Answer:
ŷ = 0.964X1 - 0.336X2 + 13.066
b1 = 0.964 which is the unit change in the value of y when x1 changes.
b2 = - 0.336 which is the unit change in the value of y when x2 changes
Step-by-step explanation:
Y
10
11
15
15
20
23
27
32
X1
1
5
5
9
7
11
16
21
X2
16
11
14
11
1
8
7
3
The general form of a multiple regression equation is in form:
ŷ = b1x1 + b2x2 + c
Where,
ŷ = predicted or dependent variable
b1 and b2 = slope or gradient Coefficient for the independent or predictor variables x1 and X2 respectively.
c = intercept (constant)
Using the online multiple regression calculator, the model obtained by Inputting the values is written below:
ŷ = 0.964X1 - 0.336X2 + 13.066
Value of b1 = 0.964 which is the unit change in the value of y when x1 changes.
Value b2 = - 0.336 which is the unit change in the value of y when x2 changes
Calculate the nominal rate of interest convertible once every four years that is equivalent to a nominal rate of discount convertible quarterly. Let d^(4) be the nominal rate of discount convertible quarterly.
Answer:
i am having issues using the math editor and my time is almost running out. i added an attachment.
Step-by-step explanation:
which expression is equivalent to(x²y)³?
Answer:
x^6 y^3
Step-by-step explanation:
(x²y)³
We know that (ab) ^c = a^c * b^c
(x²y)³ = x^2 ^3 * y^3
We know that a^b^c = a^(b*c)
(x²y)³ = x^2 ^3 * y^3 = x^( 2*3) y^3 = x^6 y^3
What value does the 2 in the number 0.826?
Answer:
.02
Step-by-step explanation:
2 is in "Hundredths' place in .826
So, the number is multiplied with 1/100 or .01
=> 2 x 1/100
=> 2/100
=> .02
=> 2 x .01
=> .02
The value of 2 in .826 is .02
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 407 gram setting. It is believed that the machine is underfilling the bags. A 20 bag sample had a mean of 397 grams with a standard deviation of 13. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. State the null and alternative hypotheses.
Answer:
Null hypothesis: μ = 407
Alternative hypothesis: μ < 407.
Step-by-step explanation:
In this case, the machine is SUPPOSED to fill the bag so that the bag weighs 407 grams. So, the null hypothesis will be that the machine is doing what it is supposed to be doing. And so, μ = 407 grams would be the null.
The worker thinks the machine is filling the bags to LESS THAN what it is supposed to. So, the alternative hypothesis is that the machine is NOT doing what it is supposed to and μ < 407 grams.
Hope this helps!
PLEASE HELP ME I DONT HAVE THAT MANY POINTS AND ITS DUE TODAY I NEED HELP ASAP
The table contains the data for your first weeks sales. Complete the table by calculating your commission and earnings for each day of the week
Answer with explanation:
Sales Commission(10% of sales)
$2,200 0.1×$2,200= $220
$2,000 0.1× $2,000= $200
$3,134 0.1×$3,134=$313.4
$2,417 0.1×$2,417=$241.7
$2,579 0.1×$2,579 =$257.9
The completed table is given as follows
Day Sales Commission Non-Sales pay Earning
(10% of sales) (Commission +Non Sales pay)
Mon $2,200 $220 $9.50 $220+ $9.50=$229.50
Tue $2,000 $200 $9.50 $200 +$9.50=$209.50
Thurs $3,134 $313.4 $9.50 $313.4+ $9.50=$322.9
Fri $2,417 $241.7 $9.50 $241.7+$9.50= $251.2
Sat $2,579 $257.9 $9.50 $257.9+$9.50=$267.4
I cannot find the answer to my question
Answer:
14M
Step-by-step explanation:
7*2*M
14*M
14M
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
Which graph is the result of reflecting f(x) = One-fourth(8)x across the y-axis and then across the x-axis?
Answer:
f(x) = -0.5x
Step-by-step explanation:
.25*8 = 2 which is really a slope of 2/1
place a negative in front flips it over the y axis and flipping the slope flips it over the x axis.
