Of 1000 randomly selected cases of lung cancer, 823 resulted in death within 10 years.
a. Calculate a 95% two-sided confidence interval on the death rate from lung cancer.
b. Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.03?
c. How large must the sample be if you wish to be at least 95% confident that the error in estimating p is less than 0.03, regardless of the true value of p?
Answers
Answer:
a) \(0.823 - 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.799\)
\(0.823 + 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.847\)
The 95% confidence interval would be given by (0.799;0.847)
b) \(n=\frac{0.823(1-0.823)}{(\frac{0.03}{1.96})^2}=621.79\)
And rounded up we have that n=622
c) \(n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11\)
And rounded up we have that n=1068
Step-by-step explanation:
Part a
\(\hat p=\frac{823}{1000}=0.823\)
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \(\alpha=1-0.95=0.05\) and \(\alpha/2 =0.025\). And the critical value would be given by:
\(z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96\)
The confidence interval for the mean is given by the following formula:
\(\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}\)
If we replace the values obtained we got:
\(0.823 - 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.799\)
\(0.823 + 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.847\)
The 95% confidence interval would be given by (0.799;0.847)
Part b
The margin of error for the proportion interval is given by this formula:
\( ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}\) (a)
And on this case we have that \(ME =\pm 0.03\) and we are interested in order to find the value of n, if we solve n from equation (a) we got:
\(n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}\) (b)
And replacing into equation (b) the values from part a we got:
\(n=\frac{0.823(1-0.823)}{(\frac{0.03}{1.96})^2}=621.79\)
And rounded up we have that n=622
Part c
\(n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11\)
And rounded up we have that n=1068
Related Questions
From the top of the 140-foot high tower, an air traffic controller observes an airplane on the runway at an angle of depression of 18°.
18°
140 ft
How far is it from the base of the tower to the airplane? Round your answer to the nearest tenth of a foot.
Answers
Answer:
Step-by-step explanation:
The angle of depression is the downward angle the air traffic controller
looks down from in the tower. It also equals the angle of elevation which is the angle formed by the runway and the line of sight.
With this information you can find the remaining angle:
180 - (90 + 18)
180 - 108 = 72
Let Angle B = 72°
Angle A = 18°
Angle C =90°
We have one side - 140 feet - this is side a - it is across from angle A.
There is a right triangle formed by the runway (side b) the tower, side a, and the line of sight (side c)
Using the law of sines:
sin A/a = sinB/b
sin 18°/a = sin72°/b
.3090/140 = .9510/x
cross multiply and then divide
140 × .9510/.3090
133.14/.3090
430.873 ft
round to a tenth = 430.9 ft
Select the correct answer.
What is the solution to this equation?
g^x-1=2
A. -1/2
B. 1/2
C. 2
D. 1
Answers
9514 1404 393
Answer:
B. 1/2
Step-by-step explanation:
Maybe you want the solution to ...
\(9^x-1=2\)
You can use logarithms, or your knowledge of powers of 3 to solve this.
\(9^x=3\qquad\text{add 1}\\\\3^{2x}=3^1\qquad\text{express as powers of 3}\\\\2x=1\qquad\text{equate exponents of the same base}\\\\\boxed{x=\dfrac{1}{2}}\qquad\text{divide by 2}\)
Using logarithms, the solution looks like ...
\(x\cdot\log{9}=\log{3}\\\\x=\dfrac{\log{3}}{\log{9}}=\dfrac{1}{2}\)
Pre Calc for one of my classes
Answers
Therefore your question becomes (log 2.3 (13))/9 = x
And rounding to 3 decimals gives you 0.342
Is 1.65 greather than 16.5
Answers
Answer:
No
Step-by-step explanation:
Answer: No , 16.5 is greater though than 1.65 .
Step-by-step explanation:
Order of Operations with and without variables
Answers
Answer:
51
Step-by-step explanation:
First, we plug 3 into the x values to get:
45-3+9
Then we do order of operations to get 51 as our answer.
For the given pair of events A and B, complete parts (a) and (b) below. A: When a page is randomly selected and ripped from a 29-page document and destroyed, it is page 15. B: When a different page is randomly selected and ripped from the document, it is page 24.
