Answer:
J' = (-2, -4)
Step-by-step explanation:
It appears that point J is (-3, -6). The dilation by 2/3 about the origin causes each of these coordinates to be multiplied by 2/3:
J' = ((2/3)(-3), (2/3)(-6))
J' = (-2, -4)
Answer:
(-2, -4)
Step-by-step explanation:
J = (-3, -6)
J' = 2/3(-3, -6)
J' = (-2, -4)
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 18 Southwest flights and observing whether they arrive on time.
(a) Find the probability that at least 13 flights arrive late .
Answer:
The probability that at least 13 flights arrive late is 2.5196 [tex]\times 10^{-6}[/tex].
Step-by-step explanation:
We are given that Southwest Air had the best rate with 80 % of its flights arriving on time.
A test is conducted by randomly selecting 18 Southwest flights and observing whether they arrive on time.
The above situation can be represented through binomial distribution;
[tex]P(X = x) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.........[/tex]
where, n = number of trials (samples) taken = 18 Southwest flights
r = number of success = at least 13 flights arrive late
p = probability of success which in our question is probability that
flights arrive late, i.e. p = 1 - 0.80 = 20%
Let X = Number of flights that arrive late.
So, X ~ Binom(n = 18, p = 0.20)
Now, the probability that at least 13 flights arrive late is given by = P(X [tex]\geq[/tex] 13)
P(X [tex]\geq[/tex] 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18)
= [tex]\binom{18}{13}\times 0.20^{13} \times (1-0.20)^{18-13}+ \binom{18}{14}\times 0.20^{14} \times (1-0.20)^{18-14}+ \binom{18}{15}\times 0.20^{15} \times (1-0.20)^{18-15}+ \binom{18}{16}\times 0.20^{16} \times (1-0.20)^{18-16}+ \binom{18}{17}\times 0.20^{17} \times (1-0.20)^{18-17}+ \binom{18}{18}\times 0.20^{18} \times (1-0.20)^{18-18}[/tex]
= [tex]\binom{18}{13}\times 0.20^{13} \times 0.80^{5}+ \binom{18}{14}\times 0.20^{14} \times 0.80^{4}+ \binom{18}{15}\times 0.20^{15} \times 0.80^{3}+ \binom{18}{16}\times 0.20^{16} \times 0.80^{2}+ \binom{18}{17}\times 0.20^{17} \times 0.80^{1}+ \binom{18}{18}\times 0.20^{18} \times 0.80^{0}[/tex]
= 2.5196 [tex]\times 10^{-6}[/tex].
What is the solution to the system of equations
Answer:
Step-by-step explanation:
Hello
I believe there is an error in the question
we have two equations and need to find x and y
[tex](1) \dfrac{1}{4}x+\dfrac{1}{2}y=\dfrac{5}{8}\\(2) \dfrac{3}{4}x-\dfrac{1}{2}y=3\dfrac{3}{8}[/tex]
let s multiply by 8 so that we can get rid of the fractions
(1) becomes 2x+4y=5
(2) becomse 6x-4y=9
if we sum it gives
2x+4y+6x-4y=9+5
8x=14
x = 14/8 = 7/4
and then from the first equation
4y = 5 - 7/4
<=> 16y = 20-7 = 13
y = 13/16
the solutions is (7/4,13/16)
The average financial aid package for students admitted to a particular college five years ago was $49 comma 250. A student organization plans to investigate whether this average has changed for students admitted this year. Define the population parameter of interest and state the null and alternative hypotheses for this investigation.'
Answer:
The parameter of interest = the average financial aid package for students admitted μ.
Null hypothesis H0; μ = $49,250
Alternative hypothesis Ha; μ ≠ $49,250
Step-by-step explanation:
The population parameter of interest is the parameter in which the data is focused on. For the case above, the parameter of interest is the average financial aid package for students admitted.
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
Let μ represent the average financial aid package for students admitted given as $49,250.
The null hypothesis is that the average financial aid package for students admitted is equal to $49,250.
H0; μ = $49,250
The alternative hypothesis is that the average financial aid package for students admitted is not equal to $49,250.
