A certain manufactured product is supposed to contain 23% potassium by weight. A sample of 10 specimens of this product had an average percentage of 23.2 with a standard deviation of 0.2. If the mean percentage is found to differ from 23, the manufacturing process will be recalibrated.
a. State the appropriate null and alternate hypotheses.
b. Should the process be recalibrated? Explain.
c. Compute the P-value.
Answers
Answer:
(a) Null Hypothesis, \(H_0\) : \(\mu\) = 23%
Alternate Hypothesis, \(H_A\) : \(\mu\) \(\neq\) 23%
(b) We conclude that the mean percentage is different from 23 and the manufacturing process will be re-calibrated.
(c) P-value is 0.6%.
Step-by-step explanation:
We are given that a certain manufactured product is supposed to contain 23% potassium by weight.
A sample of 10 specimens of this product had an average percentage of 23.2 with a standard deviation of 0.2.
Let \(\mu\) = mean percentage of potassium by weight.
(a) Null Hypothesis, \(H_0\) : \(\mu\) = 23% {means that the mean percentage is equal to 23 and the manufacturing process will not be re-calibrated}
Alternate Hypothesis, \(H_A\) : \(\mu\) \(\neq\) 23% {means that the mean percentage is different from 23 and the manufacturing process will be re-calibrated}
The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;
T.S. = \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\) ~ \(t_n_-_1\)
where, \(\bar X\) = sample mean percentage = 23.2
s = sample standard deviation = 0.2
n = sample of specimens = 10
So, the test statistics = \(\frac{23.2-23}{\frac{0.2}{\sqrt{10} } }\) ~ \(t_9\)
= 3.162
The value of t test statistic is 3.162.
Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of -2.262 and 2.262 at 9 degree of freedom for two-tailed test.
(b) Since our test statistic doesn't lie within the range of critical values of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the mean percentage is different from 23 and the manufacturing process will be re-calibrated.
(c) The P-value of the test statistics is given by;
P-value = P( \(t_9\) > 3.162) = 0.006 or 0.6%
(a) Null Hypothesis, \(H_o:\mu\): = 23%
Alternate Hypothesis, \(H_A:\mu\neq\) : 23%
(b) We conclude that the mean percentage is different from 23 and the manufacturing process will be re-calibrated.
(c) P-value is 0.6%.
What is a null hypothesis?The hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.
We are given that a certain manufactured product is supposed to contain 23% potassium by weight.
A sample of 10 specimens of this product had an average percentage of 23.2 with a standard deviation of 0.2.
Let = mean percentage of potassium by weight.
(a) Null Hypothesis, \(H_o:\mu\): = 23% {means that the mean percentage is equal to 23 and the manufacturing process will not be re-calibrated}
Alternate Hypothesis, \(H_A:\mu\neq\): 23% {means that the mean percentage is different from 23 and the manufacturing process will be re-calibrated}
The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;
\(TS=\dfrac{X-\mu}{\frac{s}{\sqrt{n}}}\) ~ \(t_{n-1}\)
where, = sample mean percentage = 23.2
s = sample standard deviation = 0.2
n = sample of specimens = 10
So, the test statistics = \(\dfrac{23.2-23}{\frac{0.2}{\sqrt{10}}}\) ~ \(t_g\)
= 3.162
The value of t test statistic is 3.162.
Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of -2.262 and 2.262 at 9 degree of freedom for two-tailed test.
(b) Since our test statistic doesn't lie within the range of critical values of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the mean percentage is different from 23 and the manufacturing process will be re-calibrated.
(c) The P-value of the test statistics is given by;
P-value = P( \(t_g\) > 3.162) = 0.006 or 0.6%
Hence ,
(a) Null Hypothesis, \(H_o:\mu\): = 23%
Alternate Hypothesis, \(H_A:\mu\neq\) : 23%
(b) We conclude that the mean percentage is different from 23 and the manufacturing process will be re-calibrated.
(c) P-value is 0.6%.
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Related Questions
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Quincy and his mom are planting vegetables in their garden. Quincy has finished planting 1 row of carrots so far and is planting new rows at a rate of 4 rows per hour. His mom has finished 8 rows of tomatoes and will continue planting at 3 rows per hour. Once the pair get to the point where they have finished the same number of rows, they will take a break and decide what to plant next. How long will that take? How many rows will they each have completed? In _______ hours, Quincy and his mom will each have planted _______ rows of vegetables.