I need help please, m bda =
And m bca =
Step-by-step explanation:
Exterior angle BOA = 250°
Interior angle BOA = 360°- 250° = 110°
Now,
(A) BDA = interior angle BOA / 2 = 55°( Property of circles)
(B) From the figure, we observe that AOBC is a cyclic quadrilateral (i.e. sum of opposite angles is 180°).
Therefore, BCA + BOA = 180°
BCA = 180° - 110° = 70°
What is the measure of FEG?
A. 30 degrees
B. 40 degrees
C. 50 degrees
D. 70 degrees
Please include ALL work!! <3
Answer:
C. 50 degrees
Step-by-step explanation:
Because 6x + 5x = 110° and x = 10
5×10 = FEG 50°
Combine like terms to create an equivalent expression. 1/7 - 3 (3/7n - 2/7)
━━━━━━━☆☆━━━━━━━
▹ Answer
1 - 9/7n
▹ Step-by-Step Explanation
1/7 - 3(3/7n - 2/7)
Remove the parentheses (Distribute -3 among the parentheses):
1/7 - 9/7n + 6/7
Calculate:
1 - 9/7n
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
1-9/7n
Step-by-step explanation:
[tex]\frac{1}{7}-3(\frac{3}{7}n-\frac{2}{7} ) \\=\frac{1}{7}-\frac{9}{7}n +\frac{6}{7} \\=\frac{1-9n+6}{7} \\=\frac{7-9n}{7}\\=1-\frac{9}{7}n[/tex]
When traveling with the wind, it takes an airplane 3 hours to travel 1800 miles. It takes the same airplane 3.6 hours to travel the same 1800 miles when traveling against the wind. Assuming the airplane travels at a constant speed during both trips, what is the speed of the airplane and the speed of the wind?
Answer:
The speed of the airplane in still air is 550 mph.
The speed of the wind is 50 mph.
Step-by-step explanation:
speed = distance / time
distance = speed * time
or simply
d = st
Let v be the speed of the airplane with no wind.
Let w = speed of wind
With the wind:
d = 1800; s = v + w; t = 3
1800 = 3(v + w)
Against the wind:
d = 1800; s = v - w; t = 3.6
1800 = 3.6(v - w)
We have a system of two equations:
3(v + w) = 1800
3.6(v - w) = 1800
Divide both sides of the first equation by 3. Divide both sides of the second equation by 3.6.
v + w = 600
v - w = 500
Add the equations.
2v = 1100
v = 550
The speed of the airplane in still air is 550 mph.
v + w = 600
550 + w = 600
w = 50
The speed of the wind is 50 mph.
Which equations has no solution?
Answer: I think it is C
Step-by-step explanation:
There is no answer because A can be many solutions, B is x = -25, you just cannot solve C, and D is y = 7/6
Find the length of AB¯¯¯¯¯¯¯¯ A. 19.56 B. 51.86 C. 42.99 D. 34.98
Answer:
Apllying cos on the triangle
cos(angle)= Base/ Hyp
cos(34)= 29/ AB
AB= 29/0.8290
AB=34.98
Step-by-step explanation:
The length of AB is 34.98 units which the correct answer would be an option (D).
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
Given that ΔABC
∠C = 90°
Here base = BC = 29 units and hypotenuse = AB
To determine the length of AB
Apply the cosine on the given right triangle
⇒ cos(θ) = Base/hypotenuse
⇒ cos(34) = 29/ AB
∴ cos(34°) = 0.8290
⇒ 0.8290 = 29/ AB
⇒ AB= 29/0.8290
⇒ AB = 34.98 units
Hence, the length of AB is 34.98 units
Learn more about Trigonometric functions here:
https://brainly.com/question/6904750
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What is the perimeter of the image attached?? (PLEASE HELP I WILL MARK BRAINLIEST)
Answer:
[tex] Perimeter = 3x + 3 [/tex]
Step-by-step explanation:
Perimeter of the given triangle in the figure is the sum of all three sides.
The expressions for the 3 sides are given as, [tex] x, (x - 3), (x + 6) [/tex].
