y^x and y=2x?
Answer:
x=0, y=0
x=2, y=4
Step-by-step explanation:
x^y= y^xy= 2xx^(2x)= (2x)^x(x^2)^x= (2x)^xx^2=2xx(x-2)=0x=0 ⇒ y=0x=2 ⇒ y=4Answer:
x = 2, y = 4.
Step-by-step explanation:
x^y = y^x
Substitute y = 2x in the above:
x^2x = (2x)^x
x^2x = 2*x * x^x Divide both sides by x^x:
x^2x / x^x = 2*x
x^(2x-x) = 2^x
x^x = 2^x
So x = 2.
and y = 2x = 4.
We can also make x = 0 and y = 0 but
I'm not sure if this result is valid because 0^0 is undefined.
Looking further into this there seems to be different opinions on this with some mathematicians say 0^0 = 1, so x=0, y = 0 may be acceptable.
2(x + 14) = 42 can someone please help me with a step by step explanation
Answer:
Nah bro I gotchu! 2x+28=42
2x=42-28
2x=14
x=7
:)
Step-by-step explanation:
In a marketplace, a box of peaches can be purchased for $78.95 per box. One box contains 50 peaches. How much would you have to pay to buy 9 peaches?
(Hint: Convert 9 peaches into dollars.)
Round your answer to the nearest hundredth. Do not type the units ($) in the space below.
Answer:
The cost of 9 peaches will be 9/50 th of the price of 50 peaches. Therefore, the answer is 9/50 * 78.95 ≈ $14.21.
Answer:
14.21
Step-by-step explanation:
To find the cost of 9 peaches, you would need to find the cost of one peach. To do this, you would need to divide 78.95 by 50. This comes out to 1.579 per peach. To find the cost of nine peaches, you would multiply this number by 9 to get 14.211. We are not done yet since you have to round to the nearest hundredth. When rounded, you get 14.21.
Hence,
the cost of nine peaches is 14.21 dollars.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
A bag contains 75 marbles:35 are blue and 25 of these blue marbles are swirled. The rest of them are red, and 30 of the red ones are swirled. The marbles that are not swirled are clear. What is the probability of drawing? (a) A blue marble (b) A blue swirled marble (c) A red clear marble.
Answer:
a) 35/75
b)25/75
c)10/75
Step-by-step explanation:
6. the price of an item with a 15% discount
The price of an item with a 15% discount would be 85% of the original price, so if the original price was x, the discounted price would be: [tex]\frac{85x}{100}[/tex]
Which measurements could create more than one triangle?
2 of 4 QUESTION
A triangle with sides measuring 10 cm and 20 cm and an included angle
measuring 65°
A triangle with sides measuring 15 inches, 20 inches, and 25 inches
O A triangle with sides measuring 20 cm, 9 cm, and 10 cm
O A right triangle with acute angles measuring 45° and 45°
Answer: A right triangle with acute angles measuring 45° and 45°
Step-by-step explanation:
This question is related to the criteria of congruence for triangles.
The criteria are:
SSS (you know the 3 sides)
SAS (you know two sides, and the angle between those two sides)
ASA (you know two angles, and the side between those two angles)
AAS (you know two angles, and one side).
So for the given examples, the only one that does not reach any of those criteria is the last option, where we only have the angles:
45°, 45° and 90°.
This means that we can craft multiple triangles with this data:
this is a triangle rectangle where the length of the cathetus is the same, that is the only restriction.
For example we can have lengths:
1, 1 and √2
or 2, 2 and √(2^2 + 2^2) = √8
Answer:
A right triangle with acute angles measuring 45° and 45°
Step-by-step explanation:
US consumers are increasingly using debit cards as a substitute for cash and checks. From a sample of 100 consumers, the average amount annually spent on debit cards is $7,790. Assume that this average was based on a sample of 100 consumers and that the population standard deviation is $500.
A. At 99% confidence, what is the margin of error?
B. Construct the 99% confidence interval for the population mean amount spent annually on a debit card.
Answer:
A. Margin of error = 128.79
B. The 99% confidence interval for the population mean is (7661.21, 7918.79).
Step-by-step explanation:
We have to calculate a 99% confidence interval for the mean.
The population standard deviation is know and is σ=500.