Answers
Step-by-step explanation:
rc = planted rows of carrots
rt = planted rows of tomatoes
h = number of hours
rc = 4h + 1 (starting with 1 already finished row there will be 4 additional rows every hour)
rt = 3h + 8 (staying with 8 already finished rows there will be 3 additional rows every hour).
when will they have planned the same number of rows ?
when rc = rt, of course.
so,
4h + 1 = 3h + 8
h = 7
4×7 + 1 = 28 + 1 = 29 rows
after 7 hours Quincy and his mom will each have planted 29 rows of vegetables.
Find the median of the data in the box plot below.
problems
Number of math problems
assigned by Ms. O'Brien
HH
0 2 4 6 8
HHHHH
14 16
20
10
12
18.
What is the median?
Answers
Answer:
median = 11
Step-by-step explanation:
The median is represented by the vertical line inside the boxplot
That is the median = 11
Answer:
11
Step-by-step explanation:
Where the line is ,it's at 11.
Also i got it correct on khan
The fee for using a gym is $25 a year plus $3 for each visit. If someone visits v times a year, which expression represents the amount he or she pays per year?
Answers
Answer:
y=3v+25.............
Answer:
$25 + $3v
Step-by-step explanation:
$25 + $3v
Ming makes 6 trays of muffins. Each tray requiers 1.75 pounds of apples. How many pounds of apples does ming use?
Answers
Answer:
10.5
Step-by-step explanation:
Answer:
He would use 10.5 lbs of apples.
I need someone to solve b ASAP please help
Answers
b) The 99% confidence interval for the population proportion is given as follows: (0.57, 0.68).
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which the variables used to calculated these bounds are listed as follows:
\(\pi\) is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.
The parameters for this problem are given as follows:
\(n = 520, \pi = \frac{325}{520} = 0.625\)
Then the lower bound of the interval is given as follows:
\(0.625 - 2.575\sqrt{\frac{0.625(0.375)}{520}} = 0.57\)
The upper bound of the interval is given as follows:
\(0.625 + 2.575\sqrt{\frac{0.625(0.375)}{520}} = 0.68\)
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Lenny bought a motorcycle. He paid 10.5% in tax. The Tax added $1260 to the price of the motorcycle.
What is the price of the motorcycle not including tax?
Answers
The price of the motorcycle not including tax will be $12,000.
Given that:
Lenny bought a motorcycle. He paid 10.5% in tax.
The percentage is given as,
Percentage (P) = [Tax] / Initial value x 100
The price of the motorcycle not including tax is calculated as,
10.5 = (1260 / Initial value) x 100
0.105 = 1260 / Initial value
Initial value = 12,000
The price of the motorcycle is $12,000.
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5h-6-8+7h what’s the answer ?
Answers
help meh pleaseeeeeee
Answers
Answer:
In step 2, 5-7= -2 instead of +2
Step-by-step explanation:
Answer:
3+5=8
=8-7
8-7=1
=1
Step-by-step explanation:
I need help on all of them I’ll take some if not all!
Answers
Note that the angles are found using the principle of the circle theorems.
What are the measure of the angels given?The angle of the circumference is half of the angle at the center of the circle by an arc.
AB = 78°
∠5 = 39°
Angles intercepted by the same arc are equal.
∠4 = 39°
FE= 105°
∠16 =105°
ED = 27°
∠17 =27°
CD = 42°
∠10 =21°
∠3 =21°
The angle of the semi-circle is 90°.
∠2 =90°
∠8=∠9 = (180-48)/2
∠8= 66°
∠9= 66°
∠7=90°-∠8 = 90°-66°
∠7=24°
∠17 = 180°-∠15-∠16
∠17 = 180°-48°-105°
∠17 =27°
∠6=∠15/2 = 48/2
∠6=24°
∠21 = 180°-∠7-∠16
∠21 = 180°-24°-105°
∠21 =51°
∠19 =51°
∠18 = 180°-∠17-∠6
∠18 = 180°-27°-24°
∠18 = 129°
∠20 = 129°
BC = 60°
∠1 = 60/2
∠1 =30°
∠11=180°-∠1-∠2
∠11=180°-30°-90°
∠11=60°
∠13=60°
∠12=180-∠11
∠12=180°-60°
∠12=120°
∠14=120°
∠15=48°
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In ΔQRS, s = 980 cm, r = 300 cm and ∠R=34°. Find all possible values of ∠S, to the nearest 10th of a degree.
