Answer:
The point estimate for estimating the true proportion of employees who prefer that plan is 0.436
Step-by-step explanation:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
In this problem, we have that:
Lower bound: 0.366
Upper bound: 0.506
Point estimate:
(0.366 + 0.506)/2 = 0.436
The point estimate for estimating the true proportion of employees who prefer that plan is 0.436
Answer:
[tex]\hat p = \frac{0.366+0.506}{2}= 0.436[/tex]
And the point of estimate for the proportion of employees who prefer plan is on this case 0.436 or 43.6%.
Step-by-step explanation:
We define the parameter of interest as the proportion of employees who prefer plan p and we want to estimate this true parameter
The confidence interval for the this proportion is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
After calculate the 95% confidence interval we got (0.366, 0.506)
We can obtain the best estimate for the proportion of employees who prefer plan like this:
[tex]\hat p =\frac{Upper +Lower}{2}[/tex]
Where Upper and Lower represent the limits for the confidence interval and replacing we got:
[tex]\hat p = \frac{0.366+0.506}{2}= 0.436[/tex]
And the point of estimate for the proportion of employees who prefer plan is on this case 0.436 or 43.6%.
The margin of error can be estimated using the fact that this confidence interval is symmetrical and we got:
[tex]ME=\frac{Upper-Lower}{2}= \frac{0.506-0.366}{2}=0.07[/tex]
5.62 (6.2+6.2) divided by 2
Look at the attached picture z
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Hope it will help u...
Find the measure of x
A. x=2
B. x = 6
C. x=8
D. X=10
Answer:
x = 6º
Step-by-step explanation:
120º = 15(x + 2)
120 = 15x + 30
15x = 120 - 30
15x = 90
x = 90/15
x = 6º
The measure of x is 6°, which corresponds to option B: x = 6, using the property of parallel lines.
We can observe that the given lines are parallel cut by a transversal.
So, the angles 120° and 15(x + 2) are alternate exterior angles which are equal.
So, 120° = 15(x + 2)
To find the value of x:
1. Start by isolating the variable x on one side of the equation.
Subtract 30 from both sides to move the constant term to the other side:
120° - 30° = 15(x + 2) - 30°
2. Simplify the equation:
90° = 15(x + 2)
3. Now, divide both sides of the equation by 15 to solve for x:
(90°) / 15 = (15(x + 2)) / 15
4. Calculate:
90° / 15 = 6°
So, x = 6°.
Therefore, the correct answer is: B. x = 6.
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The amount of chill is _ times the amount of cream cheese
Answer:
6 Chili / 3 cream cheese = 2 Timeschilli compared to cream cheese.
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
There are 6 for chilli and 3 for cream cheese.
3 *2 is 6, there fore it is 2 times as much
Hope this is helpful! :)
Four red candies and three green candies can be combined to make many different flavors. Flavors are different if the percent red is different, so 3 red / 0 green is the same flavor as 2 red / 0 green; and likewise 4 red / 2 green is the same flavor as 2 red / 1 green. If a flavor is to be made using some or all of the seven candies, how many different flavors are possible
Answer:
11
Step-by-step explanation:
:):
How many times greater is 70 million than 4 million?
Answer:
66 million
Step-by-step explanation:
4 million on 70 million is 66 million
Answer:
17.5
Step-by-step explanation:
hope we can be friends
can i please get brainliest
We randomly place 200 balls independently in 100 boxes in the most natural uniform way. That is, each ball is placed independently from the rest of the balls in such a way that the probability to put it into the ith box is one-percent (1 ≤ i ≤ 100). Let X denote the number of empty boxes at the end. What is the expected value of X? I also want the numerical value.
Answer:
The expected value of X is 13.4.