The sample mean is M=7790.
The sample size is N=100.
As σ is known, the standard error of the mean (σM) is calculated as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{N}}=\dfrac{500}{\sqrt{100}}=\dfrac{500}{10}=50[/tex]
The z-value for a 99% confidence interval is z=2.576.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_M=2.576 \cdot 50=128.79[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 7790-128.79=7661.21\\\\UL=M+t \cdot s_M = 7790+128.79=7918.79[/tex]
The 99% confidence interval for the population mean is (7661.21, 7918.79).
Explain why the following expression is false. |x| < -4
Step-by-step explanation:
Whenever we put a negative number inside a modulus function it will give us the positive output. For example , |-3| = 3 , |-6|=6, |5|= 5 ,etc.
So a modulus function i.e. |x| is always greater than zero ( positive ) when x is any number except 0 and it is equal to zero when the value of x is 0.
So |x| can't be less than -4 as |x| is always positive . So the statement is false.
The expression |x| < -4 is false because all Positive numbers are greater than all negative numbers.
Modulo of a numberThe modulo of a number x as denoted by; |x| is the positive value of number x irrespective of the value of x.
Hence, the number x, whether positive or negative becomes a positive number and hence;
|x| > -4 which renders the given expression falseRead more on modulo of a number;
https://brainly.com/question/25734188
The area of a triangle is 36 sq. inches. If the base of the triangle is 6 inches, what is its height?
Answer:
12 inches
Step-by-step explanation:
The formula for the area of a triangle is A=bh1/2. Using this formula we can find it backwards....
12 times 6 times 1/2 equals 36.
A bread recipe calls for 2 1/2 cups of whole wheat flour 2/3 cups of rice flour 2 1/4 cups of white flour how many total cups of flour are needed write your answer as a simplified mixed number
Answer:
5 5/12
Step-by-step explanation:
you find the common denominator which is 12
2 6/12
8/12
2 3/12
now u add them all
hope this helps
Answer:
5 5/12 cups
Step-by-step explanation:
The scores for all the sixth graders at Roberts School on a statewide test are normally distributed
with a mean of 76 and a standard deviation of 10.
1. What percent of the scores were below 66
Answer:
15.87%
Step-by-step explanation:
z-score referred to standard score and it provide idea of the difference from the mean a data point it gives measurement of all standard deviations that falls below as well as above the mean in a given score
we were given:
mean of 76
deviation of 10
To calculate the z- scores
z-score = (the given score of interest - mean score given)/ standard deviation.
Z- score =66 - 76)/10
= -10/10 = -1.
Hence our z- score= -1
The next step is to look up the z-score of -1 on a z-table z-table
if you look for A z-score of -1 on the z- score table you will see that a z- score of (-1) has 15.87% of all scores below it.
Therefore, the percent of the scores that were below 66 is 15.87%
BELOW IS THE ATTACHMENT OF THE Z-SCORE TABLE
If you are given only the measurements of the three angles of a right triangle, can you find the lengths of the three sides?
Answer:
No
Because you can't find any of the length if you don't have two other lengths
Step-by-step explanation:
study cosine rule and sine rule
you use cosine rule when you have one angle in-between two length
while you use sine rule when you have two angles and one length
just study cosine rule and sine rule you will understand what am saying
Answer:
no
Step-by-step explanation:
What is LCM? And what is the formula for that?
Answer:
LCM stands for Least Common Multiple
To calculate LCM you need to divide the no.s given by smallest divisor going to the greatest until the no.s can be divided no more
A line through the points (2, -9) and (j, 17) is parallel to the line 2x + 3y = 21. What is the value of j?