Answers
Answer:
S=sin −1 (1.8266968)=ERROR
No possible triangles
Step-by-step explanation:
If your cookie has 2 eyes and 3 buttons that have a radius of 0.75 cm. What would the circumference of 1 button be?
Answers
Each button has a radius of r=0.75cm
To calculate the circumference of a circle you have to multiply the value pi by the diameter.
Since the diameter is twice the radius, we can express the calculation as
\(C=\pi2r\)For the button the circumference is
\(\begin{gathered} C=\pi2\cdot0.75 \\ C=\frac{3}{2}\pi \\ C\cong4.71 \end{gathered}\)There are 5 different pairs of gloves, where left and right are distinguishable. Select 4 of the 10 gloves. (a) How many are there to select 2 pairs of gloves? (b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
Answers
Answer:
(a) How many are there to select 2 pairs of gloves?
10 ways
(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
130 ways
Step-by-step explanation:
We solve the above questions using Combination
Combination = C(n, r) = nCr
= n!/n! ×(n - r)!
(a) How many are there to select 2 pairs of gloves?
We have 5 pairs of gloves. Therefore, the number of ways to select 2 gloves =5C2
= 5!/2! × (5 - 2)!
= 5!/2! × 3!
= 5 × 4 × 3 × 2 × 1/(2 × 1) × (3 × 2 × 1)!
= 10 ways.
(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
We are told to select 4 gloves out of the 10 gloves = 10C4
We have 5 pairs, we need to make sure that two out of the selected 4 make a pair = 5 × 2⁴
= 80
Hence,
10C4 - 5C4
= [10!/4! × (10 - 4)!] - 80
= 210 - 80
= 130 ways
Someone help
A)17/15
B)15/17
C)17
D)8/17
E)17/8
Answers
Answer:
B) 15/17
Step-by-step explanation:
You want the sine of acute angle A in the right triangle shown.
SineThe sine of the angle is the ratio ...
Sin = Opposite/Hypotenuse
We can go to the trouble to figure the hypotenuse, or we can choose the only suitable answer from the list provided. (It is the one marked already.)
The leg lengths of the triangle shown are 8 and 15, with leg 15 being opposite angle A. This is the first clue that the ratio will have 15 in the numerator. Only answer choice B matches.
CheckThe value of the sine function is never greater than 1, eliminating answer choices A, C, and E, leaving choices B and D.
Since the side opposite angle A is the longest of the two legs, we know that angle A is more than 45°, and its sine is more than √2/2. That means choice D can be eliminated, since it is less than 1/2.
The sine of angle A is 15/17.
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Conditional: If it dog scratches at the back door, then the dog needs to go outside.
Converse: If the dog needs to go outside, then the dog scratches at the back door.
Which of the following biconditional statements can be written from the given statements?
A. The dog scratched at the door to go outside.
B. The dog needs to go outside, so the dog scratches at the back door.
C. The dog scratches at the back door, if the dog needs to go outside.
D. The dog scratches at the back door if and only if the dog needs to go outside.
Answers
Answer:c
Step-by-step explanation:Because there giving you a signal
Which graph shows a rate of change 1/2 between -4 and 0 the x-axis
Answers
Two beetles sit at the top edge of a house roof. The roof has two faces. The first face is such that the horizontal shift by 3cm along this face means 2cm shift vertically. Simultaneously, the beetles start moving downwards, the first beetle by the first face, the second - by the second face of the roof. First beetle moves twice as fast as the second beetle. Find the altitude of the first beetle above the second beetle when they will be 72 cm apart horizontally, if the second face of the roof
has the same incline as the first face or is perpendicular to the base
Answers
Answer:
16
mark me brainliest
Step-by-step explanation:
A student said that since –9 is less than 4, then |–9| is less than |4|. Is the student correct? Explain why or why not.
Answers
Answer:
The student is incorrect because I I or absolute value would make the -9 to positive 9.
Step-by-step explanation:
-9<4
on a numberline
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4
but the absolute value of -9 (or) |–9|
is actually positive 9
9>4
on a number line
4 5 6 7 8 9
please help, 6 possible outcomes
Answers
Answer: Landing on X and heads, landing on Y and heads, landing on Z and heads, landing on X and tails, landing on Y and tails, landing on Z and tails
Step-by-step explanation:
There are three possible spinner options and 2 possible coin options. 3 * 2 = 6, leading to 6 possible outcomes.