Therefore,
[tex] Perimeter = x + (x - 3) + (x + 6) [/tex]
Simplify,
[tex] Perimeter = x + x - 3 + x + 6 [/tex]
Collect like terms
[tex] Perimeter = x + x + x - 3 + 6 [/tex]
[tex] Perimeter = 3x + 3 [/tex]
Use A = -h(a + b) to find the area A of a
2
be trapezium when a = 15, b = 9 and h = 7
Step-by-step explanation:
Putting values
A = - 7(15 + 9)
A = - 7(24)
A = - 168
(3) In a group of 60 seldiers have enough food for
20 days - How many soldiers should leave the group
so that the food is enough for 100 days ? Find it.
Answer:
48 soldiers
Step-by-step explanation:
60 soldiers 20 days
x soldiers 100 days
60 x 20 = 1200 = 100x
Therefore x = 1200/100 = 12
60 - 12 = 48
Hope that helped!!! k
Answer:
30 Soldiers
Step-by-step explanation:
Given:
1) No of soldiers=60
No of days=20
2) No of days=100
No of soldiers=?
No of soldiers to leave=?
Solution:
Let us use the cross multiplication method.
Let x be the no of soldiers.
No of days No of soldiers
1) 20 60
2) 100 x
by cross multiplying,
20x=100 x 60
20x=600
x=600/20
x=30 soldiers
Therefore, No of soldiers to leave =60-30=30 soldiers
Fine the surface area
Answer:
88 if a rectangular prism, 64 based on the net.
Step-by-step explanation:
A = 4 * 2
B = 6 * 2
C = 4 * 2
D = 6 * 2
E = 6 * 4
A/C= 8
B/D= 12
E = 24
2(8) + 2(12) + 24 = 64
Surface Area: 64
However, a rectangular prism must have 6 faces, so unless this is a box, the answer would be 88, and E = F, the last face.
Determine the value of x in the figure. Question 1 options: A) x = 90 B) x = 85 C) x = 45 D) x = 135
Answer:
A.) x=90°
Step-by-step explanation:
Note:
The triangle shown is an isosceles triangle, which means that it has 2 congruent sides (as shown by the small intersecting lines), and this also means that it has two congruent angles.
We are given an angle measure adjacent to one of the missing angles. These two form supplementary angles, which means that they're sum is equal to 180°, or a straight line. So, to find:
[tex]180=135+y[/tex]
y is the unknown angle. Solve for y:
[tex]180-135=y\\\\y=45[/tex]
y is 45°. Since this and the other angle are congruent, add:
[tex]45+45=90[/tex]
Note:
Triangles angles will always add up to a total of 180°.
To find the missing angle x°, use:
[tex]180=a+b+c[/tex]
These are the angles in a triangle. Substitute any known values and solve:
[tex]180=45+45+x\\\\180=90+x\\\\180-90=x\\\\x=90[/tex]
The missing angle x° is 90°.
:Done
If A and B are independent events with P( A) = 0.35 and P( B) = 0.55, then P( A| B) is:_________.
a. .19
b. 1.57
c. .64
d. .91
Answer:
P( A| B)= 0.35. None of the options are correctStep-by-step explanation:
Two events A and B are said to be independent if the occurrence of one of the events does not affect the other occurring. For example, the event of tossing two coins is an independent event since they occur simultaneously. Two events are therefore independent if the following are true.
P(A|B) = P(A)
P(B|A) = P(B)
P(A and B) = P(A)P(B)
If A and B are independent events with P( A) = 0.35 and P( B) = 0.55,
then P( A| B) is a probability of A occurring provided that B has occurred. This is known as conditional probability for an independent event.
From the condition above for independent events, P(A|B) = P(A) and since P(A) = 0.35, hence P(A|B) =0.35
The base of a right rectangular prism has an area of 173.6 square centimeters and a height of 9 centimeters. What is the volume, in cubic centimeters, of the right rectangular prism?
Answer:
D) 1562.4 cubic centimeters
Step-by-step explanation:
volume = area of the base × height
volume = 173.6cm² × 9 cm
volume = 1562.4 cm³
Please help me solve for the median !!!
Answer:
50.93
Step-by-step explanation:
Add up the frequencies:
2 + 5 + 14 + 15 + 21 + 18 + 15 + 9 + 2 = 101
Divide by 2: 101/2 = 50.5
So the median is the 51st number, with 50 below and 50 above.
Add up the frequencies until you find the interval that contains the 51st number.
