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A manufacturer of nails claims that only 4% of its nails are defective. A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective. Is it fair to reject the manufacturer's claim based on this observation?
Answer:
The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.
Step-by-step explanation:
A manufacturer of nails claims that only 4% of its nails are defective.
At the null hypothesis, we test if the proportion is of 4%, that is:
[tex]H_0: p = 0.04[/tex]
At the alternative hypothesis, we test if the proportion is more than 4%, that is:
[tex]H_a: p > 0.04[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
4% is tested at the null hypothesis
This means that [tex]\mu = 0.04, \sigma = \sqrt{0.04*0.96}[/tex]
A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective.
This means that [tex]n = 20, X = 0.1[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.1 - 0.04}{\frac{\sqrt{0.04*0.96}}{\sqrt{20}}}[/tex]
[tex]z = 1.37[/tex]
P-value of the test and decision:
Considering an standard significance level of 0.05.
The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.
Looking at the z-table, z = 1.37 has a p-value of 0.9147
1 - 0.9147 = 0.0853
The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.
Answer:
Considering an standard significance level of 0.05.
The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.
Looking at the z-table, z = 1.37 has a p-value of 0.9147
1 - 0.9147 = 0.0853
The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.
Step-by-step explanation:
At a hockey game, a vender sold a combined total of 228 sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
9514 1404 393
Answer:
152 sodas76 hot dogsStep-by-step explanation:
Of the items sold, sodas were 2/(2+1) = 2/3 of the total.
(2/3)(228) = 152 . . . sodas were sold
152/2 = 76 . . . . hot dogs were sold
A city has a population of 350,000 peopleSuppose that each year the population grows by 7.75%What will the population be after 6 years Use the calculator provided and round your answer to the nearest whole number
Answer:
547737
Step-by-step explanation:
So first when know that the equation for exponentinal growth is f(x)=a(1+r)^x
Then you need to substitue so it would be f(x)=350,000(1+0.0775)^6
So then you would add the 1 and 0.0775 to equal 1.0775
So now its f(x)=350,000(1.0775)^6
So after that following PEMDAS, you would basically do 1.0775 to the power of 6 and get 1.56496155465
After you would do 1.56496155465 times 350,000 and that would be 547736.544129 and since its to the nearest whole number the answer would be 547737
Hopefully, that helped. If I did end up making a mistake then just comment on my answer. :)
Use a linear approximation (or differentials) to estimate the given number. (Round your answer to five decimal places.) 3 217
Using a linear approximation, the estimated cube root of 217 is 6.00925.
Given that the number is,
The cube root of 217
Now, for the cube root of 217 using a linear approximation, use differentials.
So, the derivative of the function [tex]f(x) = x^{(1/3)[/tex] at a known point.
Taking the derivative of [tex]f(x) = x^{(1/3)[/tex], we get:
[tex]f'(x) = (\dfrac{1}{3} )x^{-2/3[/tex]
Now, we can choose a point near 217 to evaluate the linear approximation.
Let's use x = 216, which is a perfect cube.
Substituting x = 216 into the derivative, we get:
[tex]f'(216) = (\dfrac{1}{3} )(216)^{-2/3[/tex]
[tex]= 0.00925[/tex]
Next, use the linear approximation formula:
Δy ≈ f'(a)Δx
Since our known point is a = 216 and we want to estimate the cube root of 217,
since 217 - 216 = 1
Hence, Δx = 1
Δy ≈ f'(216)
Δx ≈ 0.00925 × 1
≈ 0.00925
Finally, add this linear approximation to the known value at the known point to get our estimate:
Estimated cube root of 217 ;
f(216) + Δy = 6 + 0.00925
= 6.00925
Therefore, the estimated cube root of 217 is 6.00925.
To learn more about the linear approximation visit:
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I really need help with this problem
Step-by-step explanation:
(x)+(x+1)<832x+1<832x<83-1x<82/2x<41hope it helps.stay safe healthy and happy....Answer:
[tex]x<41[/tex]
Step-by-step explanation:
[tex](x)+(x+1)<83[/tex]
simplify both sides
[tex]2x+1<83[/tex]
subtract one from the both sides to isolate the variable
[tex]2x<82[/tex]
divide both sides by 2 to isolate the variable
[tex]x<41[/tex]
30 students in grade 8 finished their summer packet before August 15.