Step-by-step explanation:
For each boox any time a ball is placed, there are only two possible outcomes. Either the ball is put into the box, or it is not. The boxes are independent. So the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
200 balls placed in boxes:
This means that [tex]n = 200[/tex]
For each box, the ball has 1/100 probability of being put there:
This means that [tex]p = \frac{1}{100} = 0.01[/tex]
The probability of a box being empty:
This is P(X = 0).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{100,0}.(0.01)^{0}.(0.99)^{200} = 0.1340[/tex]
Let X denote the number of empty boxes at the end. What is the expected value of X?
Each box has a 0.1340 probability of being empty at the end.
There are 100 boxes.
So
0.1340*100 = 13.4
The expected value of X is 13.4.
What must be true regarding the distribution of the population? A. The population must be normally distributed and the sample size must be large. B. There are no requirements on the shape of the distribution of the population. C. The population must be normally distributed. nothing Your answer is correct.D. Since the sample size is large enough comma the population distribution does not nbsp need to be normal.
Answer:
C. The population must be normally distributed.
Step-by-step explanation:
Population distribution have to do with the classification of people living in a particular geographical area into different segment such as Age, Occupation, Sex, Geographical location.
For instance
If Age distribution is use, the total number of people living in say New york will classified into 0-10 11-19years 20-29years and so on
Sex distribution involves distribution into the male and Female Category
Occupation distribution of Population involves classification of occupant of an area according to their Job.. I.e.Drives-15 people, Lawyer =2 people and so on.
Geographical location distribution of population involves the classification of people living in a particular country according to their geographical names. I.e. Abuja=3.5million people etc.
The requirements on the distribution of the population can vary depending on the analytical methods being used. Some methods require the population to be normally distributed, while others, such as those based on the Central Limit Theorem, can work reliably with large sample sizes regardless of whether the population is normally distributed.
Explanation:In the field of statistics, when you are drawing conclusions or inferences from a dataset (sample), there are different requirements depending on the method used. Generally speaking, the assumption about the distribution of the population can vary.
For instance, if you are using methods based on the Central Limit Theorem (CLT), you might not require the population to be normal if your sample size is sufficiently large, as per option D. This is because the CLT states that if the sample size is large enough, the distribution of the sample means will approximate a normal distribution, regardless of the shape of the population distribution.
However, some analytical methods might require the population to be normally distributed for the method to produce reliable results. So, although there is not a one-size-fits-all answer, the requirements on the distribution of the population depend largely on the analytical methods being used.
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A study of the effect of exposure to color (red or blue) on the ability to solve puzzles used 42 subjects. Half the subjects (21) were asked to solve a series of puzzles while in a red-colored environment. The other half were asked to solve the same series of puzzles while in a blue-colored environment. The time taken to solve the puzzles was recorded for each subject. The 21 subjects in the red-colored environment had a mean time for solving the puzzles of 9.64 seconds with standard deviation 3.43; the 21 subjects in the blue-colored environment had a mean time of 15.84 seconds with standard deviation 8.65.
The two-sample t statistic for comparing the population means has value _____ (± 0.001).
Answer:
The two-sample t statistic for comparing the population means is -3.053.
Step-by-step explanation:
We are given that the time taken to solve the puzzles was recorded for each subject.
The 21 subjects in the red-colored environment had a mean time for solving the puzzles of 9.64 seconds with standard deviation 3.43; the 21 subjects in the blue-colored environment had a mean time of 15.84 seconds with standard deviation 8.65.
Let [tex]\mu_1[/tex] = average time taken to solve the puzzle in red-colored environment.
[tex]\mu_2[/tex] = average time taken to solve the puzzle in blue-colored environment.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex] {means that there is no difference in time taken to solve both the puzzles}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1\neq \mu_2[/tex] {means that there is difference in time taken to solve both the puzzles}
The test statistics that would be used here Two-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_-_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample average time for solving the puzzles in the red-colored environment = 9.64 seconds
[tex]\bar X_2[/tex] = sample average time for solving the puzzles in the blue-colored environment = 15.84 seconds
[tex]s_1[/tex] = sample standard deviation for red-colored environment = 3.43 seconds
[tex]s_2[/tex] = sample standard deviation for blue-colored environment = 8.65 seconds
[tex]n_1[/tex] = sample of subjects in the red-colored environment = 21
[tex]n_2[/tex] = sample of subjects in the blue-colored environment = 21
Also, [tex]s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(21-1)\times 3.43^{2}+(21-1)\times 8.65^{2} }{21+21-2} }[/tex] = 6.58
So, test statistics = [tex]\frac{(9.64-15.84)-(0)}{6.58 \sqrt{\frac{1}{21}+\frac{1}{21} } }[/tex] ~ [tex]t_4_0[/tex]
= -3.053
The value of two-sample t test statistics is -3.053.
A recent Gallup poll found that 36% of U.S. teens aged from 13 to 17 years old have a computer with [(6)] Internet access in their rooms. The poll was based on a random sample of 1028 teens. (a) In words, determine the population parameter, p, that this sample is estimating. [1] (b) Produce a 99% confidence interval for the population proportion, p, and interpret what it means in [3] this context. Round your answers to three decimals. (c) How big of a sample must we take in order to ensure that we are within 1% of the true proportion [2] with 99% confidence
Answer:
Step-by-step explanation:
a) The population parameter is the population proportion.
b) Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 1028
p = 36/100 = 0.36
q = 1 - 0.36 = 0.64
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.99 = 0.1
α/2 = 0.01/2 = 0.005
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.05 = 0.995
The z score corresponding to the area on the z table is 2.58. Thus, confidence level of 99% is 2.58
Therefore, the 99% confidence interval is
0.36 ± 2.58 × √(0.36)(0.64)/1028
The lower limit of the confidence interval is
0.36 - 0.039 = 0.321
The upper limit of the confidence interval is
0.36 + 0.039 = 0.399
Therefore, with 99% confidence interval, the proportion of U.S. teens aged from 13 to 17 years old that have a computer with Internet access in their rooms is between 0.321 and 0.399
c) for a margin of error of 1%, that is 1/100 = 0.01, then
0.01 = 2.58 × √(0.36)(0.64)/n
0.01/2.58 = √0.2304/n
0.00387596899 = √0.2304/n
Square both sides
0.00001502314 = 0.2304/n
n = 0.2304/0.00001502314
n = 15336
Mary made $1,850 last month. A 25% deduction was subtracted from her pay. What was her deduction?
Answer:$462.50
Step-by-step explanation:multiply $1,850 by .25 to get your answear
Which hypotheses are being tested by the chi-square test? The distribution of gender is different for the three different goals. The null hypothesis is that the most important goal is the same for each gender, and the alternative is that the means differ. The distribution of most important goals is different for men and women. The null hypothesis is that the most important goal and gender are independent, and the alternative is that they are dependent.
Answer:
The null hypothesis is that the most important goal and gender are independent, and the alternative is that they are dependent.
Step-by-step explanation:
Chi Square test is used to test relationship between categorical (nominal) variables of a population. Eg : Testing men & women for any attribute, lets say empathy
Null Hypothesis states that there is no relationship between the attribute & categorical variable, they are independent.Alternate Hypothesis states that there is relationship between the attribute & categorical variable, they are dependent.Eg : Null hypothesis states that there is no difference of empathy level in men & women. Alternate Hypothesis states that there is difference of empathy level in men & women.
A random sample of size 13 is selected from men with hypertension. For each person, systolic blood pressure was measured right before and one hour after taking the medicine. The mean reduction of the blood pressures was 10.1 and the standard deviation of the difference was 11.2. Test if there is sufficient evidence to conclude that the hypertension medicine lowered blood pressure. What is the value of the test statistic (round off to second decimal place)
Answer:
Yes, hypertension drugs lowers blood pressure.
Step-by-step explanation:
Claim: The hypertension medicine lowered blood pressure.
The null and alternative hypothesis is
H0:\mu_{d}\geq 0
H1:\mu_{d}< 0
Level of significance = 0.05
Sample size = n = 13
Sample mean of difference = \bar{d} = 10.1
Sample standard deviation of difference = s_{d} = 11.2
Test statistic is
t=\frac{\bar{d}}{s_{d}/\sqrt{n}}
t = ((10.1) / (11.2 /squre root of 13)) = 3.251
Degrees of freedom = n - 1 = 13 - 1 = 12
Critical value =2.179( Using t table)
Test statistic | t | > critical value we reject null hypothesis.
In Conclusion: The hypertension medicine lowered blood pressure
Triangle ABC has vertices at A(-5, 4), B(4, 1), and C(1, -8). Choose the terms below which correctly describe this triangle:
Answer:
An ISOSCELES TRIANGLE
Step-by-step explanation:
Given a triangle ABC with vertices at A(-5, 4), B(4, 1), and C(1, -8), to know the type of triangle this is, we need to find the three sides of the triangles by taking the distance between the points.
Distance between two points is expressed as:
D = √(x2-x1)²+(y2-y1)²
For side |AB|:
A(-5, 4) and B(4, 1)
|AB| = √(4-(-5))²+(1-4)²
|AB| = √9²+3²
|AB| = √90
For side |BC|
B(4, 1), and C(1, -8)
|BC| =√(1-4)²+(-8-1)²
|BC| = √3²+9²
|BC| = √90
For side |AC|:
A(-5, 4) and C(1, -8).
|AC| = √(1-(-5))²+(-8-4)²
|AC| = √6²+12²
|AC| = √36+144
|AC| = √180
Based on the distances, it is seen that side AB and BC are equal which shows that two sides of the triangle are equal. A triangle that has two of its sides to be equal is known as an ISOSCELES TRIANGLE. Therefore the term that correctly describes the triangle is an isosceles triangle.
Jesse has 252 inches of string how many yards of string does he have
Answer:
7 yards
Step-by-step explanation:
252/12=21 21/3=7
Todos los días, Luna utiliza 12 regaderas de medio litro para regar su jardín. ¿Cuántos litros de agua utiliza al día?
The question in English:
Every day Luna uses 12 half-liter watering cans to water her garden. How many liters of water does she use per day?
Answer:
Español:
Luna utiliza 6 litros de agua al día.
¡Espero que esto ayude!
English:
Luna uses 6 liters of water a day.
Hope this helps!
The amount water used by Luna is equivalent is 6 liters.
What is water?Water is a tiny molecule. It consists of three atoms : two of hydrogen and one of oxygen. Water molecules cling to each other because of a force called hydrogen bonding.
Given is that every day, Luna uses 12 half-liter watering cans to water her garden.
The amount water used by Luna is equivalent to -
A{w} = 1/2 x 12
A{w} = 6 liters
Therefore, the amount of water used by Luna is equivalent is 6 liters.
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{Question in english -
Every day, Luna uses 12 half-liter watering cans to water her garden. How many liters of water she use per day?}
How is the graph of y =(x-1)2 - 3 transformed to produce the graph of y = 5(X+4)??
The graph is translated left 5 units, compressed vertically by a factor of 5, and translated up 3 units.
The graph is stretched vertically by a factor of 3, translated left 5 units, and translated up 3 units
The graph is translated left 5 units, compressed horizontally by a factor of 2, and translated down 3 units
The graph is stretched horizontally by a factor of 2, translated left 5 units, and translated down 3 units
Answer:
The graph is translated left 5 units, compressed vertically by a factor of 5, and translated up 3 units.Step-by-step explanation:
The initial function is
[tex]y=(x-1)^{2} -3[/tex]
The transformed function is
[tex]y=5(x+4)^{2}[/tex]
Notice that the first function represents a parabola with vertex at (1, -3), and the secong function represents a parabola with vertex at (-4, 0). That means the function was shifted three units up and 5 units to the left. Additionally, the function was compressed by a scale factor of 5, because that's the coffecient of the quadratic term.
Therefore, the right answer is the first choice.
Answer:
A.
Step-by-step explanation:
The graph is translated left 5 units, compressed vertically by a factor of One-half, and translated up 3 units.
One conveyor belt can move 1000 boxes in 9 minutes. Another can move 1000 boxes in 11 minutes. If another conveyor belt is added and all three are used, the boxes are moved in 3 minutes. How long would it take the third conveyor belt alone to do the same job?
Answer:
It would take 7.62 minutes for the third conveyor belt alone to do the same job
Step-by-step explanation:
The together rate is the sum of each separate rate.
In this question:
First conveyor: Rate of 1/9.
Second: Rate of 1/11.
Third: Rate of 1/x.
Total: 1/3
So
[tex]\frac{1}{9} + \frac{1}{11} + \frac{1}{x} = \frac{1}{3}[/tex]
[tex]\frac{11x + 9x + 99}{99x} = \frac{1}{3}[/tex]
[tex]\frac{20x + 99}{99x} = \frac{1}{3}[/tex]
[tex]3(20x + 99) = 99x[/tex]
[tex]60x + 297 = 99x[/tex]
[tex]39x = 297[/tex]
[tex]x = \frac{297}{39}[/tex]
[tex]x = 7.62[/tex]
It would take 7.62 minutes for the third conveyor belt alone to do the same job
PLEASE HELP ME I WILL MARK BRAINLIEST!!!
Answer:
v= 205.3
Step-by-step explanation:
The formula to solve a pyramid is v=(l*h*w)/3.
11*7*8=616
616/3=205.333.... (repeating 3)
about 205.3
~sorry I couldn't draw it out~
Find the value of x
Answer:
x = 66
Step-by-step explanation:
The sum of the angles of a quadrilateral is 360 degrees
103+133+58+x = 360
Combine like terms
294+x = 360
Subtract 294 from each side
294+x-294 = 360-294
x = 66
Mr. Ramirez purchased 20 concert tickets for a total of $225. The concert tickets costs $15 for adults and $10 for children under the age of 12. Write the system of equations and solve algebraically.
Answer:
C = 15
Step-by-step explanation:
Let A = # of adults and C = # of children.
A + C = 20
15A + 10C = 225
There are several ways to solve this system; here is one of them.
From the first equation: C = 20 - A
Substitute into the second equation: 15A + 10(20 - A) = 225
Multiply, collect terms, and subtract 200 from each side: 5A = 25 => A = 5
Since C = 20 - A, C = 15
The number of children's ticket bought is 15 and the number of adult tickets bought is 5.
The system of equations that can be derived from the question are:
a + b = 20 equation 1
15a + 10b = 225 equation 2
Where:
a = number of children's ticket bought
b = number of adult tickets bought
In order to determine the value of b, multiply equation 1 by 15.
15a + 15b = 300 equation 3
Subtract equation 2 from 3
5b = 75
b = 15
In order to determine the value of a, substitute for b in equation 1
a + 15 = 20
a = 20 - 15
a = 5
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Order the numbers from least to greatest typical number of hours of sleep per employee
Answer:What?
Step-by-step explanation:
What is the volume of a prism with base 32inches squared and height of 8
Answer:
V =256 in^3
Step-by-step explanation:
The volume of a prism is given by
V = Bh where B is the area of a base and h is the height
V = 32 * 8
V =256 in^3
8 people share 1 pizza. How much each person receive ?
Answer:
1
Step-by-step explanation:
because one pizza is cut into 8 so
1 piece would be even
=1
The amount of pizza received by each person is 0.125.
What are arithmetic operations?The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.
The number of pizza is 1.
And, the total number of people is 8.
Now, the share of each people can be obtained as follows,
Consider that each people get the equal share.
The arithmetic operation used in this case is division.