Ha; μ ≠ $49,250
Assume Shelley Kate decides to take her social security at age 63. What amount of social security benefit will she receive each month, assuming she is entitled to $720 per month
She will receive a lot more money because she is already retired from work already and will win as bit more money
N is an element of the set {0.4, 0.5, 1.1, 2.0, 3.5}, and (4.9N)/1.4 is an integer. What is N?
Answer:
Step-by-step explanation:
if N=2.0
4.9 N=4.9×2=9.8
9.8/1.4=7
which is an integer.
so N=2.0
A trust fund eels is 6% simple interest divide into its members accounts every month if a member has $5000 in the funds account how much money would be in that account after three months
Answer:
$5073.37
Step-by-step explanation:
We can use the simple interest rate (appreciation) formula: A = P(1 + r)^t
Because it gives us 3 months, we need to put it in terms of years. That will give us 1/4 of a year:
A = 5000(1 + 0.06)^0.25
When you plug that into the calc, you should get 5073.37 as your final answer!
A
What is the factored form of the equation?
y = x2 – x-6
L
Previous Answer
(-2,0) and (3,0)
25
Answer:
[tex]y=(x+2)(x-3)[/tex]
Step-by-step explanation:
Given: [tex]y=x^2-x-6[/tex]
To find: a factored form of the given equation
Solution:
The equation [tex]y=ax^2+bx+c[/tex] can be written in factored form as [tex]y=a(x-r_1)(x-r_2)[/tex].
To find the x-intercepts, put [tex]y=0[/tex].
Graph of the equation [tex]y=a(x-r_1)(x-r_2)[/tex] represents a parabola.
[tex]y=x^2-x-6\\=x^2+(-1)x-6\\=x^2+(-3+2)x-6\\=x^2-3x+2x-6\\=x(x-3)+2(x-3)\\=(x+2)(x-3)\\\Rightarrow y=(x+2)(x-3)[/tex]
A candy bar and a piece of bubble gum together cost $1.10. The candy bar costs a dollar more than the bubble gum. How much does the candy bar cost, in dollars?
Answer:
$1.05
Step-by-step explanation:
Say the price of a piece of bubble gum is x. This means that we can represent our scenario with the equation (x+1)+x=1.10, with (x+1) representing the price of a candy bar. We can then solve from there.
(x+1)+x=1.10 - Given
2x+1=1.10 - Simplify
2x=0.10 - Subtract From Both Sides (sorry, I forgot the name of this property)
x=0.05 - Divide From Both Sides
So now we have the price of the piece of bubble gum, but we want the cost of the candy bar. Fortunately, we know it costs one dollar more than the piece of bubble gum, so just do 0.05 + 1. This means our candy bar costs $1.05.
The candy bar cost, in dollars, is $1.05
Say the price of a piece of bubble gum is x.
This means that we can represent our scenario with the equation (x+1)+x=1.10, with (x+1) representing the price of a candy bar.
We can then solve from there.
We have given that,
(x+1)+x=1.10
Simplify above expression
2x+1=1.10
2x=0.10 - Subtract From Both Sides
x=0.05 - Divide From Both Sides
So now we have the price of the piece of bubble gum, but we want the cost of the candy bar.
What is the cost?Cost is the value of money that a company had to spend to produce its goods or services.
Fortunately, we know it costs one dollar more than the piece of bubble gum, so just do 0.05 + 1. This means our candy bar costs $1.05.
To learn more about the cost visit:
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. Trisha walked
ofa mile to school.
She shaded a model to show how far
she had walked.
Which decimal shows how far Trisha
walked?
Answer:
b
Step-by-step explanation:
she walked for the first place in a while to be crying for a sec
Pythagorean triplet whose one member is 15
Answer:
8,15 and 17 are Pythagorean triplets,the Pythagorean triplets of 15 are: (15,112 and113),(15,8 and 17),(15,20 and 25),(15,9and 12),(15,36 and 39)
Answer:
(8, 15, 17); (9, 12, 15); (15; 20; 25)Step-by-step explanation:
If
[tex]a=m^2-n^2;\ b=2mn;\ c=m^2+n^2[/tex]
for m > n, then a, b, c make a Pythagorean triplet.