This was 12% of all the students. How many students are in grade 8?
Step-by-step explanation:
12/100=30/x
12x=3000
x=250
hiii! !!
Each side of a square is increasing at a rate of 4 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 25 cm2
Answer:
The area of the square is increasing at a rate of 40 square centimeters per second.
Step-by-step explanation:
The area of the square ([tex]A[/tex]), in square centimeters, is represented by the following function:
[tex]A = l^{2}[/tex] (1)
Where [tex]l[/tex] is the side length, in centimeters.
Then, we derive (1) in time to calculate the rate of change of the area of the square ([tex]\frac{dA}{dt}[/tex]), in square centimeters per second:
[tex]\frac{dA}{dt} = 2\cdot l \cdot \frac{dl}{dt}[/tex]
[tex]\frac{dA}{dt} = 2\cdot \sqrt{A}\cdot \frac{dl}{dt}[/tex] (2)
Where [tex]\frac{dl}{dt}[/tex] is the rate of change of the side length, in centimeters per second.
If we know that [tex]A = 25\,cm^{2}[/tex] and [tex]\frac{dl}{dt} = 4\,\frac{cm}{s}[/tex], then the rate of change of the area of the square is:
[tex]\frac{dA}{dt} = 2\cdot \sqrt{25\,cm^{2}}\cdot \left(4\,\frac{cm}{s} \right)[/tex]
[tex]\frac{dA}{dt} = 40\,\frac{cm^{2}}{s}[/tex]
The area of the square is increasing at a rate of 40 square centimeters per second.
Find the distance between the two points in simplest radical form. (8,−8) and (−1,−5)
Answer:
Solution given:
[tex]x_{1},y_{1}=(8,-8)[/tex]
[tex]x_{2},y_{2}=(-1,-5)[/tex]
Now
Distance between them is:
d=[tex]\sqrt{(x_{2}-x_{1})²+(y_{2}-y_{1})²}[/tex]
d=[tex]\sqrt{(-1-8)²+(-5+8)²}=3\sqrt{10}[/tex]
Distance between them is [tex]\bold{3\sqrt{10}}[/tex]
Cho hàm số f(x, y) = ln(x
2 + y
2
).
a) Tính f
′
x
, f′
y
;
b) Tính f
′
x
(2; 1), f′
y
(2; 1).
Answer:
Sorry, I can't understand in which language you have written......
Step-by-step explanation:
So if you tell me the question in English then I can answer
find from first principle the derivative of 3x+5/√x
Answer:
[tex]\displaystyle \frac{d}{dx} = \frac{3x - 5}{2x^\bigg{\frac{3}{2}}}[/tex]
General Formulas and Concepts:
Algebra I
Exponential Rule [Powering]: [tex]\displaystyle (b^m)^n = b^{m \cdot n}[/tex]Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex] Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \frac{3x + 5}{\sqrt{x}}[/tex]
Step 2: Differentiate
Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle \frac{3x + 5}{x^\bigg{\frac{1}{2}}}[/tex]Quotient Rule: [tex]\displaystyle \frac{d}{dx} = \frac{(x^\bigg{\frac{1}{2}})\frac{d}{dx}[3x + 5] - \frac{d}{dx}[x^\bigg{\frac{1}{2}}](3x + 5)}{(x^\bigg{\frac{1}{2}})^2}[/tex]Simplify [Exponential Rule - Powering]: [tex]\displaystyle \frac{d}{dx} = \frac{(x^\bigg{\frac{1}{2}})\frac{d}{dx}[3x + 5] - \frac{d}{dx}[x^\bigg{\frac{1}{2}}](3x + 5)}{x}[/tex]Basic Power Rule [Derivative Property - Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx} = \frac{(x^\bigg{\frac{1}{2}})(3x^{1 - 1} + 0) - (\frac{1}{2}x^\bigg{\frac{1}{2} - 1})(3x + 5)}{x}[/tex]Simplify: [tex]\displaystyle \frac{d}{dx} = \frac{3x^\bigg{\frac{1}{2}} - (\frac{1}{2}x^\bigg{\frac{-1}{2}})(3x + 5)}{x}[/tex]Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle \frac{d}{dx} = \frac{3x^\bigg{\frac{1}{2}} - (\frac{1}{2x^{\frac{1}{2}}})(3x + 5)}{x}[/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle \frac{d}{dx} = \frac{3\sqrt{x} - (\frac{1}{2\sqrt{x}})(3x + 5)}{x}[/tex]Simplify [Rationalize]: [tex]\displaystyle \frac{d}{dx} = \frac{3x - 5}{2x^\bigg{\frac{3}{2}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