Then, the problem can be solved by dividing 1 by 8 as follows,
⇒ 1 ÷ 8 = 1/8 = 0.125
The result of the division is a decimal number which shows that the amount of pizza for each people is the smallest part less than the whole.
Hence, the share of pizza received by each person is 0.125.
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what’s the value of x?
Answer:
D
Step-by-step explanation:
Answer:
x = 29.1m
Step-by-step explanation:
X= 71 x =
Y = y = 28.2 m
Z = z = 20.9 m
[tex]x^{2} = y^{2} + z^{2} - 2yz cos x\\(28.2 )^{2} + (20.9)^{2} - 2(28.2 )(20.9) cos (71)\\795.24 + 436.81 - 1178.76cos(71)\\1232.05 - 1178.76 cos (71)\\{1232.05-383.767}\\\\\sqrt{x^{2} } = \sqrt{1232.05 - 383.767}\\ x = 29.1[/tex]
A researcher has collected the following sample data. The mean of the sample below is 5.
3 , 5 , 12 , 3 , 2
Find the coefficient of variation
Answer:
The coefficient of variation is 72.66%
Step-by-step explanation:
Data : 3 , 5 , 12 , 3 , 2
We are given that The mean of the sample is 5.
Formula of standard deviation =[tex]\sigma = \sqrt{\frac{\sum(x-\bar{x})^2}{n}[/tex]
Substitute the values :
[tex]\sigma = \sqrt{\frac{(3-5)^2+(5-5)^2+(12-5)^2+(3-5)^2+(2-5)^2}{5}}=3.633[/tex]
Coefficient of variation=[tex]\frac{\sigma}{\mu} \times 100=\frac{3.633}{5} \times 100 =72.66\%[/tex]
Hence The coefficient of variation is 72.66%
The coefficient of variation of the data set, 3 , 5 , 12 , 3 , 2, is: 72.7%
Recall:
Coefficient of variation = Standard deviation / mean x 100%Given, the following data:
3 , 5 , 12 , 3 , 2Mean is given as: 5We are not given the standard deviation.
First, find the standard deviation of the data set, using the formula, [tex]\mathbf{SD = \sqrt{\frac{\sum (x - \bar{x}) }{n} } }[/tex]
Thus:SD = [tex]\sqrt{\frac{66}{5} } = \sqrt{13.2}[/tex]
SD = 3.633
Next, find the coefficient of variation:
Cov. = 3.633/5 x 100 = 72.7%
Therefore, the coefficient of variation of the data set, 3 , 5 , 12 , 3 , 2, is: 72.7%
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Consider the graph of the quadratic function y = 2(x + 3)2 – 3 with two real zeros. What number can be added to the right side of the equation to change it to a function with one real zero?.
Answer: 3
Step-by-step explanation:
Answer: I am pretty sure it is 3 but I apologize if it is incorrect.
Step-by-step explanation:
For every truck a police officer encounters she writes down T, for every car C, for every van V, and for every vehicle that is not a car, truck or van O (for "other"). Estimate the probability that the next vehicle the police officer encounters is not a car, truck, or van.
T T T C V O O V C T T C C C C C C V O
Answer:
5 = T
8 = C
3 = V
3 = O
which means its other because it said it is not a car, truck or van so its other meaning O
O = other
Answer: O
Step-by-step explanation: Theirs really nothing to it just pay attention to the hint :)
Answer:
3/19
Step-by-step explanation:
Gradpoint
An aquarium manager wants to study gift shop browsing. She randomly observes 120 couples that visit the aquarium with children and finds that 107 enter the gift shop at the end of their visit. She randomly observes 76 couples that visit the aquarium with no children and finds that 59 enter the gift shop at the end of their visit. Find the lower bound of the 95% confidence interval for the difference in population proportions of couples with children that enter the gift sho
Answer:
95% confidence interval for the difference in population proportions of couples with children and with no children is [0.00134 , 0.219].
Step-by-step explanation:
We are given that an aquarium manager wants to study gift shop browsing.
She randomly observes 120 couples that visit the aquarium with children and finds that 107 enter the gift shop at the end of their visit. She randomly observes 76 couples that visit the aquarium with no children and finds that 59 enter the gift shop at the end of their visit.
Firstly, the pivotal quantity for 95% confidence interval for the difference between population proportions is given by;
P.Q. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of couples that visit the aquarium with children who enters the gift shop at the end of their visit = [tex]\frac{107}{120}[/tex] = 0.89
[tex]\hat p_2[/tex] = sample proportion of couples that visit the aquarium with no children who enters the gift shop at the end of their visit = [tex]\frac{59}{76}[/tex] = 0.78
[tex]n_1[/tex] = sample of couples that visit the aquarium with children = 120
[tex]n_2[/tex] = sample of couples that visit the aquarium with no children = 76
Here for constructing 95% confidence interval we have used Two-sample z proportion statistics.
So, 95% confidence interval for the difference between population proportions, 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_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] < [tex]{(\hat p_1-\hat p_2)-(p_1-p_2)}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ) = 0.95
P( [tex](\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] < [tex](p_1-p_2)}[/tex] < [tex](\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ) = 0.95
95% confidence interval for [tex](p_1-p_2)}[/tex] =
[[tex](\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex],[tex](\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex]]
= [ [tex](0.89-0.78)-1.96 \times {\sqrt{\frac{0.89(1-0.89)}{120}+ \frac{0.78(1-0.78)}{76}} }[/tex] , [tex](0.89-0.78)+1.96 \times {\sqrt{\frac{0.89(1-0.89)}{120}+ \frac{0.78(1-0.78)}{76}} }[/tex] ]
= [0.00134 , 0.219]
Therefore, 95% confidence interval for the difference in population proportions of couples with children and with no children is [0.00134 , 0.219].
8300 dollars is placed in an account with an annual interest rate of 6.5%. How much
will be in the account after 14 years, to the nearest cent?
Answer:
(About) 20043.46 after 14 years
Step-by-step explanation:
~ Let us apply a compound interest formula not through substituting values, but through a similar way of following this formula ~
1. First let us assign the values:
interest ⇒ 6.5 percent ( % ), principle number - start value ⇒ $ 8300, time ⇒ 14 years
2. Now let us convert interest ⇒ decimal form: 0.065
3. Add 1 to this value 0.065 ⇒ 1 + 0.065 = 1.065
4. Now let us take 1.065 exponentially to the power of itself 14 times, or in other words to the power of time ( 14 years ): 1.065^ 14 = 2.414874185.......
5. Multiply this infinite number by the principle number P, or most commonly known as the start value: 2.414874185....... * 8300 ⇒
(About) 20043.46 after 14 years
Using the formula for compound interest and substituting accordingly, the given investment grows to approximately 18,108.80 dollars after 14 years.
Explanation:To solve this, we'll use the formula for compound interest, which is P(1 + r/n)^(nt), where P is the principle amount (initial investment), r is the annual interest rate, n is the number of times that interest is compounded per unit t, and t is the time the money is invested for.
In this case, P = 8300 dollars, r = 6.5/100 = 0.065 (we need the rate in decimal form), n = 1 (since the interest is given annually), and t = 14 years.
Substitute these values into the formula:
A = 8300(1 + 0.065/1)^(1*14) which simplifies to A = 8300(1.065)^14.
Using a calculator, A ≈ 18,108.80 dollars. So, after 14 years, the account will have approximately 18,108.80 dollars.
Learn more about Compound Interest here:https://brainly.com/question/14295570
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If g(x) = x square - 2x + 11, find g(-2)
Answer:
g(-2) = 19
Step-by-step explanation:
g(x) = x ^2 - 2x + 11,
Let x= -2
g(-2) = (-2)^2 -2(-2) +11
= 4 +4 +11
=19
Answer:
-2
Step-by-step explanation: