A previous survey of Washington residents showed that 18% of residents accessed a state park within the last 12 months. This year, the state would like to re-administer the survey, but wants to be sure the Margin of Error in their new study will be at most 4%. Assuming they believe the previous survey's results were reliable, how many samples should they take to ensure their Margin of Error is at most 4% if they plan to analyze the data using a 95% confidence interval
Using the z-distribution for the margin of error, it is found that 355 samples should be taken.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The estimate is of 18%, hence [tex]\pi = 0.18[/tex].
95% confidence, hence [tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].
The minimum sample size is n for which M = 0.04, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.18(0.82)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96\sqrt{0.18(0.82)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.18(0.82)}}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.18(0.82)}}{0.04}\right)^2[/tex]
[tex]n = 354.4[/tex]
Rounding up, 355 samples should be taken.
A similar problem is given at https://brainly.com/question/14936818
A company produces electric insulators. The strength of the insulators is important since a broken insulator may cause a short circuit. Unfortunately, the strength varies significantly due to the material. Because of the expense, only a limited number of insulators could be tested. The engineers sampled 25 insulators (From a production run of 200), and conducted a destructive test to determine the force that was required to break the insulators. The mean value of this force was 1723 lbf with a sample standard deviation of 90 lbf. You may approximate the population standard deviation with the sample standard deviation for the following questions.
a. Determine if the population is large enough or if a finite population correction (FPC) factor is needed. If so, what is the FPC factor?
b. For 95% confidence, determine the margin of error (+ lbf)
c. For these conditions, estimate the range of the probable population mean. Provide lower and upper values. For 95% confidence, determine the margin of error ( Assume the same mean and sample standard deviation. What is one advantage and one disadvantage of using 50 insulators instead of 25 insulators?
d. lbf) if 50 insulators were tested.
Answer:
A company produces electric insulators. The strength of the insulators is important since a broken insulator may cause a short circuit. Unfortunately, the strength varies significantly due to the material. Because of the expense, only a limited number of insulators could be tested. The engineers sampled 25 insulators (From a production run of 200), and conducted a destructive test to determine the force that was required to break the insulators. The mean value of this force was 1723 lbf with a sample standard deviation of 90 lbf. You may approximate the population standard deviation with the sample standard deviation for the following questions. a. Determine if the population is large enough or if a finite population correction (FPC) factor is needed. If so, what is the FPC factor? b. For 95% confidence, determine the margin of error (+ lbf) c. For these conditions, estimate the range of the probable population mean. Provide lower and upper values. For 95% confidence, determine the margin of error ( Assume the same mean and sample standard deviation. What is one advantage and one disadvantage of using 50 insulators instead of 25 insulators? d. lbf) if 50 insulators were tested.
Step-by-step explanation:
A school wants to investigate the amount of exercise students do.
There are 1200 students at the school.
a Suggest a sensible number of students to be sampled.
Answer:
100-200 Step-by-step explanation: yes 600 is half the students most of them are going to be in class
Jake Visits his relatives on Thanksgiving. He first travels to his parents'
place which is 5 miles straight NORTH. He then travels to his grandparents'
which is 5 miles straight WEST from his parent's house. What is the total
distance of Jake's Journey? What is the total displacement of Jake's
Journey?*
Distance 10 Miles: Displacement 10 Mlles
Distance 5 Miles: Displacement 5 miles
Distance 10 miles: Displacement 7.07 miles
Distance 5 miles : Displacement 7.07 miles
Answer:
Distance 10 miles: Displacement 7.07 miles
Step-by-step explanation:
Let's depict Jake's journey on the Cartesian coordinate axis. Let Jake initially be at the point (0 ; 0 ) . Then you can determine how far from the starting point (0; 0) it has moved away (displacement ). According to the Pythagorean theorem , we will find it He walked 10 miles And displacement is found by the Pythagorean theorem
[tex]\bf displacement = \sqrt{5^2+5^2} =\sqrt{50} \approx 7.07m[/tex]
Then the answer is : Distance 10 miles: Displacement 7.07 miles
Plz plz plz plz help me do this will give brainleiest.