The spinner could land on X, Y, or Z.
The coin could land on heads or tails.
If we type out all of these possibilities (each spinner section and heads, each spinner section and tails) we end up with;
➜ Landing on X and heads
➜ Landing on Y and heads
➜ Landing on Z and heads
➜ Landing on X and tails
➜ Landing on Y and tails
➜ Landing on Z and tails
what is p - 5, for p = 19 in Algebraic Expressions 14 7 44 79
Answers
Answer:
p - 5 = 14 for p = 19
Step-by-step explanation:
Hi there!
p - 5
We're given that p = 19. Replace p with 19:
= 19 - 5
= 14
I hope this helps!
Answer:
\(\large\boxed{\boxed{\underline{\underline{\maltese{\pink{\pmb{\sf{\: Solution \rightarrow \: p = 14 }}}}}}}}\)
Step-by-step explanation:
We've the algebraic expression \(\twoheadrightarrow\) p - 5.
Here, we need to substitute the value of 'p' as 19 & solve the equation.
So,
\(\mathfrak{p - 5}\\\\\\\Longrightarrow\mathfrak{If \: \: p = 19}\\\\\\\mathfrak{p - 5}\\\mathfrak{= (19) - 5} \\\mathfrak{= 19 - 5}\\\boxed{\mathfrak{=14}}\)
So, the value of p is 14.__________
Hope it helps!
\(\mathfrak{Lucazz}\)
Solve the following system of equations for x to the nearest hundredth : y + 2x + 1 = 0; 4y - 4x ^ 2 - 12x = - 7
Answers
Answer:
We can start by solving the first equation for y:
y + 2x + 1 = 0y = -2x - 1We can then substitute this expression for y into the second equation:
4y - 4x^2 - 12x = -74(-2x - 1) - 4x^2 - 12x = -7-8x - 4 - 4x^2 - 12x = -7-4x^2 - 20x + 3 = 0We can solve for x using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2awhere a = -4, b = -20, and c = 3.
x = (-(-20) ± sqrt((-20)^2 - 4(-4)(3))) / 2(-4)x = (20 ± sqrt(400 + 48)) / (-8)x = (20 ± sqrt(448)) / (-8)x = (20 ± 4sqrt(7)) / (-8)x ≈ -0.85 or x ≈ -2.93Verification:To verify these solutions, we can substitute them back into the original equations:
For x ≈ -0.85:
y + 2x + 1 = 0y + 2(-0.85) + 1 = 0y ≈ 0.74y - 4x^2 - 12x = -74(0.7) - 4(-0.85)^2 - 12(-0.85) = -7-2.8 - 2.89 + 10.2 = -7This checks out, so x ≈ -0.85 is a valid solution.
For x ≈ -2.93:y + 2x + 1 = 0y + 2(-2.93) + 1 = 0y ≈ 4.864y - 4x^2 - 12x = -74(4.86) - 4(-2.93)^2 - 12(-2.93) = -719.44 - 33.45 + 35.16 = -7.85This does not check out, so x ≈ -2.93 is not a valid solution.
Therefore, the only solution to the system of equations to the nearest hundredth is x ≈ -0.85, and the corresponding value of y is y ≈ 0.7.
We can start by isolating y in the first equation:
y + 2x + 1 = 0
y = -2x - 1
Then, we can substitute this expression for y into the second equation:
4y - 4x^2 - 12x = -7
4(-2x - 1) - 4x^2 - 12x = -7
-8x - 4 - 4x^2 - 12x = -7
-4x^2 - 20x - 3 = 0
We can solve for x using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = -4, b = -20, and c = -3. Substituting these values, we get:
x = (-(-20) ± sqrt((-20)^2 - 4(-4)(-3))) / 2(-4)
x = (20 ± sqrt(400 - 48)) / (-8)
x = (20 ± sqrt(352)) / (-8)
x = (20 ± 18.78) / (-8)
So the solutions are:
x ≈ -0.11 or x ≈ -4.39
Therefore, the system of equations has two solutions for x: x ≈ -0.11 and x ≈ -4.39 (rounded to the nearest hundredth).
Please help been stuck on this for hours
Answers
The size of angle ACB to the nearest degree is 88 degree.
How is a triangle ABC put together?