[tex]m^2-n^2=15\to(m-n)(m+n)=15\\\\(m-n)(m+n)=(3)(5)\to m-n=3\ \wedge\ m+n=5[/tex]
We have the system of equations:
[tex]\underline{+\left\{\begin{array}{ccc}m-n=3\\m+n=5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2m=8\qquad\text{divide both sides by 2}\\.\qquad\boxed{m=4}[/tex]
Substitute to the second equation:
[tex]4+n=5\qquad\text{subtract 4 from both sides}\\\boxed{n=1[/tex]
Therefore we have:
[tex]a=4^2-1^2=16-1=15\\b=2(4)(1)=8\\c=4^2+1^2=16+1=17[/tex]
[tex]2mn=15[/tex] it's impossible, because 15 is not an even number.
[tex]m^2+n^2=15[/tex]
Let's consider all possible sums of two numbers resulting in 15.
We will check which of the numbers are perfect squares.
1 + 14
2 + 13
3 + 12
4 + 11
5 + 10
6 + 9
7 + 8
(Bold not perfect squares)
There are no two perfect squares among the listed pairs of numbers.
Other:
15, 112, 113
We know the Egyptian triangle with sides of length 3, 4, 5.
By modifying this Pythagorean triplet by multiplying by 3 we get:
(3)(3) = 9; (3)(4) = 12; (3)(5) = 15
By modifying this Pythagorean triplet by multiplying by 5 we get:
(5)(3) = 15; (5)(4) = 20; (5)(5) = 25
Supplier claims that they are 95% confident that their products will be in the interval of 20.45 to 21.05 you take samples and find that the 95% confidence interval of what they are sending is 20.48 to 21.02 what conclusion can be made
Options:
The supplier products have a lower mean than claimed
The supplier is more accurate than they claimed
The supplier products have a higher mean than claimed
The supplier is less accurate than they have claimed
Answer:
The supplier is less accurate than they have claimed
Step-by-step explanation:
Confidence Interval for supplier claim, CI = (20.45, 21.05)
Confidence Interval for your claim, CI = (20.48, 21.02)
Calculate the mean of the Confidence Interval for the supplier's claim:
[tex]\bar{X_s} = \frac{20.45 + 21.05}{2} \\\bar{X_s} = \frac{41.50}{2}\\\bar{X_s} = 20.75[/tex]
Calculate the mean of the Confidence Interval for your claim :
[tex]\bar{X_y} = \frac{20.48 + 21.02}{2} \\\bar{X_y} = \frac{41.50}{2}\\\bar{X_y} = 20.75[/tex]
Both the supplier and you have the equal mean
Margin of Error by the supplier = 21.05 - 20.75 = 0.30
Margin of Error by you = 21.02 - 20.75 = 0.27
Since the margin of error for the supplier is more, you can conclude that the suppler is less accurate than they have claimed.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Supplier claims that they are 95% confident that their products will be in the interval of 20.45 to 21.05. You take samples and find that the 95% confidence interval of what they are sending is 20.48 to 21.02. What conclusion can be made?
The supplier products have a lower mean than claimed
The supplier is more accurate than they claimed
The supplier products have a higher mean than claimed
The supplier is less accurate than they have claimed
Answer:
The margin of error reported by the supplier is greater as compared to the actual margin of error. A greater margin of error results in less accuracy.
Therefore, we can conclude that the supplier is less accurate than they have claimed.
Step-by-step explanation:
Supplier claims that they are 95% confident that their products will be in the interval of 20.45 to 21.05.
The mean is given by
Mean = (Upper limit + Lower limit)/2
Mean = (21.05 + 20.45)/2
Mean = (41.50)/2
Mean = 20.75
The margin of error in this case is
MoE = Upper limit - Mean
MoE = 21.05 - 20.75
MoE = 0.30
You take samples and find that the 95% confidence interval of what they are sending is 20.48 to 21.02.
The mean is given by
Mean = (Upper limit + Lower limit)/2
Mean = (21.02 + 20.48)/2
Mean = (41.50)/2
Mean = 20.75
The margin of error in this case is
MoE = Upper limit - Mean
MoE = 21.02 - 20.75
MoE = 0.27
As you can notice the margin of error reported by the supplier is greater as compared to the actual margin of error. A greater margin of error results in less accuracy.
Therefore, we can conclude that the supplier is less accurate than they have claimed.
Simplify 12 5/8-74/5
Answer:
12x8+5=101/8
101/8-74/5
40/8=5
5x101=505
40/5=8
8x74=592
therefore 505/40-592/40=
-87/40=-2.175
Answer:
The correct answer would be 2.175
Step-by-step explanation:
i got it right :))
The perimeter of the shape is 28 cm. Find the value of radius.
Answer:
r = 4.2805cm
Step-by-step explanation:
ok first the shape its made of two slant height and and an arc of degree 70°
The total perimeter = 28cm
The formula for the total perimeter= 2l + 2πl(70/360)
Where l is the radius of the shape.
But l = 2r
So
= 2l + 1.2217l
= 3.2217l
28 = 3.2217l
l = 28/3.2217
l = 8.691
Recall that l = 2r
8.691= 2r
r = 8.691/2
r = 4.2805cm
Please help! Correct answer only, please! The following information matrices show how many of each vehicle type sold and the bonus amount each salesperson receives for selling that type of vehicle for the car dealership for the week. Which salesperson sold the most vehicle for the week described?A. Scott B. Each sold the same number of vehicles C. Kelly D. Mark
Answer: b) Each sold the same number of vehicles
Step-by-step explanation:
This question is only asking for the quantity of vehicles (not the total amount earned) so we can disregard the second matrix and find the sum of each row in the first matrix.
Kelly: 8 + 2 + 6 = 16
Scott: 7 + 8 + 1 = 16
Mark: 10 + 4 + 2 = 16
The total number of vehicles sold by each person is the same
The height of water in a bathtub ,h, is a function of time ,t, let p represent this function height is measured in inches and time in minutes
The complete question is;
The height of water in a bathtub,h, is a function of time,t. Let P represent this function. Height is measured in inches and time in minutes.
Match each statement in function notation with a description.
A: P(0) = 0
B: P(4) = 10
C: P(10) = 4
D: P(20) = 0
1:After 20 minutes, the bathtub is empty.
2:The bathtub starts out with no water.
3:After 10 minutes, the height of the water is 4 inches.
4:The height of the water is 10 inches after 4 minutes.
Answer:
-option D is the correct answer for sentence 1.
-option A is the correct answer for sentence 2.
-option C is the correct answer for sentence 3.
-option B is the correct answer for sentence 4
Step-by-step explanation:
The height of water in a bathtub h is a function of time t.
-If t = 20 minutes, then height of water represented by P is empty so, P(20) = 0. Thus, option D is the correct option for sentence 1.
-The bath tub starts out with no water. Thus, P(0) = 0. So option A is the correct option for sentence 2.
-After 10 minutes, the height of the water is 4 inches. Thus, P(10) = 4. So, option C is the correct option for sentence 3.
- The height of the water is 10 inches after 4 minutes. Thus, P(4) = 10. So option B is the correct answer for sentence 4
If Aizuddin borrowed RM 6.300 from a bank which offers an interest of 8%
compounded annually, find.
(a) the future value
(b) the amount of interest charged
Answer:
(a) The formula to calculate the amount of money (A) that Aizuddin must pay the bank after n years, with the original amount of borrowed money is 6300 RM, interest of 8%, compounded annually, is described as following:
A = principal x (1 + rate)^(time in year)
A = 6300 x (1 + 8/100)^n
(b) The amount of interest charged (AC) that Aizuddin must pay after n years:
AC = A - 6300
AC = 6300 x (1 + 8/100)^n - 6300
AC = 6300 x [(1 + 8/100)^n - 1]
Hope this helps!
The average of 12, 25 , 33 , and N is 120. Find N.
Answer:
So the formula for mean is you add up all of the numbers and divide by the number of numbers, that will give you the mean/average. So that means that (12+25+33+N)/4 = 120. We can simplify by first adding all of the numbers and multiplying both sides by 4 which will cancel out the four on the right side.
70+N/4 = 120
480 = 70+N
So then we subtract 70 from both sides. Then we get 410 = N.