Answer:
50 in²
Step-by-step explanation:
The area of the rectangle = 8 × 4 = 32 in²
area of Δ NPO = [tex]\frac{1}{2}[/tex] × PO × PN = [tex]\frac{1}{2}[/tex] × 3 × 4 = 6 in² ( PN = RM )
area of Δ PQR = [tex]\frac{1}{2}[/tex] × RP × 3 = [tex]\frac{1}{2}[/tex] × 8 × 3 = 12 in² ( RP = MN )
area of MNOPQR = 32 + 6 + 12 = 50 in²
what is the slope of the line of (8,10) (-7,14)
The answer is : -4/15
Answer:
-4/15
Step-by-step explanation:
slope is simply the rise over the run which is the change in y over the change in x.
( (y_2) - (y_1) ) / ( (x_2) - (x_1) )
if you plug in your variables that gives you
(14-10) / (-7-8)
which equals
4/-15
- (4/15)
a health status survey in a few villages revelaed that the normal serum protein value of children in that locality is 7.0g/100ml. A group of 16 children, who received high protein food for a period of 6months had serum protein values shown below.Can we consider that the mean serum protein level of these who were fed on high protein is different from that of general population
We can consider that the mean serum protein level of the group of children who received high protein food is different from that of the general population with a normal serum protein value of 7.0g/100ml.
To determine whether the mean serum protein level of the group of 16 children who received high protein food is different from that of the general population with a normal serum protein value of 7.0g/100ml, we can perform a hypothesis test.
Let's denote:
μ1 = Mean serum protein level of the general population (assumed to be 7.0g/100ml)
μ2 = Mean serum protein level of the group fed on high protein food
The null hypothesis (H0) would be that there is no difference between the mean serum protein levels of the two groups:
H₀: μ₁ = μ₂
The alternative hypothesis (Ha) would be that there is a difference between the means:
Hₐ: μ₁ ≠ μ₂
Next, we calculate the sample mean and standard deviation of the group that received high protein food from the given serum protein values.
Assuming the serum protein values (in g/100ml) for the 16 children are as follows:
8.2, 7.6, 7.8, 7.4, 8.0, 7.9, 7.7, 7.5, 7.2, 7.3, 8.1, 7.6, 8.3, 8.0, 7.8, 7.9
Sample mean (x') = (sum of values) / (number of values) = (121.8) / (16) ≈ 7.613 g/100ml
Sample standard deviation (s) ≈ 0.352 g/100ml
Next, we perform a two-sample t-test (assuming equal variances) to compare the means of the two groups. We use the formula:
t = (x'₁ - x'₂) / √[(s₁² / n₁) + (s₂² / n₂)]
where x'₁ and x'₂ are the sample means of the two groups, s₁ and s₂ are the sample standard deviations, and n₁ and n₂ are the sample sizes.
Substituting the values, we get:
t ≈ (7.613 - 7.0) / √[(0.352² / 16) + (0.0² / 16)] ≈ 3.584
Now, we need to find the critical t-value at a given significance level (commonly set at 0.05) and degrees of freedom (df = n1 + n2 - 2). Since we have 16 + 16 - 2 = 30 degrees of freedom, the critical t-value (two-tailed test) is approximately 2.042.
Since the calculated t-value (3.584) is greater than the critical t-value (2.042), we reject the null hypothesis (H0). This means that there is a significant difference between the mean serum protein levels of the two groups.
In conclusion, based on the given data and the hypothesis test, we can consider that the mean serum protein level of the group of children who received high protein food is different from that of the general population with a normal serum protein value of 7.0g/100ml.
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what is 20% of 30? how would you calculate it? please answer asap
Answer:
Working out 20% of 30
If you are using a calculator, simply enter 20÷100×30 which will give you 6 as the answer.
Step-by-step explanation:
Answer:
6Step-by-step explanation:
what is 20% of 30? how would you calculate it?