Construction Steps:
Create a line segment BC with the property AC = 4 cm.
Draw two arcs that meet at point A by using B as the centre and a radius of 4 cm, and C as the centre and a radius of 7 cm.
Join AB and AC now. Consequently, the necessary triangle is ABC.
With the use of a compass, draw a line segment AB = 7 cm from A, cutting an arc AC = 4 cm.
Cut an arc of 3 cm from point B.
Embrace BC and AC
Triangle with angle ABC is necessary.
< ACB = 88 degree
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HELP PLEASE WHAT IS THE VERTEX
Answers
Vertex form: y=(x+1)^2-4
What is x in this figure?
Answers
Answer: x=36
Assuming that O is the centre of the circle,
108+a+a=180(sum of the interior angles of a triangle is 180)
2a=180-108
2a=72
a=72÷2
a=36
a=x (angles in the same segment are equal)
Therefore x=36
Step-by-step explanation:
which of the following numbers are equivalent to 3 hundreths
Answers
Answer : OPTION A and B
Hundreths means having a two decimal places
\(\begin{gathered} 3\text{ x }\frac{1}{100} \\ \frac{1}{100}\text{ means one hundredths} \\ 3\text{ x 0.01 = 0.03} \end{gathered}\)Five star, brainliest, and a thanks for the correct answers.
Answers
Answer:
3.46 gallons
Step-by-step explanation:
write your ratio: x gallons/800in^3 = 1 gallon/231in^3
cross multiply: 1*800 = 231*x
simplify: 800 = 231x
divide both sides by 231: 3.4632034632 = x
round+flip: x = 3.46 gallons
Ray-Ann bounces a basketball to Steve as shown in the diagram below. What is the
distance between Ray-Ann and Steve? Round your answer to the nearest tenth of a
foot. Enter deg after any degree value.
7 ft
124°
6 ft
Answers
The distance between Ray-Ann and Steve, using the law of cosines, is given as follows:
11.5 feet.
What is the law of cosines?The law of cosines states that we can find the length of the missing side c of a triangle as follows:
c² = a² + b² - 2abcos(C)
The parameters of the equation are given as follows:
C is the opposite angle to the missing side C.a and b are the sides that are adjacent to the angle C.In the context of this problem, the values of these parameters are given as follows:
C = 124º.a = 6 ft, b = 7 ft.Hence the distance between Ray-Ann and Steve is obtained as follows:
c² = 6²+ 7² - 2 x 6 x 7 x cos(124)º
c² = 132
c = square root of 132
c = 11.5 feet.
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here’s the repostttt
Answers
1. we have to find what number lie at A and B , and that too between and 1 and 2 , so these two numbers must be decimal numbers!! So let's find the number of scales between 1 and 2 , we get 8 scales !! So the question is how much place 1 scale will occupy ?? we have to find certain numbers between 1 and 2 , suppose between 1 and 2 we have 1 unit and those 1 unit occupies 8 scales !! so much place 1 scale occupies ?? to get it divide 1 by 8 and we get 0.125 !! so between 1 and 2 ,each blank space or scale occupies 0.125 unit!! now what numbers lie at A ? count the number of scale between 1 and A , we get 3 scales ! now multiply 3 by 0.125 , we get 0.375 , add 1 to 0.375 , we get 1.375 !! hence 1.375 lies at A ! now we have to find which number lies at B ? count the number of blanks or scale , we get 4 ! multiply 4 by 0.125 and we get 0.5 ! add this 0.5 to 1 , we get 1.5 ! therefore the number 1.5 lies at B !!
2. for 2nd number solution refer to the attachment! !
PLEASEE HELPPP!!! BRAINLIEST!!
Answers
Answer:
B. j || k, by the converse of the same side interior angles Postulate.
Step-by-step explanation:
\( \because \: m \angle \: 1 + m \angle \:2 = 180 \degree \\ \therefore \: j \parallel k, \: by \: converse \: of \: the \: same \: side \: \\ interior \: angles \: postulate.\)
What is f(4) for the function f(x)= 6x+7?
Answers
Answer:
31
Step-by-step explanation:
f(4) = 6x4 + 7
= 24 + 7
= 31
If 900x2= 1800 then what does 1800x400-40+3000000=? please help
Answers
Answer:
720,000-3,000,040= -2279960 or positive if you minus the other way
Answer:
-2279960
Step-by-step explanation: