What is the formula for margin of error?
ME = StartFraction z times StartRoot s EndRoot Over StartRoot n EndRoot EndFraction
ME = StartFraction z times StartRoot s EndRoot Over n EndFraction
ME = StartFraction z times s Over StartRoot n EndRoot EndFraction
ME = StartFraction z times s Over n EndFraction
ANSWER IS:
C) ME = StartFraction z times s Over StartRoot n EndRoot EndFraction
Answers
Answer:
Margin of error = Critical value x Standard error of the sample.
Step-by-step explanation:
The margin of error can be calculated in two ways, depending on whether you have parameters from a population or statistics from a sample: Margin of error = Critical value x Standard deviation for the population. Margin of error = Critical value x Standard error of the sample.
Its C. ME= (z*s)/ sqrt n
Related Questions
The poll found that 38% of a random sample of 1012 American adults said they believe in ghosts. What is the lower bound for a 90% confidence interval for the percentage of all American adults who believe in ghosts?
Answers
Answer:
The lower bound for a 90% confidence interval for the percentage of all American adults who believe in ghosts is 0.3549
Step-by-step explanation:
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]1-\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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 1012, \pi = 0.38[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.38 - 1.645\sqrt{\frac{0.38*0.62}{1012}} = 0.3549[/tex]
The lower bound for a 90% confidence interval for the percentage of all American adults who believe in ghosts is 0.3549
please help im clueless
Answers
To create a scale drawing of an Olympic standard swimming pool with a scale of 1 inch to 10 meters, the scaled dimensions would be approximately 2.5 inches for the width and 5 inches for the length.
To create a scale drawing of an Olympic standard swimming pool using a scale of 1 inch to 10 meters, we need to find the scaled dimensions. The actual dimensions of the pool are given as 50 meters in length and 25 meters in width.
Width:
Actual width: 25 meters
Scale factor: 10 meters per 1 inch
Scaled width = Actual width / Scale factor
Scaled width = 25 meters / 10 meters per 1 inch
Scaled width = 2.5 inches
Length:
Actual length: 50 meters
Scale factor: 10 meters per 1 inch
Scaled length = Actual length / Scale factor
Scaled length = 50 meters / 10 meters per 1 inch
Scaled length = 5 inches
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Solve the following expression using order of operations 58-2x3+1
Answers
58-6+1
52+1
53
Teen obesity:
The 2013 National Youth Risk Behavior Survey (YRBS) reported that 13.7% of U.S. students in grades 9 through 12 who attend public and private schools were obese. [Source: Kann, L., Kinchen, S., Shanklin, S.L., Flint, K.H., Hawkins, J., Harris, W.A., et. al.(2013) YRBS 2013]
Suppose that 15% of a random sample of 300 U.S. public high school students were obese. Using the estimate from the 2013 YRBS, we calculate a standard error of 0.020. Since the data allows the use of the normal model, we can determine an approximate 95% confidence interval for the percentage of all U.S. public high school students who are obese.
Which interval is the approximate 95% confidence interval?
A) 0.097 to o.177
B) 0.117 to 0.157
C) 0.110 to 0.190
D) 0.013 to o.170
Answers
Answer:
95% confidence interval for the percentage of all U.S. public high school students who are obese is [0.110 , 0.190].
Step-by-step explanation:
We are given that 15% of a random sample of 300 U.S. public high school students were obese.
Firstly, the pivotal quantity for 95% confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample % of U.S. public high school students who were obese = 15%
n = sample of U.S. public high school students = 300
p = population percentage of all U.S. public high school students
Here for constructing 95% confidence interval we have used One-sample z proportion statistics.
So, 95% confidence interval for the population proportion, p is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
95% confidence interval for p = [[tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]]
= [ [tex]0.15-1.96 \times {\sqrt{\frac{0.15(1-0.15)}{300} } }[/tex] , [tex]0.15+1.96 \times {\sqrt{\frac{0.15(1-0.15)}{300} } }[/tex] ]
= [0.110 , 0.190]
Therefore, 95% confidence interval for the percentage of all U.S. public high school students who are obese is [0.110 , 0.190].