2 + 5 + 14 + 15 = 36
2 + 5 + 14 + 15 + 21 = 57
So the median is in the group 49.5 − 51.5. To estimate the median, we use interpolation. Find the slope of the line from (36, 49.5) to (57, 51.5).
m = (51.5 − 49.5) / (57 − 36)
m = 2/21
So at x = 51:
2/21 = (y − 49.5) / (51 − 36)
y = 50.93
If 2 = 5, what is 2 3 − 4?
Answer:
27.5
Step-by-step explanation:
3 = 7.5
4 = 10
5*7.5=37.5-10=27.5
Seriously. 2=5 contradicts.
Suppose you do not know the population mean fee charged to H&R Block customers last year. Instead, suppose you take a sample of size n-8 and find a sample mean of 350. Assume that the distribution for fees is normally distributed with a sample standard deviation of $100.
i. Before conducting the survey, suppose you believed based on your previous observations, your best guess for population standard deviation of fee charged to H&R Block is $50. With this assumption in mind, What should your sample size n approximately be if you want:
Margin-of-Error of to be 2 % and confidence level to be 95 %?
Margin-of-Error of to be 4% and confidence level to be 95%?
Margin-of-Error of to be 4 % and confidence level to be 99%?
ii. 90% confidence interval for the population mean of fees H&R Block.
a. Calculate the margin of error (MOE) of x using a 10% significance level.
b. Calculate the 90 % confidence interval.
c. Suppose an analyst belief that the population mean fee is equal to $185. Using a 90% confidence level. can we conclude the analyst is right? Why or why not?
Answer:
i [tex]\to[/tex] a
[tex]n = 96040000[/tex]
i [tex]\to[/tex] b
[tex]n_1 =24010000[/tex]
i [tex]\to[/tex] c
[tex]n_2 =41602500[/tex]
ii[tex]\to[/tex]a
[tex]E = 58.16[/tex]
ii[tex]\to[/tex]b
[tex]291.84 < \mu < 408.16[/tex]\
ii[tex]\to[/tex]c
There is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 8[/tex]
The sample mean is [tex]\= x = \$ 350[/tex]
The sample standard deviation is [tex]\$ 100[/tex]
Considering question i
i [tex]\to[/tex] a
At [tex]E = 0.02[/tex]
given that the confidence level is 95% = 0.95
the level of significance would be [tex]\alpha =1-0.95 = 0.05[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
So the sample size is mathematically evaluated as
[tex]n = [ \frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ]^2[/tex]
=> [tex]n =[ \frac{ 1.96 * 100}{ 0.02} ]^2[/tex]
=> [tex]n = 96040000[/tex]
i [tex]\to[/tex] b
At [tex]E_1 = 0.04[/tex] and confidence level = 95% => [tex]\alpha_1 = 0.05[/tex] => [tex]Z_{\frac{\alpha_1 }{2} } = 1.96[/tex]
[tex]n_1 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_1} ]^2[/tex]
=> [tex]n_1 =[ \frac{ 1.96 * 100}{ 0.04} ]^2[/tex]
=> [tex]n_1 =24010000[/tex]
i [tex]\to[/tex] c
At [tex]E_2 = 0.04[/tex] confidence level = 99% => [tex]\alpha_2 = 0.01[/tex]
The critical value of [tex]\frac{\alpha_2 }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{ \alpha_2 }{2} } = 2.58[/tex]
=> [tex]n_2 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_2} ]^2[/tex]
=> [tex]n_2 =[ \frac{ 2.58 * 100}{ 0.04} ]^2[/tex]
=> [tex]n_2 =41602500[/tex]
Considering ii
Given that the level of significance is [tex]\alpha = 0.10[/tex]
Then the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.645 * \frac{100 }{\sqrt{8} }[/tex]
[tex]E = 58.16[/tex]
Generally the 90% confidence interval is mathematically evaluated as
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]350 - 58.16 < \mu < 350 + 58.16[/tex]
=> [tex]291.84 < \mu < 408.16[/tex]
So the interpretation is that there is 90% confidence that the mean fee charged to H&R Block customers last year is in the interval .So there is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval.
A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 3 percentage points with 99% confidence if (a) he uses a previous estimate of 22%?