The answer is
410 is Answerwork out the value of 7^2+4^3 divided by 2^5
113/32
Step-by-step explanation:
7 squared is 49, 4 cubed is 64, 2 to the 5th power is 32.
49 plus 64 is 113 divided by 32
3.53125
Step-by-step explanation:
7^2+4^3/2^5
= 49+64/32
= 113/32
= 3.53125
HELP ME PLEASE I DONT UNDERSTAND
Answer:
6.75
Step-by-step explanation:
divide 4.50 by 40 to find the cost per pencil
4.50 ÷ 40 = .1125
each pencil costs .1125 or 11.25 cents, keep the cost per pencil as .1125
then multiply .1125 by 60. because each pencil costs
.1125 and there are 60 pencils the answer is 6.75
In a class there are 30 boys and 10 girls. The ratio of boys to girls is
Given that -
Boys in a class = 30
Girls in a class = 10
Answer -
Ratio [tex] \implies \frac{30}{1 0} \\ [/tex]
[tex] \implies \frac{3}{1 } \\ [/tex]
Boys : Girls = 3 : 1 .
Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola. (Round your answers to the nearest hundredth.) y = 6 - x2
If one of the vertices on the x-axis is (x, 0), then the other vertex on the same axis is (-x, 0), so that the rectangle has base 2x. The other two vertices on the parabola are the points (x, 6 - x²) and (-x, 6 - x²), so the height of the rectangle is 6 - x².
Then the area of the rectangle is given by the function
[tex]A(x)=2x(6-x^2)=12x-2x^3[/tex]
Compute the critical points of A:
[tex]A'(x)=12-6x^2=0\implies x=\pm\sqrt2[/tex]
So the maximum area is obtained when the vertices are the points (-√2, 0), (√2, 0), (√2, 4), and (-√2, 4). This rectangle has base 2√2 and height 4, giving a maximum area of 8√2.
The maximum area is obtained when the vertices are the points
(-√2, 0), (√2, 0), (√2, 4), and (-√2, 4).
This rectangle has base 2√2 and height 4, giving a maximum area of 8√2.
The area of a rectangle is expressed as shown:
A = xy
x is the length of the rectangle
y is the width
Given that y = 6 - x²
If its other two vertices above the x-axis and lying on the parabola, hence
the length of the rectangle will be 2x
The area of the rectangle will be A = 2x(6-x²)
If the dimension of the rectangle is at the maximum, hence dA/dx=0
A = 12x - 2x³
dA/dx = 12 - 6x²
0 = 12 - 6x²
6x² = 12
x² = 12/6
x² = 2
x = ±√2
Hence the maximum area is obtained when the vertices are the points
(-√2, 0), (√2, 0), (√2, 4), and (-√2, 4).
This rectangle has base 2√2 and height 4, giving a maximum area of 8√2.
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What’s the correct answer for this question?
Answer
A. 18(3/4)π
Explanation
In the attached file
A bookstore charges $4 for shipping, no matter how many books you buy. Irena makes a graph showing the shipping cost for I to 5 books. She claims that the points she graphed lie on a line. Does her statement make sense? Explain
Answer:
Yes
Step-by-step explanation:
1 book = $4
2 books = 2*$4
3 books = 3*$4
4 books = 4*$4
5 books = 5*$4
This can be shown as: y=4x
y=ax+b is linear function, Irena is right
Fertilizer must be mixed with water in a 1:4 ratio. If you use 3
cups of fertilizer how much water do you need?
Answer:
12
Step-by-step explanation:
1:4 = 3:12
Answer:
12 cups of water
Step-by-step explanation:
The ratio of fertilizer is 1. To get to 3 you times it by 3. Therefore to find how much water you need you'd have to do the same to the other side of the ratio, times it by three. So it would be 3:12
Suppose a simple random sample of size n= 11 is obtained from a population with u = 62 and a = 14.
(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample me
(b) Assuming the normal model can be used, determine P(x < 65.8).
(c) Assuming the normal model can be used, determine P(x 2 64.2).
Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2).
(a) What must be true regarding the distribution of the population?
O A. Since the sample size is large enough, the population distribution does not
need to be normal.
B. The population must be normally distributed and the sample size must be large.
OC. The population must be normally distributed.