The correct answer is option (c). The approximate 95% confidence interval is [tex]\[0.1108 \text{ to } 0.1892\][/tex]
To determine the approximate 95% confidence interval for the percentage of all U.S. public high school students who are obese, we'll use the standard error provided and the normal model.
The formula for the confidence interval is:
[tex]\[\hat{p} \pm Z \cdot \text{SE}\][/tex]
Now, we calculate the margin of error:
[tex]\[\text{Margin of Error} = Z \cdot \text{SE} = 1.96 \cdot 0.020 = 0.0392\][/tex]
Then, we determine the confidence interval by adding and subtracting the margin of error from the sample proportion:
[tex]\[\hat{p} - \text{Margin of Error} = 0.15 - 0.0392 = 0.1108\][/tex]
[tex]\[\hat{p} + \text{Margin of Error} = 0.15 + 0.0392 = 0.1892\][/tex]
Therefore, the approximate 95% confidence interval is:
[tex]\[0.1108 \text{ to } 0.1892\][/tex]
An article reported that for a sample of 52 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO2 level (ppm) was 654.16, and the sample standard deviation was 164.55.
a) calculate and interpret a 95% confidence interval for true average CO2 level in the population of all homes from which the sample was selected .
b) Suppose the investigators had made a rough guess of 175 for the value of s before collecting data .What sanple size would be necessary to obtain an interval width of 50 ppm for confidence level of 95% ?
Answers
Answer:
a) [tex]654.16-2.01\frac{164.55}{\sqrt{52}}=608.29[/tex]
[tex]654.16+2.01\frac{164.55}{\sqrt{52}}=700.03[/tex]
And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm
b) [tex]n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189[/tex]
Step-by-step explanation:
Part a
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=52-1=51[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,51)".And we see that [tex]t_{\alpha/2}=2.01[/tex]
Replacing we got:
[tex]654.16-2.01\frac{164.55}{\sqrt{52}}=608.29[/tex]
[tex]654.16+2.01\frac{164.55}{\sqrt{52}}=700.03[/tex]
And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm
Part b
The margin of error is given by :
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
The desired margin of error is ME =50/2=25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex] (b)
The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got [tex]z_{\alpha/2}=1.960[/tex], and we use an estimator of the population variance the value of 175 replacing into formula (b) we got:
[tex]n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189[/tex]
A train leaves Little Rock, Arkansas, and travels north at 60 kilometers per hour. Another train leaves at the same time & travels south at 65 kilometers per hour. How long will it take before they are 500 kilometers apart?
Answers
Answer:
3.704 Hours
Step-by-step explanation:
This problem can be solved by using concept of relative speed. relative speed is speed of one body in comparison of other.
If two bodies are moving in same direction their relative speed is calculated by taking difference of each other speed.
If two bodies are moving in opposite direction their relative speed is calculated by taking sum of each other speed.
In the problem stated two bodies are moving in north and south direction, hence they are moving in opposite direction, thus their speed can be taken sum of individual speed.
which is
(60+65) Km/Hr = 135 km/hour
Now given in question distance between two bodies is 500 KM
and relative speed = 135 km/hour
using formula of speed distance and time
Time = distance / speed = 500/135 = 3.704 Hours
Therefore it will take 3.704 Hours for both of the trains to be 500 km apart.
You are building a play area for the children. It will be 20 feet long. The total perimeter is 50 feet. What is the width of the play area?
Answers
Answer:
5
Step-by-step explanation:
20+20=40
50-40=10
10/2=5
To check our work we find the perimeter with our new width. 20+20+5+5=50
So we are right!!!
uppose a 95% confidence interval for the average forearm length of men was (24cm, 27cm). How would we then interpret this interval? 95% of all men have a forearm length between 24cm and 27cm. In confidence intervals calculated from many random samples, 95% would contain a sample average forearm length between 24cm and 27cm. The average forearm length of all men is between 24cm and 27cm 95% of the time. 95% of men in this sample of 9 men have a forearm length between 24cm and 27cm. In confidence intervals calculated from many random samples, 95% would contain the average forearm length for all
Answers
Answer:
in many random samples, 95% of the confidence intervals will contain a sample average between 24cm and 27cm.
Step-by-step explanation:
We then interpret this interval that 95% would contain a sample average forearm length between 24cm and 27cm.
What is average?The average is defined as the mean equal to the ratio of the sum of the values of a given number to the total number of values in the set.
The formula for finding the average of given numbers or values is very simple. We just need to add all the numbers and divide the result by the given number of values. So the formula for mean in mathematics is given as follows:
Mean = sum of values/ number of values
Suppose we have given n as number of values like x1, x2, x3 ,..., xn. The average or mean of the given data is equal to:
Mean = (x1 x2 x3 … xn)/n
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A large company that must hire a new president prepares a final list of five candidates, all of whom are equally qualified. Two of these candidates are members of a minority group. To avoid bias in the selection of the candidate, the company decides to select the president by lottery. a. What is the probability one of the minority candidates is hired
Answers
Final answer:
The probability of one of the minority candidates being hired is 40%.
Explanation:
To find the probability that one of the minority candidates is hired, we need to determine the number of favorable outcomes (one of the minority candidates being selected) and divide it by the total number of possible outcomes (selecting any candidate from the final list of five).
Since there are two minority candidates and five candidates total, the probability of selecting one of the minority candidates is
P(one of the minority candidates being hired) = 2/5 = 0.4 = 40%
What do the solutions of a quadratic equation represent graphically? What is the maximum number of solution(s) given by solving a quadratic?
Answers
Answer:
The solutions of a quadratic equation on a graph is the point where the graph cuts across the x and y axes. The maximum number of solutions given by solving a quadratic equation is 2 solutions because the maximum power in a quadratic equation is power 2
The solutions of a quadratic equation represent the points where the graph, or parabola, crosses the x-axis. Those points are known as the roots of the equation. A quadratic equation can have up to two solutions.
Explanation:In mathematics, the solutions of a quadratic equation graphically represent the points where the parabola (graph of the equation) crosses the x-axis. These points are commonly known as the roots or zeros of the quadratic equation. The maximum number of solutions a quadratic equation can have is two. This is due to the highest power in a quadratic equation (ax² + bx + c = 0) being '2'. However, it's also possible for it to have one or no solutions, depending on the values of a, b, and c, specifically their discriminant value (b² - 4ac).
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Which of the following it true about the graph below?
Answers
Answer:
B
Step-by-step explanation:
choose brainliest
Suppose that the money demand function takes the form If output grows at rate and the nominal interest rate is constant, at what rate will the demand for real balances grow
Answers
Complete Question
Suppose that the money demand function takes the form
(M/P)^d = L(i,Y) = Y/(5i)
a. If output grows at rate and the nominal interest rate is constant, at what rate will the demand for real balances grow
b. What is the velocity of money in this economy
Answer:
a. See explanation below
b. Velocity = 5i
Step-by-step explanation:
a. Suppose that the nominal interest rate remains constant, the demand for real balances will grow at the same rate at which the output grows.
b.
Given that (M/P)^d = L(i,Y) = Y/(5i)
Money equation is written as;
Total Spending = MV
Where M = Amount of Money..
V = Velocity of Circulation
Total Spending = PY;
So, PY = MV --- Make V the subject of formula
PY/M = V --- Rearrange
V = PY/M ---- (1)
Also,
M/P = Y/5i --- Cross Multiply
M * 5i = P * Y --- Make 5i the subject of formula
5i = PY/M ---- (2)
Compare 1 and 2
5i = V = PY/M
So, 5i = V
V = 5i
Hence, Velocity = 5i
The limit of a rational function at 5 equals the value of the rational function at 5 true or false
Answers
Mike heats some soup to 216 F. In order to eat the soup, he decides to let the soup cook in his kitchen. The following function represents the temperature of the soup, located in the kitchen with the air temperature of 73 F, after x minutes, where k is the constant rate at which the soup is cooking. T(x)= 73 +143 *e^(kx) If the temperature of the soup is 180 F after 8 minutes, then what is the approximate constant rate of cooling?
Answers
Answer:
-0.04
Step-by-step explanation:
The initial temperature of the soup is 216° F. After 8 minutes, the temperature of the soup is 180° F.
Set T(x) equal to 180, and set x equal to 8. Then, solve for r.
Therefore, the approximate constant rate of cooling is -0.04.
Answer:
Mark me brainliest please
Step-by-step explanation:
f(x) = 10x-4 and g(x) = . What is the value of f(g(-4))?
Answers
This is a composite function problem in high school mathematics. To solve the problem, first evaluate g(-4), then substitute that result into the function f(x). Using these steps, the composite function f(g(-4)) equals -114.
Explanation:First, it is crucial to identify that this is a question involving composite functions, specifically applying the function f(g(x)). In this case, the function g(x) is not provided in the question, so I'll assume we have a typo. If g(x) has been given as 3x + 1, then g(-4) would equal -11. We substitute -11 into the function f(x)=10x-4, we get f(-11)=10*(-11)-4, which results in f(-11)=-114.
The composite function f(g(-4)) is thus -114.
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A town has a population of 17000 and grows at 4% every year. What will be the population after 12 years?
Answers
Final answer:
To find the population of a town after 12 years with an initial population of 17,000 and an annual growth rate of 4%, use the exponential growth formula. After the calculations, the town's estimated future population would be around 26,533 residents.
Explanation:
To calculate the future population of a town that currently has 17,000 residents and grows at a rate of 4% per year, we can use the formula for exponential growth: future population = current population × [tex](1 + growth \ rate)^n,[/tex] where n is the number of years the population is growing. In this case, the formula becomes [tex]17000 \times (1 + 0.04)^n[/tex], because we're looking to find the population after 12 years.
Calculating this, we have: future population = [tex]17,000 \times (1.04)^{12}[/tex]. Using a calculator, we get approximately 26,533, meaning after 12 years, the population of the town is expected to be around 26,533 residents.
The accompanying technology output was obtained by using the paired data consisting of foot lengths (cm) and heights (cm) of a sample of 40 people. Along with the paired sample data, the technology was also given a foot length of 15.2 cm to be used for predicting height. The technology found that there is a linear correlation between height and foot length. If someone has a foot length of 15.2 cm, what is the single value that is the best predicted height for that person?
Answers
Answer:
76 inches
Step-by-step explanation:
It should be understood that 15.2cm is equal to 5 inches.
Since the height = 5 * size of the foot
= 5 * 15.2 = 76
Therefore, a person with 15.2cm as the size of the foot will have the height of 76 inches.
Using the regression model produced by the technology output. The best predicted value for the person's height would be 123.288 cm.
Using the Regression equation produced by the technology used :
Height = 52.0 + 4.69(foot length)For a foot length of 15.2 cm :
The predicted height value can be calculated by substituting the foot length value into the equation thus :
Height = 52.0 + 4.69(15.2)
Height = 52.0 + 71.288
Height = 123.288 cm
The best predicted value for the person's height would be 123.288 cm.
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Sadie’s family orders a medium pizza with one topping, a large pizza with three toppings, two salads, and an order of breadsticks. What is the cost of the bill before tax or tip?
A. $40.25
B. $43.00
C. $44.00
D. $39.25
Answers
Answer:the answers is B
Step-by-step explanation:
Solve the equation (y-10)^2=0
Answers
Answer:
y=10
Step-by-step explanation:
(y-10)^2=0
Take the square root of each side
sqrt((y-10)^2)=sqrt(0)
y-10 =0
Add 10 to each side
y-10+10=0+10
y = 10
A rectangular tank with a square base, an open top, and a volume of 5324 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.
Answers
Answer:
Step-by-step explanation:
I can't unless you give me the length and width or its impossible
Which letter represents the maximum of the data set on the box plot?
A
B
C
D
E
30
35
40
45
50
Answers
How many stripes does each zebra have if there are 6 zebras at the zoo, 162 stripes in all, and all the zebras have the same number of stripes?
Answers
Answer:
27 stripes
Step-by-step explanation:
162/6=27
Since each zebra has the sam amount of stripes, you will divide the amount of stripes my the amount of zebras.
Rearrange this to make a the subject
Answers
Answer:
w = 3(2a + b) - 4
w = 6a + 3b - 4
a = (w - 3b + 4) / 6
Answer:
[tex]a = \frac{w + 4 - 3b}{6} [/tex]
Step-by-step explanation:
[tex]w = 3(2a + b) - 4 \\ w + 4 = 6a + 3b \\ w + 4 - 3b = 6a \\ \frac{w + 4 - 3b }{6} = \frac{6a}{6} \\ \\ a = \frac{w + 4 - 3b}{6} [/tex]
Are the ratios 14:18 and 1:3 equivalent?
Answers
Answer:
PLEASE MARK AS BRAINLIEST PLZ
NOPE
Step-by-step explanation:
14:18 if you want to find the divisible number it is 2 now divide them both by 2it will be 7:9 and that's the most simple way
Answer:
No
Step-by-step explanation:
A way you can do it is to simplify the ratio, to make it smaller, but still equal to 14:18.
14:18 can be divided by 2, and turn to 7:9
This cannot be simplified so it is not equivalent.
Final answer
No
What is (f+g)(x)?
f(x)=-x
g(x)=3x+3
Write your answer as a polynomial or a rational function in simplest form.
Answers
Answer:
There u go
Step-by-step explanation:
(-x+3x+3)×x=2x^2+3x
2x^2+3x=x(2x+3)
The sum of the functions f(x) = -x and g(x) = 3x + 3 is computed as (f+g)(x) = f(x) + g(x), which simplifies to 2x + 3. This denotes a polynomial in simplest form.
Explanation:The question is asking to compute the sum of two functions, f(x) = -x and g(x) = 3x+3 and to express it as a polynomial or a rational function in simplest form.
The sum of the two functions can be computed by adding together the outputs of the individual functions. In mathematical bricolage, this is known as function addition. The function sum (f+g)(x) can be calculated as f(x) + g(x).
If f(x) = -x and g(x) = 3x + 3, then (f+g)(x) can be calculated as follows:
(-x) + (3x + 3) = (-1x + 3x) + 3 = 2x + 3
So, (f+g)(x), in this case, is 2x + 3 which is a polynomial function in simplest form.
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Solve the equation.
3* = 27
x=L(Simplify your answer.)
Answers
Answer:
3³ = 27
This is because:
3x3x3 = 27
3x3x3
\/ x 3
9 x 3
\ /
27
pLLLLSSSS HELPP IM MARKING BRAINLIEST
The water usage at a car wash is modeled by the equation W(x) = 3x3 + 4x2 − 18x + 4, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours.
Write a function, C(x), to model the water used by the car wash on a shorter day.
C(x) = 2x3 + 2x2 − 18x − 11
C(x) = 3x3 + 2x2 − 18x + 11
C(x) = 3x3 + 2x2 − 18x − 11
C(x) = 2x3 + 2x2 − 18x + 11
Answers
Answer:
A C(x) =2x³+2x²-18x-11
Step-by-step explanation:
C(x) = W(x) - D(x)
plug W(x) and D(x) into equation
C(x) = 3x³+4x²-18x+4 - (x³+2x²+15)
add like terms now
C(x) =2x³+2x²-18x-11
I ended up with C(x)=2X^3+2X^2-18X-11 (option 1) Let me know if you have any questions.
WILL GIVE BRAINLIEST ANSWER TO CORRECT ANSWER I need help with questions 2 part a,b,c and question 3 part a,b,c. Please, thank you !
Answers
Answer:
Q2
a) total sweets: 5 + 3 = 8
i) P(red) = 5/8
ii) P(yellow) = 3/8
b) for the second one:
4 red and 3 yellow left
i) P(red) = 4/7
ii) P(yellow) = 3/7
c) for the second one:
5 red and 2 yellow left
i) P(red) = 5/7
ii) P(yellow) = 2/7
Q3
a) total probability is 1
⅙ + ¼ + ⅓ + x = 1
x = 1 - (⅙ + ¼ + ⅓)
x = ¼
b) most likely is the color with highest probability, which is green
c) P(not red) = 1 - P(red)
= 1 - ⅙ = ⅚
3. The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = .17 and a sample of 800 households will be selected from the population. a. Show the sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries. b. What is the probability that the sample proportion will be within ±.02 of the population proportion? c. Answer part (b) for a sample of 1600 household
Answers
Answer:
A)sample proportion = 0.17, the sampling distribution of p can be calculated/approximated with normal distribution of sample proportion = 0.17 and standard error/deviation = 0.013281
B) 0.869
C)0.9668
Step-by-step explanation:
A) p ( proportion of population that spends more than $100 per week) = 0.17
sample size (n)= 800
the sample proportion of p = 0.17
standard error of p = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex] = 0.013281
the sampling distribution of p can be calculated/approximated with
normal distribution of sample proportion = 0.17 and standard error/deviation = 0.013281
B) probability that the sample proportion will be +-0.02 of the population proportion
= p (0.17 - 0.02 ≤ P ≤ 0.17 + 0.02 ) = p( 0.15 ≤ P ≤ 0.19)
z value corresponding to P
Z = [tex]\frac{P - p}{standard deviation}[/tex]
at P = 0.15
Z = (0.15 - 0.17) / 0.013281 = = -1.51
at P = 0.19
z = ( 0.19 - 0.17) / 0.013281 = 1.51
therefore the required probability will be
p( -1.5 ≤ z ≤ 1.5 ) = p(z ≤ 1.51 ) - p(z ≤ -1.51 )
= 0.9345 - 0.0655 = 0.869
C) for a sample (n ) = 1600
standard deviation/ error = 0.009391 (applying the equation for calculating standard error as seen in part A above)
therefore the required probability after applying
z = [tex]\frac{P-p}{standard deviation}[/tex] at p = 0.15 and p = 0.19
p ( -2.13 ≤ z ≤ 2.13 ) = p( z ≤ 2.13 ) - p( z ≤ -2.13 )
= 0.9834 - 0.0166 = 0.9668
The sampling distribution of the sample proportion can be approximated by a normal distribution. The probability of the sample proportion being within a certain range can be calculated using z-scores.
Explanation:a. The sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries, can be approximated by a normal distribution with a mean of p and a standard deviation of √[(p(1-p))/n], where p is the population proportion and n is the sample size.
b. To find the probability that the sample proportion will be within ±0.02 of the population proportion, we calculate the z-scores for both values and find the area under the normal curve between those z-scores.
c. The probability of the sample proportion being within ±0.02 of the population proportion will remain the same for a sample of 1600 households, as long as the population proportion remains the same.
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Suppose a simple random sample of size nequals36 is obtained from a population with mu equals 74 and sigma equals 6. (a) Describe the sampling distribution of x overbar. (b) What is Upper P (x overbar greater than 75.9 )? (c) What is Upper P (x overbar less than or equals 71.95 )? (d) What is Upper P (73 less than x overbar less than 75.75 )?
Answers
Final answer:
The Central Limit Theorem explains the sampling distribution of the sample mean. We calculate probabilities using z-scores in the normal distribution for different scenarios. Understanding the concepts of sampling distributions and z-scores is essential for handling such questions in statistics.
Explanation:
The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the population distribution.
(a) The mean of the sampling distribution of x equals the population mean, which is 74, and the standard deviation of the sampling distribution σ/√n equals 6/√36 = 1.
(b) To find Upper P(x > 75.9), we standardize the value: z = (75.9 - 74) / 1 = 1.9. Consulting a z-table, we find P(z > 1.9) ≈ 0.0287.
(c) For Upper P(x< 71.95), we standardize: z = (71.95 - 74) / 1 = -2.05. From the z-table, P(z < -2.05) ≈ 0.0202.
(d) To find Upper P(73 < x < 75.75), we standardize both values, giving z(73) = (73 - 74) / 1 = -1 and z(75.75) = (75.75 - 74) / 1 = 1.75. Then, P(-1 < z < 1.75) = P(z < 1.75) - P(z < -1) ≈ 0.9599 - 0.1587 = 0.8012.