Answer:
j = -37
Step-by-step explanation:
First find the slope of 2x + 3y = 21
Solve for y
Subtract 2x from each side
2x-2x + 3y =-2x+ 21
3y = -2x+21
Divide by 3
3y/3 = -2x /3 + 21/3
y = -2/3 x +7
This is in slope intercept form y = mx+b where m is the slope and b is the y intercept
m = -2/3
The slope of parallel lines are equal
Using the two points
m = (y2-y1)/(x2-x1)
-2/3 = (17 - -9)/(j-2)
-2/3 = (17 +9)/(j-2)
Using cross products
-2(j-2) = 3 ( 17+9)
-2j +4 = 26*3
-2j +4 = 78
Subtract 4 each side
-2j = 78-4
-2j = 74
Divide by -2
-2j/-2 = 74/-2
j = -37
Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = –6. Which function could Heather be writing? f(x) = x2 + 36x + 12 f(x) = x2 – 36x – 12 f(x) = –x2 + 12x + 36 f(x) = –x2 – 12x – 36
Answer:
f(x) = –x^2 – 12x – 36
Step-by-step explanation:
The parent function, x^2, touches the x-axis at x=0. Translating it 6 units left replaces x with x-(-6) = x+6, so the function is ...
f(x) = (x+6)^2 = x^2 +12x +36
Reflecting the graph across the x-axis doesn't change the x-intercept, so Heather could be writing ...
f(x) = -x^2 -12x -36
It's D.
I have to have at least 20 characters.
geometry question, please help thank you.
Answer:
26. 138 , 27. x=45
Step-by-step explanation:
26.
QRP= 90° bcs it is tangent
QSP=90° bcs it is tangent
Four sided(Over all)= 360°
RQS= X
RPS= 42°
X + 90+90+42 = 360
X= 138°
27.
Over all= 360°
PRQ=PSQ
PRQ= 90° bcs it is tangent
360= 90+90+X+ 3X
X = 45°
-73 + 28
Can anybody help me with this
Answer:
-45 is the answer
Step-by-step explanation:
PLZZ MARK BRAINLIEST
What is the length of AC ?
Answer:
D. 24
Step-by-step explanation:
AM: 12 (radius)
AC: 24 (diameter)
If a person invests $290 at 6% annual interest, find the approximate value of the investment at the end of 15 years.
Answer:
$261
Step-by-step explanation:
Simple equation to remember.
I = PRT
In this case, "I" means investment, "P" means principal, a fancy term for saying the starting money, "R" means rate in decimal form (just move the decimal two places to the left to convert the percent to decimal), and "T" means time, which is usually in years.
All you do is just plug in 290 as P, 0.06 as R, and 15 as the T, and then you multiply that all together to get.
However, this is only the simple investment equation, there are other equations such as the compound equation used for interest. I'm assuming you're only using the normal interest equation.
Anybody get this? Thanks in advanced
Answer:
x = 6 and y = 2
Step-by-step explanation:
2x + 3y = 18 .......... Eqn 1
3x - 3y = 12 ........... Eqn 2
Add both Equations to eliminate y
we have
2x + 3x + 3y - 3y = 18 + 12
5x = 30
Divide both sides by 5
5x / 5 = 30/5
x = 6
Substitute x = 6 into any of the Equations
Using equation 1
we have
2(6) + 3y = 18
3y = 18 - 12
3y = 6
Divide both sides by 3
That's
3y/3 = 6/3
y = 2
Therefore x = 6 and y = 2
Hope this helps
The amount of time spent updating websites for small businesses averages 50 minutes per week with a standard deviation of 10 minutes per week. if we consider the distribution of times as mound-shaped and symmetric, use the standard deviation to explain where we would expect "most" of the times will fall each week?
a) Way too long
b) Between 30 and 70 minutes
c) Between 40 and 60 minutes
d) Between 20 and 80 minutes
Answer:
I think the answer is C - Between 40 and 60 minutes
Step-by-step explanation:
Since each week the amount of time spend updating websites takes 50 minutes per week with an addition of 10 minutes it would be 1 hour per week (60 minutes)
A rectangular prism made of wood has a length of 10 centimeters, a width of 8 centimeters, and a height of 12 centimeters. A rectangular hole
with a length of 2 centimeters and a width of 3 centimeters is cut through the prism as shown. What is the volume of the resulting figure?
3 cm
2 cm
12 cm
8 cm
10 cm
Answer: its B 888 cm
Step-by-step explanation: hope this helps let me know if wrong ill fix it
The slope of the line passing through the points (7, 5) and (21, 15) is
Answer:
5/7
Step-by-step explanation:
We are given two points so we can find the slope by using
m = (y2-y1)/(x2-x1)
= (15-5)/(21-7)
=10/14
5/7
10 задание пожалуйста
pls say the question more easily