The area of a circle is 3.142cm square.find the radius and diameter of the circle
Answer:
50.24 or 50.272
Step-by-step explanation:
Square radius and then times by 3.14 or 3.142
4^2*3.14 = 50.24
4^2*3.142 = 50.272
Joe's Auto Insurance Company customers sometimes have to wait a long time to speak to a
customer service representative when they call regarding disputed claims. A random sample
of 25 such calls yielded a mean waiting time of 22 minutes with a standard deviation of 6
minutes. Construct a 95% and 99% confidence interval for the population mean of such
waiting times. Explain what these interval means.
Answer:
The 95% confidence interval for the population mean of such waiting times is between 19.5 and 24.5 minutes. This means that we are 95% sure that the true mean waiting time of all calls for this company is between 19.5 and 24.5 minutes.
The 99% confidence interval for the population mean of such waiting times is between 18.6 and 25.4 minutes. This means that we are 99% sure that the true mean waiting time of all calls for this company is between 18.6 and 25.4 minutes.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 25 - 1 = 24
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0639
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.0639\frac{6}{\sqrt{25}} = 2.5[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 22 - 2.5 = 19.5 minutes
The upper end of the interval is the sample mean added to M. So it is 22 + 2.5 = 24.5 minutes
The 95% confidence interval for the population mean of such waiting times is between 19.5 and 24.5 minutes. This means that we are 95% sure that the true mean waiting time of all calls for this company is between 19.5 and 24.5 minutes.
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.797
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.797\frac{6}{\sqrt{25}} = 3.4[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 22 - 3.4 = 18.6 minutes
The upper end of the interval is the sample mean added to M. So it is 22 + 3.4 = 25.4 minutes
The 99% confidence interval for the population mean of such waiting times is between 18.6 and 25.4 minutes. This means that we are 99% sure that the true mean waiting time of all calls for this company is between 18.6 and 25.4 minutes.
What is the minimum of y=1/3 x^2 + 2x + 5
Answer:
min at x = -3
Step-by-step explanation:
steps are in the pic above.
Solve by graphing. Round each answer to the nearest tenth.
6x2 = −19x − 15
a: −2, 1.7
b: −1.7, −1.5
c: −1.5, 1.5
d: −1.5, 1.7
9514 1404 393
Answer:
b: -1.7, -1.5
Step-by-step explanation:
The graph is shown below. We have annotated the x-intercepts for the equivalent equation ...
6x^2 +19x +15 = 0
Based on the graph, find the set of all x-values for which the points P(x,y) are on the graph y>0. Enter your answer using interval notation
Answer:
The solution set is: (-1,3)
We want to find the set of the x-values of the points that belong to the given graph and have an y-value larger than zero.
The set is: s = (-1, 3)
To find the set, we need to see the x-values of the points on the graph such that y > 0.
y > 0 means that we only look at the region of the graph that is above the x-axis.
We can see that this region goes from x =-1 to x = 3
Then for all the x-values between x = -1 and x = 3 the points p(x, y) on the graph have an y-value larger than zero.
Notice that because the value must be larger than zero, then the particular x-values:
x = -1 and x = 3 are not in the set.
So the set must be written as:
s = (-1, 3)
This is the set in the interval notation.