30 : 100 * 20 = 6
or
30 * 0.20 = 6
What are the zeros of the polynomial function f(x)=(x−2)(x+4)(x−5)?
Three times eight M equals fourteen. Which of the following equations represents this statement?
Answer:
3x8m= 14 is the equation that matches the description.
Step-by-step explanation:
It is simply the number three, multiplied by eight with the variable m, and is equal to the number 14.
Please take a look at the picture
Answer:
A) -3/-11
Step-by-step explanation:
-3/-11-3/11
-3/-11
Reduce the fraction with -1.
3/11
Hope this help :)
If an item is $6.49 for 36 ounces, then it is $
Answer:
0.18
Step-by-step explanation:
A new hotel was built with r rooms. The first weekend it was open, 3/5 of them were reserved. Which of the following expressions represents the number of rooms which were reserved?
A r-3/5
B r x 3/5
C r+3/5
D ÷3/5
Answer:
D ÷3/5 that's the answer i think I worked it out myself
What is the best estimate of 687 × 391?
280,000
210,000
240,000
180,000
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Original equation/problem:}[/tex]
[tex]\mathbf{687\times391}[/tex]
[tex]\mathbf{= 391\times687}[/tex]
[tex]\mathbf{= 268,617}[/tex]
[tex]\huge\textbf{Now, we're going to solve for your}\\\huge\textbf{question:}[/tex]
[tex]\huge\text{Assuming you want us to estimate to the}\\\huge\text{nearest hundred. So we will do so, because}\\\huge\text{it is easier to understand it like that.}[/tex]
[tex]\mathbf{687 \rightarrow 700}\\\mathbf{391\rightarrow 400}[/tex]
[tex]\huge\textbf{New equation:}[/tex]
[tex]\mathbf{700 \times 400}[/tex]
[tex]\mathbf{= 400\times700}[/tex]
[tex]\mathbf{= 280,000}[/tex]
[tex]\huge\text{Therefore, your answer is: \boxed{\mathsf{Option\ A.\ 280,000}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Can someone please explain this to me please?
Will give brainly if you actually answer the question
Answer:
Step-by-step explanation:
24)
3x - 10 > 2
3x - 10 + 10 > 2 + 10
3x > 12
3x/3 > 12/3
x > 4
5x - 15 < -5
5x - 15 + 15 < -5 + 15
5x < 10
5x/5 < 10/5
x < 2
B) x > 4 or x < 2
25) 1.5/60 = 12/x
x = 12(60) / 1.5
x = 480
B) 480 miles
This distance from Old Faithful to Mammoth Hot Springs is actually about 52 miles by road, so there must have been MASSIVE number of road closures to get this result...or else their scale is incorrect. 1.5 inch to 6.0 miles would be a much more accurate scale making the distance 48 miles.
evaluate the expression when c=-3/4 and x=2/3
c-2x
Answer:
-2.0833333333333333333
Step-by-step explanation:
I used demos scientific
Question 2
Which statement best explains
why the sum of the areas of the
two white squares in Figure 2 is
the same as the area of the white
square in Figure 1?
The combined area of the four triangles is equal to the area of the large white
square.
In each triangle, the length of side a plus the length of side b equals the length
of side c. That means that a? + b2 = c?.
In each figure the total area is equal and the area of the 4 triangles is equal, so
the remaining white area in each figure must also be equal.
Answer:
the third option
Step-by-step explanation:
that is actually the proof for Pythagoras :
both squares have the total area of (a + b)².
each of the triangles (4 in figure 1, 4 in figure 2) has the same area as the others : a×b/2
so, for figure 1
(a + b)² = 4×a×b/2 + c² = 2×a×b + c²
and for figure 2
(a + b)² = 4×a×b/2 + a² + b² = 2×a×b + a² + b²
2×a×b + c² = 2×a×b + a² + b²
c² = a² + b²
How many gallons of a 90% antifreeze solution must be mixed with 100 gallons of 10% antifreeze to get a mixture that is 80% antifreeze? Use the six-step method.