Required:
a. Determine whether events A and B are independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be independent.)
b. Find P(A and B), the probability that events A and B both occur
Answers
Answer and Step-by-step explanation:
In probability, events are dependent when the probability of the first event ocurring influences the outcome of the second event.
a. For events A and B, after ripping one page, it is destroyed, so the total number of pages changed. Therefore, events A and B are dependent.
b. To find the probability of both events happening, first, determine the probabilities of each event:
P(A) = \(\frac{1}{29}\)
P(B) = \(\frac{1}{28}\)
P(A and B) = \(\frac{1}{29}.\frac{1}{28}\)
P(A and B) = \(\frac{1}{812}\)
Probability of A and B occur is 0.12% or \(\frac{1}{812}\).
How would you graph the two linear equations on a coordinate plane? Graph the system of equations in the same coordinate plane and determine the number of solutions for the system. If there is exactly one solution, write it as an ordered pair.
y = 3x + 1
y = 2x +2
Answers
Answer:
one solution: (1, 4)
Step-by-step explanation:
You want the graphs and number of solutions to the system of equations ...
y = 3x +1y = 2x +2GraphThe graph is attached. The first equation has a y-intercept of +1 and a slope of 3. The second equation has a y-intercept of +2 and a slope of 2.
The different slopes mean there is exactly one solution. The graph shows that solution to be (x, y) = (1, 4).
__
Additional comment
The slope is the x-coefficient when the equations are written in this "slope-intercept" form. It is the "rise/run" for the line on the graph. A slope of 3, for example, means the line has a rise of 3 grid squares for a run of 1 square (to the right). Knowing the y-intercept and slope makes it easy to graph the line.
Write the equation of the horizontal line that goes through the point (2, 4)
Answers
Answer:
y=2
Step-by-step explanation:
Maria earns $2,000 a month, plus 3% commission on everything she sells. 2
Her sales totaled x dollars this month. Which amount represents the
amount of money Maria earns this month?
Answers
Answer:
2,000 + 0.03x
Step-by-step explanation:
Find the distance between the given points. Round to the nearest tenth. 5,-2 and 1,2.
Answers
Answer:
\(4\sqrt{2}\)
Step-by-step explanation:
Use the distance equation
\(\sqrt{(x1-x2)^2+(y1-y2)^2}\)
insert values (5,-2)=(x1,y1) and (1,2)=(x2,y2)
\(\sqrt{(5-1)^2+((-2)-2)^2}\)
\(\sqrt{16+16}\)
\(4\sqrt{2}\)
Hope that helps :)
When is a repeating decimal acceptable to use during calculations? When should you convert a repeating decimal to a fraction for calculations?
Answers
A repeating decimal is acceptable to use during calculations when you require a certain level of precision
When is a repeating decimal acceptable to use during calculations?A repeating decimal is acceptable to use during calculations when you require a certain level of precision, but it's important to keep in mind that the result will be an approximation rather than an exact value.
It is commonly used in situations where a rounded value is sufficient and the level of precision doesn't significantly impact the final result.
On the other hand, you should convert a repeating decimal to a fraction for calculations when you need an exact value or when further mathematical operations or comparisons are required.
Converting a repeating decimal to a fraction allows for precise calculations and eliminates any potential rounding errors associated with working with decimal approximations.
Converting a repeating decimal to a fraction involves identifying the repeating pattern and expressing it as a fraction. This allows for exact calculations and maintains the mathematical properties of fractions.
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5. The Colorado state flag consists of three horizontal stripes of equal height. The side lengths of the flag are in the ratio 2 : 3. The diameter of the gold-colored disk is equal to the height of the center stripe. What percentage of the flag is gold?
Answers
Answer:
the diameter of the circle is ⅓ of the height
so the radius is 1/6 of the height
the area of the flag is 1*1.5 of the height
(we need to consider this)
pi*(1/6)² / 1.5
= 0.058177
so the percentage is
5.82 %
So, the required percentage is \(5.81\%\).
To understand the calculations, check below.
Area of the disk:The area of the disk is defined as the ‘ measure of surface ‘ surrounded by the round edge (circumference) of the disk. The area of a disk can be derived by breaking it into a number of identical parts of disk as units — calculating their areas and summing them up till the disk is reformed.
That is \(Area=\pi \frac{d^2}{4}\)
Let the width and the length of the flag be \(2x\) and \(3x\) respectively.