If you want to learn more, you can read:
https://brainly.com/question/24600195
Someone please help thanks
Answer:
By similar triangles: BE/20 = 18/25 BE 14.4
Also, (ED + 26) / 26 = 18/14.4
ED = 6.5 and AD = 32.5
Which point is the center of the circle?
w
Opoint w
O point X
o point Y
O point Z
Answer:
X o punto Y O punto z
Step-by-step explanation:
You have been doing research for your statistics class on the prevalence of severe binge drinking among teens. You have decided to use 2011 Monitoring the Future (MTF) data that have a scale (from 0 to 14) measuring the number of times teens drank 10 or more alcoholic beverages in a single sitting in the past 2 weeks.
a. According to 2011 MTF data, the average severe binge drinking score, for this sample of 914 teens, is 1.27, with a standard deviation of 0.80. Construct the 95% confidence interval for the true averse severe binge drinking score.
b. On of your classmates, who claims to be good at statistics, complains about your confidence interval calculation. She or he asserts that the severe binge drinking scores are not normally distributed, which in turn makes the confidence interval calculation meaningless. Assume that she or he is correct about the distribution of severe binge drinking scores. Does that imply that the calculation of a confidence interval is not appropriate? Why or why not?
Answer:
(1.218 ; 1.322)
the confidence interval is appropriate
Step-by-step explanation:
The confidence interval :
Mean ± margin of error
Sample mean = 1.27
Sample standard deviation, s = 0.80
Sample size, n = 914
Since we are using tbe sample standard deviation, we use the T table ;
Margin of Error = Tcritical * s/√n
Tcritical at 95% ; df = 914 - 1 = 913
Tcritical(0.05, 913) = 1.96
Margin of Error = 1.96 * 0.80/√914 = 0.05186
Mean ± margin of error
1.27 ± 0.05186
Lower boundary = 1.27 - 0.05186 = 1.218
Upper boundary = 1.27 + 0.05186 = 1.322
(1.218 ; 1.322)
According to the central limit theorem, sample means will approach a normal distribution as the sample size increases. Hence, the confidence interval is valid, the sample size of 914 gave a critical value at 0.05 which is only marginally different from that will obtained using a normal distribution table. Hence, the confidence interval is appropriate
An employee at a shoe store has observed that taller customers have larger shoe sizes than customers who are shorter. She knows that shoe sizes are based on foot length, so she hypothesizes: Compared with shorter people, taller people have longer feet.
Question attachment below
Answer and explanation:
Data patterns are repeated data occurrences in a certain way that is recognizable.
In the example below, the data pattern shows taller people require larger shoe sizes(the taller the person the larger the shoe size) but does make some exceptions. Example: while Denver is taller and requires a larger shoe size, Eduardo is shorter than Tim and still requires a larger shoe size than Tim.
A sociologist claims the probability that a person picked at random in Times Square in New York City is visiting the area is 0.83. You want to test to see if the claim is correct. State the null and alternative hypotheses.
Answer:
The answer is:
[tex]H_0: p=0.83\\\\H_a: p \neq 0.83[/tex]
Step-by-step explanation:
Now, we're going to test if sociologists claim to be have visited a region of 0.83 by a person picked randomly on Time In New York City.
Therefore, null or other hypotheses are:
[tex]H_0: p=0.83\\\\H_a: p \neq 0.83[/tex]
you are making meat loaf with yield: 50, 4oz portions what is the total recipe cost
Answer:
[tex]200oz[/tex]
Step-by-step explanation:
The question says that there are [tex]50[/tex] portions that are [tex]4oz[/tex] each.
Write an equation
[tex](50)4oz[/tex]
Simplify
[tex]200oz[/tex]
The owners of a baseball team are building a new baseball field for their team and must determine the number of seats to include. The average game is attended by 6,500 fans, with a standard deviation of 450 people. Suppose a random sample of 35 games is selected to help the owners decide the number of seats to include. Identify each of the following and be sure to round to the nearest whole number:
Provide your answer below:
μ =------------
μx=-----------
σx=-----------
σ=------------
n=------------
Answer:
μ = 6500
μx= 6500
σx= 76
σ= 450
n= 35
Step-by-step explanation:
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.
The average game is attended by 6,500 fans, with a standard deviation of 450 people.
This means that [tex]\mu = 6500, \sigma = 450[/tex]
35 games:
This means that [tex]n = 35[/tex]
Distribution of the sample mean:
By the Central Limit Theorem, we have [tex]\mu_x = \mu = 6500[/tex] and the standard deviation is:
[tex]\sigma_x = \frac{450}{\sqrt{35}} = 76[/tex]
Find a linear function that models the cost, C, to produce x toys given the rate of change and initial output value. The cost to produce plastic toys increases by 90 cents per toy produced. The fixed cost is 40 dollars. C(x) = dollars Write a linear model for the amount of usable fabric sheeting, F, manufactured in t minutes given the rate of change and initial output value. Fabric sheeting is manufactured on a loom at 7.25 square feet per minute. The first five square feet of the fabric is unusable. F(t) = ft^2 is the amount of usable fabric sheeting manufactured in t minutes.
Answer:
C(x) = $40 + 0.9x
F(t) = 7.25t - 5
Step-by-step explanation:
Given that :
C(x) = Cost model to produce x toys
Fixed cost of production = $40
Rate of change = 90 cent per toy produced.
A linear model will take the form :
F(x) = bx + c ;
Where ; b = rate of change or slope ; c = intercept or initial value
Therefore, a linear cost model will be :
Cost model to produce x toys = fixed cost + (rate of change * number of toys)
C(x) = $40 + 0.9x
2.)
F(t) = amount of usable factory sheets manufactured in t minutes :
Rate of production = 7.25 ft² / minute
Number of unusable fabric sheeting = 5 ft²
The function, F(t) :
F(t) = 7.25t - 5
A large bottle of water is leaking. The amount of ounces left in the bottle is shown in the function [tex]O(s) = 72-3s[/tex] is the amount of ounces left, and s is the number of seconds that is the water is leaking out. What is a reasonable domain and range for this function?
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Answer:
D: [0, 24]
R: [0, 72]
Step-by-step explanation:
The function only makes sense for non-negative values of time or water volume. The intercepts of the function are ...
y-intercept: 72
x-intercept: 72/3 = 24
so the reasonable domain is 0 ≤ s ≤ 24,
and the corresponding range is 0 ≤ O(x) ≤ 72.
2/5 e +4 = 9
Help please
Answer:
e=12.5 or e=25/2
Step-by-step explanation:
Complete this sentence: The longest side of a triangle is always opposite the
• A. angle with the smallest measure
O B. angle with the greatest measure
O C. shortest side
D. second-longest side
Answer:
B. angle with the greatest measure
opposite the largest angle
I need help with these questions
Answer:
1) 6m+8n
4) 21x+14y
7) 14c+16d
10) d+3e
Step-by-step explanation:
So for this problem I got the scientific notation however I can not seem to figure out the standard notation. I thought it is the same answer but it is not. Can someone please help me out here please?
Answer:
567000000
Step-by-step explanation:
Standard is the actual number. Multiply 5.67 and 10^8.
51
What is the inverse of the function f(x) = 2x + 1?
Oh(x) =
1
2x-
o h«x)= kx +
- 3x-2
Oh(x) =
Oh(x) =
Mark this and return
Save and Exit
Next
Submit
Type here to search
81
O
10:49 AM
^ D 0x
mamman
Answer:
let inverse f(x) be m:
[tex]m = \frac{1}{2x + 1} \\ 2x + 1 = \frac{1}{m} \\ 2x = \frac{1 - m}{m} \\ x = \frac{1 - m}{2m} [/tex]
substitute x in place of m:
[tex]{ \bf{ {f}^{ - 1}(x) = \frac{1 - x}{2x } }}[/tex]
HELP PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
Answer:
12
Step-by-step explanation:
10 - 1/2 x = 12-4/3x
60 - 3x = 72-2x
-12 = - x