Answer:
Sample size n [tex]\simeq[/tex] 1269.15
Step-by-step explanation:
From the information given ,
At 99% of confidence interval,
the level of significance ∝ = 1 - 0.99
the level of significance ∝ = 0.01
the critical value for 99% of confidence interval is:
[tex]\mathtt{\dfrac{\alpha }{2} = \dfrac{0.01}{2}}[/tex]
= 0.005
[tex]\mathtt {z_{\alpha/2} = z_{0.005/2} }[/tex]
The value for z from the standard normal tables
= 2.58
The Margin of error E= 3% = 0.03
The formula to determine the sample size n used can be expressed as follows:
[tex]\mathtt { n = (\dfrac{z_{\alpha/2}}{E})^2 \ \hat p (1 - \hat p) }[/tex]
where;
[tex]\mathtt{\hat p }[/tex] = 22% = 0.22
Then:
[tex]\mathtt { n = (\dfrac{2.58}{0.03})^2 \ \times 0.22 \times (1 - 0.22) }[/tex]
[tex]\mathtt { n = (86)^2 \ \times 0.22 \times (0.78) }[/tex]
[tex]\mathtt { n = 7396 \ \times 0.22 \times (0.78) }[/tex]
n = 1269.1536
Sample size n [tex]\simeq[/tex] 1269.15
What is the domain of f?
Answer:
-5 ≤x ≤6
Step-by-step explanation:
The domain is the values that x can take
X goes from -5 and includes -5 to x =6 and includes 6
-5 ≤x ≤6
Answer:
See attached!
Step-by-step explanation:
A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?
Answer:
Diameter of wheel in millimetres is 660.4
Step-by-step explanation:
Diameter of wheel in inches = 26
given
1 inch = 25.4 millimeters
multiplying RHS and LHS by 26
26*1 inch = 26*25.4 millimeters
=>26 inch = 660.4 mm.
Thus, diameter of wheel in millimetres is 660.4
Find the product of the roots of the equation
xl-5x - 36 = 0
Answer:
Step-by-step explanation:
Hello, I assume that you mean
[tex]x^2-5x-36[/tex]
The product is -36.
[tex]x_1 \text{ and } x_2 \text{ are the two roots, we can write}\\\\(x-x_1)(x-x_2)=x^2-(x_1+x_2)x+x_1\cdot x_2[/tex]
So in this example, it means that the sum is 5 and the product is -36.
Thank you
A probability experiment is conducted in which the sample space of the experiment is S={1,2,3,4,5,6,7,8,9,10,11,12}. Let event E={3,4,5,6,7,8}. Assume each outcome is equally likely. List the outcomes in Ec. Find P(Ec).The outcomes of Ec are {_____}P(Ec)=
Answer:
This list of all the outcome of [tex]E^c[/tex] is [tex]E^c = \{ 1,2,9,10,11,12,\}[/tex]
[tex]P(E^c ) = 0.5[/tex]
Step-by-step explanation:
From the question we are told that
The sample sample space is [tex]S = \{ 1,2,3,4,5,6,7,8,9,10,11,12 \}[/tex]
The number of elements in the sample space is [tex]n = 12[/tex]
The event is [tex]E = \{ 3,4,5,6,7,8 \}[/tex]
The number of outcomes in the Event is [tex]n_e = 6[/tex]
The objective in to obtain [tex]P(E^c)[/tex]
Now [tex]E^c[/tex] is the compliment of E and number of elements in [tex]E^c[/tex] ican be mathematically evaluated as
[tex]nE^c = n - n_e[/tex]
substituting values
[tex]E^c = 12-6[/tex]
[tex]E^c = 6[/tex]
This list of all the outcomes of [tex]E^c[/tex] is
[tex]E^c = \{ 1,2,9,10,11,12,\}[/tex]
Generally [tex]P(E^c )[/tex] which is the probability of [tex]E^c[/tex] is mathematically evaluated as
[tex]P(E^c ) = \frac{nE^c}{n}[/tex]
substituting values
[tex]P(E^c ) = \frac{6}{12}[/tex]
[tex]P(E^c ) = 0.5[/tex]
The mathematics teacher proposes to his students that whoever determines their years of Experience as a teacher will have an extra point, for this they will have to solve the following expression
-5 + {4 * 6 + 3 + 1 + (3- (4-8) + (3-2)]}
How many years of experience does the teacher have?
Answer:
29 years of experience.
Step-by-step explanation:
So let's take the expression step by step. Remember that you need to follow the order of precedence here for the operations. Parentheses, exponentials, multiplication, and addition.
-5 + { 4 * 6 + 3 + 1 + [ 3 - ( 4 - 8 ) + ( 3 - 2 ) ] }
-5 + { 4 * 6 + 3 + 1 + [ 3 - ( -4 ) + ( 1 ) ] }
-5 + { 4 * 6 + 3 + 1 + [ 3 + 4 + 1 ] }
-5 + { 4 * 6 + 3 + 1 + [ 8 ] }
-5 + { 24 + 3 + 1 + 8 }
-5 + { 36 }
29
So the teacher has 29 years of experience.
Cheers.
In a study of treatments for very painful "cluster" headaches, 140 patients were treated with oxygen and 158 other patients were given a placebo consisting of ordinary air. Among the 140 patients in the oxygen treatment group, 113 were free from headaches 15 minutes after treatment. Among the 158 patients given the placebo, 35 were free from headaches 15 minutes after treatment. Use a significance level to test the claim that the oxygen treatment is effective. A) Find test statistic z B) Find the P-value C) Construct the appropriate confidence interval D) determine if the oxygen treatment is effective
Answer:
A
[tex]t = 10.1[/tex]
B
[tex]p-value = p(t > 10.1)= 0.000[/tex]
C
[tex]0.4714 < p_1 - p_2 <0.6988[/tex]
D
The oxygen treatment is effective because
1 the is no 0 in the interval telling us that the treatments are different
2 the upper and the lower limit are positive tell us that the proportion of those treated by the oxygen treatment is greater
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 140[/tex]
The number of patient which the oxygen cured is k = 113
The second sample size is [tex]n_2 = 158[/tex]
The number of patient that placebo cured is l = 35
The first sample proportion is
[tex]\r p_1 = \frac{ 113}{140 }[/tex]
[tex]\r p_1 = 0.8071[/tex]
The second sample proportion is
[tex]\r p_2 = \frac{ 35}{ 158 }[/tex]
[tex]\r p_2 = 0.222[/tex]
The null hypothesis is [tex]H_o : p_1 = p_2[/tex]
The alternative hypothesis is [tex]H_a : p_1 > p_2[/tex]
Let assume the level of significance be[tex]\alpha = 0.05[/tex]
Generally the pooled proportion is mathematically evaluated as
[tex]p = \frac{p1 * n1 + p2 * n2}{n1 + n2}[/tex]
substituting values
[tex]p = \frac{0.8071 * 140 + 0.222 * 158}{140 + 158}[/tex]
[tex]p = 0.4969[/tex]
Generally the standard error is mathematically represented
[tex]SE = \sqrt{ p(1- p ) * [ \frac{1}{n_1} + \frac{1}{n_1}] }[/tex]
substituting values
[tex]SE = \sqrt{ 0.4969(1- 0.4969 ) * [ \frac{1}{140} + \frac{1}{158}] }[/tex]
[tex]SE = 0.0580[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \r p_1 - \r p_2}{ SE}[/tex]
[tex]t = \frac{ 0.8071 -0.222}{ 0.0580}[/tex]
[tex]t = 10.1[/tex]
The p-value is from the normal distribution table as
[tex]p-value = p(t > 10.1)= 0.000[/tex]
given that [tex]t< \alpha[/tex] the null hypothesis is rejected
From the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically the represented as
[tex]E = Z_{\frac{\alpha }{2} } * SE[/tex]
[tex]E = 1.96 * 0.0580[/tex]
[tex]E = 0.1137[/tex]
The 95% confidence interval is mathematically represented as
[tex](\r p_1 - \r p_2) - E < p_1 - p_2 < (\r p_1 - \r p_2) + E[/tex]
substituting value
[tex](0.8071 - 0.222) - 0.1137 < p_1 - p_2 < (0.8071 - 0.222) + 0.1137[/tex]
[tex]0.4714 < p_1 - p_2 <0.6988[/tex]
The oxygen treatment is effective because
1 the is no 0 in the interval telling us that the treatments are different
2 the upper and the lower limit are positive tell us that the proportion of those treated by the oxygen treatment is greater