So, the diameter of the gold-colored disk will be \(\frac{2x}{3}\)
Now, by using the above formula the area of the gold disk will be,
\(\pi \frac{d^2}{4}=\pi\times\frac{4x^2}{4\times 9} \\ =\frac{\pi x^2}{9}\)
And the area of the flag will be,
\(Area=l\times b\\=2x\times 3x\\=6x ^2\)
So, the required percentage is,
\(\frac{(\frac{\pi x^2}{9} )}{6x^2} \times 100=\frac{\pi}{54}\times 100\\ =5.81\%\)
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. How much you have to deposit in an account earning 8 percent compound monthly to pay a retired officer $1000 monthly for 12 years.
Answers
FV = PMT * [(1 + r/n)^(n*t) - 1]/(r/n)
where FV is the future value of the annuity, PMT is the payment amount, r is the annual interest rate (as a decimal), n is the number of compounding periods per year, and t is the number of years.
In this case, we have:
PMT = $1000 per month
r = 0.08 (8% annual interest rate)
n = 12 (compounded monthly)
t = 12 years
We need to solve for the future value, which represents the total amount of money that needs to be deposited to generate the $1000 monthly payment for 12 years. Plugging in the numbers, we get:
FV = $1000 * [(1 + 0.08/12)^(12*12) - 1]/(0.08/12) ≈ $149,139.77
Therefore, the retired officer would need to deposit approximately $149,139.77 in an account earning 8 percent compound monthly to pay a $1000 monthly payment for 12 years.
Question 9
The table shows the ingredients needed to make one batch of homemade slime.
Ingredient
Amount (fl oz)
Glue
Liquid Starch
Water
4
Dodi has 2 cups of liquid starch and will use the entire amount. She plans to store the slime in containers that each hold a maximum of 6 fluid
ounces. How many containers will she need? Write an argument to defend your solution. (Hint: 2 cups = 16 fluid ounces)
Dodi will need
containers.
Dodi has
fluid ounces, of liquid starch, so she will make
batches of slime. Each batch makes 4 x 3, or 12 fluid ounces, so she will make a total of
containers to hold all of the slime.
will need
4
4
+4, or
fluid ounces of slime
Answers
It is given that Dodi has two cups of liquid starch
2 cups =16 fluid ounces
1 container can hold 6 fluid ounces
We are required to find that how many containers are required
1 container contains 6 ounces
Hence 16 ounces will be contained in 3 containers
Hence Dodi will required 3 containers.
Disclaimer:
The question is incomplete and jumbled
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Can someone please answer and provide an explanation for these problems?
Answers
Step-by-step explanation:
The way you can think about volume is that we have some cross sectional area times the height of the solid.
27.
The volume of a square based pyramid is
\(v = {s}^{2} ( \frac{h}{3} )\)
where h is the height of the pyramid
s is the side length of the square base.
S=7
h=12
\(v = {7}^{2} ( \frac{12}{3} ) = 49 \times 4 = 196\)
28. The volume of a rectangular prism
\(v = l \times w \times h\)
where l is length
w is width
h is height
\(v = 11 \times 11 \times 8 = 968\)
29.
Use the same formula in 27
\(v = 100(3) = 300\)
30.
Volume of a Cylinder is
\(v = \pi {r}^{2} h\)
where r is the radius of the circle
where h is the height
r is half of the diameter
The diameter is 22, thus the radius is 11.
\(v = {11}^{2} (8)(\pi)\)
\(v = 968\pi\)
pi is approximately 3.14
\(v = 3041.06\)
31. Volume of A Sphere
\( \frac{4}{3} \pi {r}^{3} = v\)
The radius is half of diamter, thus r=7
\( \frac{4}{3} \pi( {7}^{3} ) = 1436.76\)
90×4/9=40 is this equation true
Answers
The equation is correct, and the value on both sides of the equation is 40.
To verify if the equation 90 × 4/9 = 40 is true, we can perform the calculation on both sides and compare the results.
On the left side of the equation:
90 × 4/9 = (90 × 4) / 9 = 360 / 9 = 40
On the right side of the equation:
40
Both sides of the equation evaluate to 40, which means they are equal. Therefore, the equation 90 × 4/9 = 40 is indeed true.
In summary, the equation is correct, and the value on both sides of the equation is 40.
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The segment below is dilated by a scale factor of 22 to form I ′J ′ What is the measure of I ′J ′ ?
Answers
Answer:
18
Step-by-step explanation:
When dilating a segment by a scale factor, we multiply the original length by the scale factor to find the length.
2*9 = 18
Help me don’t get please help me
Answers
Answer:
60m^2
Step-by-step explanation:
7m x 5m = 35m^2
5m x 5m = 25m^2
35m^2 + 25m^2 = 60m^2
what is 5x6
pls answer
Answers
Answer:
30
Step-by-step explanation:
6 x 5 = 30
Answer:
30
Step-by-step explanation:
NEED HELP ASAP Which side lengths form a right triangle?
Answers
Answer:
the answers is B, 3,4,5
Step-by-step explanation:
HELP ASAP PLS
A student needs to decorate a box as part of a project for her history class. A model of the box is shown.
A rectangular prism with dimensions of 24 inches by 16 inches by 2 inches.
What is the surface area of the box?
928 in2
768 in2
464 in2
160 in2
Answers
Answer:
928 in2
768 in2
464 in2
160 in2
The function is defined below. Find all values of that are NOT in the domain of g. g(x)=x^2+13+40 / x^2-9
Answers
Answer:
g(x)=x-2/x^2-9
If there is more than one value, separate them with commas.
Step-by-step explanation:
One week, Brody earned $396.10 at his job when he worked for 17 hours. If he is paid the same hourly wage, how many hours would he have to work the next week to earn $699.00?
this is worth 50 points, plus brainliest
Answers
Answer:
Brody will have to work 30 hours.
Step-by-step explanation:
First you have to divide 396.10 by 17 to get $23.30 which is how much he earns per hour. Then you divide 699.0 by 23.30 to get 30 hours.
BRAINLIEST TO CORRECT
Answers
Answer:
A- 94/17
B- A
Step-by-step explanation:
Part A:
5*17= 85
85+9= 94
Part B:
Convert 5 9/17 into decimal
Hope this helps! :)
Answer:
Part A:
94/17
Part B:
A) 5.52
Step-by-step explanation:
Part A:
First, you have to multiply 5 by 17...
Your answer should be 85. Add 85 to 9, this should be your answer...
94/17
Part B:
1. 94/17
2. 94 ÷ 17
≈ 5.5294118
Rounded, it would be 5.52
-kiniwih426
a Carnival charges $5 to enter, and $2 per ride. If you paid a total of $23, how many rides did you go at the carnival
Answers
Answer : 8$
you have 1$ left
The machinery in a cereal plant fills 350 g boxes of cereal. The specifications for the machinery permit for a certain amount of fill tolerance. It is found that the weights of filled cereal boxes are normally distributed with a mean of 350 g and a standard deviation of 4 g. What is the probability that a box of cereal is under filled by 5 g or more?
Answers
There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.
First, we can standardize the problem by using the z-score formula:
z = (x - μ) / σ
Where:
x = the weight value we want to find the probability for (345 g in this case)
μ = the mean weight (350 g)
σ = the standard deviation (4 g)
Substituting the values into the formula:
z = (345 - 350) / 4 = -1.25
Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.
The probability of obtaining a z-score less than -1.25 is approximately 0.1056.
However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.
The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.
Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
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. The table below shows the cost of making a long distance call based on the length of the call. Long Distance Rates Time (minutes) Cost 5 $0.55 6 $0.62 7 $0.69 8 $0.76 9 $0.83 10 $0.90 Refer to the above table of long distance rates. Write an expression that can be used to find the cost of an n-minute long distance call, where n is at least 5 minutes.
Answers
An expression that can be used to find the cost of an n-minute long distance call, where n is at least 5 minutes is (0.55 + (n - 5) x 0.07) dollars.
Given:
Long Distance Rates Time (minutes) Cost5 $0.556 $0.627 $0.698 $0.769 $0.8310 $0.90We need to find an expression that can be used to find the cost of an n-minute long-distance call, where n is at least 5 minutes.
The cost of making a long-distance call is given for 5 minutes, 6 minutes, 7 minutes, 8 minutes, 9 minutes, and 10 minutes.
We can observe from the above table that for every increase of 1 minute, the cost increases by $0.07.
We can conclude that the cost of n minutes long-distance call is given by: (0.55 + (n - 5) x 0.07) dollars when n is at least 5 minutes.
Therefore, the required expression is: (0.55 + (n - 5) x 0.07) dollars when n is at least 5 minutes. The above expression is based on the pattern in the table provided for long-distance call rates. We can use this expression for values of n greater than or equal to 5.
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Which of the following is the solution of -6( m - 3 )
\( \geqslant \)
- 24
![Which of the following is the solution of -6( m - 3 ) [tex] \geqslant [/tex]- 24](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/Q5CXhoHuaG7ognr2GnXH9yuzHosNy1Vn.jpeg)
Answers
Answer:
m ≤ 7Step-by-step explanation:
Let's simplify the inequality.
-6(m - 3) ≥ -24=> -6m + 18 ≥ -24=> 24 + 18 ≥ 6m=> 42 ≥ 6m=> 42/6 ≥ 6m/6=> (7 ≥ m) = (m ≤ 7)Option C is correct.
![Which of the following is the solution of -6( m - 3 ) [tex] \geqslant [/tex]- 24](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/mJxQz6BAxkodMkUFcNW3kdL6V3YHiy7U.jpeg)
Match the polynomial on the left with the appropriately factored expression on the right.
x² + 6x +9. x²-9
(x - 3)(x-3)
(x-3)(x + 3)
(x+3)(x + 3)
3(x+3)(x + 3)
Answers
The polynomials that match with other equivalent expressions are :(a) → (iii), (b) → (ii), (c) → (iv), (d) → (i)
Match the polynomial on the left ?Consider the polynomials,
(a) 4x² + 18x (i) 2x(2x + 1)
(b) 4x² + 2x + 18x +9 (ii) (2x + 1)(2x +9)
(c) (2x + 3)(2x + 3) (iii) 2x(2x + 9)
(d) 4x² + 2x (iv) 4x² + 12x + 9
Now,
Consider the polynomial 2x(2x + 1),
2x(2x + 1) = 2x(2x) + 2x(1)
2x(2x + 1) = 4x² + 2
Therefore, (d) is equal to (i).
Consider the polynomial 2x(2x + 9),
2x(2x + 9) = 2x(2x) + 2x(9)
2x(2x + 9) = 4x² + 18x
Therefore, (a) is equal to (iii).
Consider the polynomial (2x + 1)(2x +9) ,
(2x + 1)(2x +9) = (2x)(2x) + (2x)(9) + (2x)(1) + 9
(2x + 1)(2x +9) = 4x² + 18x + 2x + 9
Therefore, (b) is equal to (ii).
Consider the polynomial (2x + 3)(2x + 3),
(2x + 3)(2x + 3) = (2x)(2x) + (2x)(3) + (3)(2x) + 9
(2x + 3)(2x + 3) = 4x² + 12x + 9
Therefore, (c) is equal to (iv).
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You want to be able to withdraw $30,000 each year for 15 years. Your account earns 10% interest.
a) How much do you need in your account at the beginning?
$
b) How much total money will you pull out of the account?
$
c) How much of that money is interest?
$
Answers
In response to the given query, we can state that Therefore, at the start, interest we need to have $249,043.20 in our account.
what is interest ?Divide the capital by the interest rate, the length of time, and other factors to arrive at simple interest. Simple return = principal + interest + hours is the marketing strategy. This method makes it easiest to compute interest. The most typical method to figure out interest is as a portion of the principal sum. He will only pay his share of the 100% interest, for example, if he borrows $100 from a friend and promises to pay it back with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you give it out, you must charge interest. Interest is typically determined as an annual percentage of the loan amount. The interest on the debt is this percentage.
The present value of an annuity formula, which is: can be used to determine the solutions.
PV is equal to PMT x (1 - (1 + r)-n) / r.
The annuity's present worth is expressed as PV.
The PMT is the sum paid or withheld each year.
N is the overall number of years in the annuity, and r is the annual interest rate.
a) We can rewrite the algorithm as follows to determine the initial balance we need in our account:
PV is equal to PMT times (1 - (1 plus r))n / r, or $30,000. 0.1 PV equals $30,000 multiplied by (1 minus 0.016986) yields 8.30144 PV, which equals $249,043.20.
Therefore, at the start, we need to have $249,043.20 in our account.
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