OD. There are no requirements on the shape of the distribution of the population.
Answer:
a) C. The population must be normally distributed.
b) P(x < 65.8) = 0.8159
c) P(x > 64.2) = 0.3015
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 62, \sigma = 14, n = 11, s = \frac{14}{\sqrt{11}} = 4.22[/tex]
(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample me
n < 30, so the distribution of the population must be normal.
The correct answer is:
C. The population must be normally distributed.
(b) Assuming the normal model can be used, determine P(x < 65.8).
This is the pvalue of Z when X = 65.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{65.8 - 62}{4.22}[/tex]
[tex]Z = 0.9[/tex]
[tex]Z = 0.9[/tex] has a pvalue of 0.8159.
So
P(x < 65.8) = 0.8159
(c) Assuming the normal model can be used, determine P(x > 64.2).
This is 1 subtracted by the pvalue of Z when X = 64.2. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{64.2 - 62}{4.22}[/tex]
[tex]Z = 0.52[/tex]
[tex]Z = 0.52[/tex] has a pvalue of 0.6985.
1 - 0.6985 = 0.3015
So
P(x > 64.2) = 0.3015
Each leg of a 45-45-90 triangle has a length of 6 units what is the length of its hypotenuse
Answer:
It's the option D
6 root 2 units
72/60
Write
in simplest form.
Answer:
[tex]1 \frac{1}{6}[/tex] or 6/5
Step-by-step explanation:
72/60
= 6/5
= 1 1/5
= 1.2 (in decimal)
Answer:
6/5
Step-by-step explanation:
Results of 99% confidence intervals are consistent with results of two-sided tests with which significance level? Explain the connection. A 99% confidence interval is consistent with a two-sided test with significance level alphaequals nothing because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval ▼ contains does not contain the value in the null hypothesis.
Answer:
Yes, they are consistent.
A 99% confidence interval is consistent with a two-sided test with significance level alpha=0.01 because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval does contains the value in the null hypothesis.
Step-by-step explanation:
Yes, they are consistent.
A 99% confidence interval is consistent with a two-sided test with significance level alpha=0.01 because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval does contains the value in the null hypothesis.
The critical values of the confidence level are equivalent to the critical values in the hypothesis test. In the case that the conclusion of the test is to not reject the null hypothesis, the test statistic falls within the acceptance region: its value is within the critical values of the two-sided test.
Then, it is also within the critical values of the confidence interval and the sample mean (or other measure) will be within the confidence interval bounds.
A recent survey indicated that the average amount spent for breakfast by business managers was $9.33 with a standard deviation of $0.24. It was felt that breakfasts on the East Coast were higher than $9.33. A sample of 81 business managers on the East Coast had an average breakfast cost of $9.41. At α=0.05, what is the test value?
Answer:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{9.41-9.33}{\frac{0.24}{\sqrt{81}}}=3[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=9.41[/tex] represent the sample mean
[tex]s=0.24[/tex] represent the sample standard deviation
[tex]n=81[/tex] sample size
[tex]\mu_o =9.33[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean is higher than 9.33, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 9.33[/tex]
Alternative hypothesis:[tex]\mu > 9.33[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{9.41-9.33}{\frac{0.24}{\sqrt{81}}}=3[/tex]
Stanford University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.5% of the 451 members of the 50 Plus Fitness Association died. We are interested in the proportion of people over 50 who ran and died in the same eight year period.
Construct a 97% confidence interval for the population proportion of people over 50 who ran and died in the same eight–year period.
Define the random variable in X and P in words.
Which distribution should you use in this problem?
Answer:
Step-by-step explanation:
a) 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 = 451
x = 1.5/100 × 451 = 7
p = 7/451 = 0.02
q = 1 - 0.02 = 0.98
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.97 = 0.1
α/2 = 0.01/2 = 0.03
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.03 = 0.97
The z score corresponding to the area on the z table is 2.17. Thus, Thus, the z score for a confidence level of 97% is 2.17
Therefore, the 97% confidence interval is
0.02 ± 2.17√(0.02)(0.98)/451
= 0.02 ± 0.014
b) x represents the number of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.
P represents the proportion of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.
The distribution that should be used is the normal distribution