Twice the sum of a number and 3 is equal to three times the difference of the number and 6. Find the number.
ENER
The number is a
(ANSWER QUICKLY)
Answer: 5
Step-by-step explanation:
what is the third term of the sequence defined by f(n)=2n-1
Answer:
your Answer has to be 5
Step-by-step explanation:
f(3) = 2x3 - 1
= 6 - 1
= 5
What are the zeros of the function shown in the graph
Answer:
(-4, 0), (0, 0) and (2, 0)Step-by-step explanation:
Zero's of the function are the points of intersection of the graph with the x-axis.
From the picture we see zeros:
(-4, 0), (0, 0) and (2, 0)Zeros are
[tex]\\ \sf\longmapsto (-4,0)U(0,0)U(2,0)[/tex]
In the previous year, at Hub Motors ltd, for a particular model of Mercedes, Nissan and Ford, one could purchase (in million shillings) all three cars for a total of Ksh 150. This year, due to inflation, the same cars would cost Ksh 161. The cost of the Mercedes increased by 8%, the Nissan by 6%, and the Ford by 12%. If the price of last year's Nissan was Ksh 7 less than the price of last year's Mercedes, Use matrix inverse to find the price of each of the three cars last year?
Answer:
Step-by-step explanation:
Please verify how [tex]\frac{1-cos(x)}{sin(x)} =\frac{sin(x)}{1+cos(x)}[/tex]
Answer/Step-by-step explanation:
[tex]\frac{1-\cos \left(x\right)}{\sin \left(x\right)}=\frac{\sin \left(x\right)}{1+\cos \left(x\right)}[/tex]
When you have an equation like this, you can start from either side. So, let us start from the left side.
[tex]\underline{\mathrm{Left\:side:}} \quad\frac{1-\cos \left(x\right)}{\sin \left(x\right)}[/tex]
[tex]\sf{Rewrite\: using \:Trig \:identities=\frac{\sin \left(x\right)}{1+\cos \left(x\right)}}\\\\\mathrm{Therefore,\: it \:is \:true}[/tex]
The net price of a hand phone after allowing trade discount of 20% was RM2,000. Find what is the list price of the hand phone.
Answer:
RM1,600
Step-by-step explanation:
2000 * 0.20= 400
2000-400= 1600
A soccer goalpost is to be made of 40 feet of
Jumber. The school has 27 feet. How much
umber should be purchases?
Answer:
13 more should be purchased.
40-27=13
Solve the inequality: x + 5 < 7 x < 3 , x > -2. , x > 12. , x < 2
Answer:
(d) x < 2
Step-by-step explanation:
Subtract 5 from both sides of the inequality, the same way you would if it were an equation.
x +5 < 7 . . . . . . given
x +5 -5 < 7 -5 . . . . . show subtraction of 5
x < 2 . . . . . the solution
JACK'S bag weighed 10.5
Pounds and William's bag
weighed 10.05 POUNDS.
Who's bag weighed more?
How much more did it
weigh?
help me out guys I don't get this ?!
Answer:
B: (-2,-3)
Step-by-step explanation:
The problem basically wants you to find the vertex because that is the turning point of an absolute value graph where the slope goes from negative to positive immediately. B is the best choice because the vertex is translated 2 to the left and 3 down.
Who is the general information of accounting
Answer:
General accounting essentially refers to general ledger collection and accounting activities that include account charges in credits and debits and documenting financial statements for a quarter, calendar or fiscal year.
What is the answer to 14÷22 ?
Answer:
0.63636363636363636
Step-by-step explanation:
14/22
Answer:
7/11 or 0.6363636363... and so on in that pattern.
Step-by-step explanation:
Well 14/22 is an irrational decimal which is 0.6363636363... and it goes on forever, so to put it in simple terms you can write it as a fraction as 7/11. (Sorry for being vague).
I hope this answer helped you if it is wrong please let me know. Thank you!
