The alternative hypothesis would state that the proportion of Republicans who favor a bill to make gun ownership easier is not equal to the proportion of Democrats who favor the same.
Explanation:The question was regarding how to construct an alternative hypothesis for a study on political beliefs and opinions on firearm ownership. In this case, the alternative hypothesis statement goes against the null hypothesis. The null hypothesis would be that there's no significant difference between the proportions of Republicans and Democrats that favor a bill making gun ownership easier. So, the alternative hypothesis can be written as: 'The proportion of Republicans (Group A) who favor a bill making it easier for someone to own a firearm is not equal to the proportion of Democrats (Group B) who favor the same.'
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The alternative hypothesis can be written as: H_A: The proportion of Republicans who favor a bill to make it easier for someone to own a firearm differs from the proportion of Democrats who favor the same.
Explanation:The alternative hypothesis can be written as:
HA: The proportion of Republicans who favor a bill to make it easier for someone to own a firearm differs from the proportion of Democrats who favor the same.
Alternatively, it can be written as:
HA: pA ≠ pB
where pA is the proportion of Republicans who favor the bill and pB is the proportion of Democrats who favor the bill.
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Aaron invested $4000 in an account that paid an interest rate r compounded quarterly. After 10 years he has $5809.81. The compound interest formula is A=P (1 +r/n)^nt, where P is the principal (the initial investment), A is the total amount of money (principal plus interest), r is the annual interest rate, t is the time in years, and n is the number of compounding periods per year.
a. Divide both sides of the formula by P and then use logarithms to rewrite the formula without an exponent. Show your work.
b. Using your answer for part a as a starting point, solve the compound interest formula for the interest rate, r.
c. Use your equation from part a to determine the interest rate.
Answer:A
Step-by-step explanation:
Answer:
3.73%
Step-by-step explanation:
The formula is
[tex]A=P(1+\frac{r}{n})^{tn}[/tex]
Here we are given that A= 5809.81 , P=4000 , t=10 years and n = 4 (compounded quaterly)
Now we have to substitute them in the formula
[tex]5809.81=4000(1+\frac{r}{4})^{40}[/tex]
[tex]\frac{5809.81}{4000}=(1+\frac{r}{4})^{40}[/tex]
[tex] (\frac{5809.81}{4000})^{\frac{1}{40}}=1+\frac{r}{4}[/tex]
[tex] (1.45)^{\frac{1}{40}}=1+\frac{r}{4}[/tex]
[tex]1.0093 = 1+\frac{r}{4}[/tex]
Subtracting 1 on both sides
[tex]0.0093=\frac{r}{4}[/tex]
[tex]r=0.0093*4[/tex]
r=0.03732
Rate is 3.73%
How do you find an equation of the sphere with center (4,3,5) and radius √6?
Answer:
[tex](x-4)^2+(y-3)^2+(x-5)^2=6[/tex]
Step-by-step explanation:
The the center of the sphere is given as (a,b,c) and the radius is r, then the equation of the sphere would be:
[tex](x-a)^2+(y-b)^2+(x-c)^2=r^2[/tex]
From the info, we can say:
a = 4
b = 3
c = 5
r = [tex]\sqrt{6}[/tex]
Plugging into formula we get the equation:
[tex](x-a)^2+(y-b)^2+(x-c)^2=r^2\\(x-4)^2+(y-3)^2+(x-5)^2=(\sqrt{6} )^{2} \\(x-4)^2+(y-3)^2+(x-5)^2=6[/tex]
Remember to use
Solve |P| > 3
{-3, 3}
{P|-3 < P < 3}
{P|P < -3 or P > 3}
Answer:
{P|P < -3 or P > 3}
Step-by-step explanation:
When we remove the absolute value bars, we take the positive value, and then flip the inequality and take the negative. Since the original equation is a greater than, we use the or
p > 3 or p < -3
Answer:
[tex]\large\boxed{\{P\ |\ P<-3\ or\ P>3\}}[/tex]
Step-by-step explanation:
[tex]\text{The absolute value:}\\\\|a|=\left\{\begin{array}{ccc}a&for&a\geq0\\-a&for&a<0\end{array}\right[/tex]
[tex]|P|>3\iff P>3\ or\ P<-3[/tex]
A quadratic equation is written in four equivalent forms below.
I. y = (x - 4)(x + 6)
II. y = x(x - 4) + 6(x - 4)
III. y = (x + 1)2 - 25
IV. y = x2 + 2x - 24
Which of the forms shown above would be the most useful if attempting to find the y-intercept of the quadratic equation?
find the area between y=e^x and y=e^2x over [0,1]
Answer:
Step-by-step explanation:
Just so you see what you are trying to do, the graph shows you what you are given.
Graph
Red: y = e^x
blue: y = e^(2x)
green x = 1
equations
integral e^(2*x) = e^(2x)/2
integral e^x = e^x
Solution
e^(2x)/2 between 1 and 0 equals e^(*2*1)/2 - e^0
e^(2x) / 2 = 7.3891 - 1 = 6.3891
e^(x ) between 1 and 0 equals e^(1) - e^0
2.7183 - 1
1.7183
The area between 1 and 0 is 6.3891 - 1.7183 = 4.6708
Find the root(s) of f (x) = (x- 6)2(x + 2)2.
Answer:
[tex]x_1 = -2[/tex].[tex]x_2 = 6[/tex].Assumption: [tex]f(x)[/tex] is defined for all [tex]x\in \mathbb{R}[/tex] (all real values of [tex]x[/tex].)
Step-by-step explanation:
Evaluating [tex]f(x)[/tex] for a root of this function shall give zero.
Equate [tex]f(x)[/tex] and zero [tex]0[/tex] to find the root(s) of [tex]f(x)[/tex].
[tex]f(x) =0[/tex].
[tex](x - 6) \cdot 2 \cdot (x + 2) \cdot 2 = 0[/tex].
Multiply both sides by 1/4:
[tex]\displaystyle (x - 6) \cdot (x + 2) = 0\times\frac{1}{4} = 0[/tex].
[tex]\displaystyle (x - 6) \cdot (x + 2) = 0[/tex].
This polynomial has two factors:
(x - 6), and(x + 2) = (x - (-2)).Apply the factor theorem:
The first root (from the factor (x - 6)) will be [tex]x = 6[/tex].The second root (from the factor (x - (-2)) will be [tex]x = -2[/tex].Answer:
X=6 , X = -2
Step-by-step explanation:
For any polynomial given in factorised form , the roots are determined as explained below:
Suppose we have a polynomial
(x-m)(x-n)(x+p)(x-q)
The roots of above polynomial will be m,n,-p, and q
Also if we have same factors more than once , there will be duplicate roots.
Example
(x-m)^2(x-n)(x+p)^2
For above polynomial
There will be total 5 roots . Out of which 2(m and -p) of them will be repeated. x=m , x=n , x =-p
Hence in our problem
The roots of f(x)= (x-6)^2(x+2)^2 are
x=6 And x=-2
Find the number of subsets of the set (4,5,6)
If a set [tex]A[/tex] contains [tex]n[/tex] elements, then the number of subsets of this set is [tex]|\mathcal{P}(A)|=2^n[/tex].
[tex]A=\{4,5,6\}\\|A|=3[/tex]
[tex]|\mathcal{P}(A)|=2^3=8[/tex]
Complete this sentence after a congruence transformation the area of a triangle would be
Answer:
"unchanged"
Step-by-step explanation:
Congruence transformations (translation, rotation, reflection) do not change lengths, angles, area (of 2D figures), or volume (of 3D figures). The area would remain unchanged.
One important distinguishing feature of valid arguments is that __________. if the premises are true then the conclusion must be false if the conclusion is false, then one or more of the premises must also have been false they are shorter than invalid arguments they reveal new and important information about natural phenomena
Answer:
If the conclusion is false, then one or more of the premises must also have been false.
Step-by-step explanation:
One important distinguishing feature of valid arguments is that - if the conclusion is false, then one or more of the premises must also have been false.
An argument form is said to be valid, if and only if, when all premises are true, then the conclusion is true.
A valid argument in philosophy is characterized by the fact that if its premises are true, the conclusion must also be true. This follows a process called deductive inference. It is impossible for the premises of a valid argument to be true and the conclusion to be false
Explanation:One distinguishing feature of valid arguments is that if the premises are true, then the conclusion must also be true. This follows a process called deductive inference. A premise in an argument is a statement or assumption that forms the basis for a conclusion. An argument is set to be valid when its structure or form guarantees the truth of the conclusion if the premises upon which it's built are true.
In a valid argument, therefore, the truth of its premises guarantees the truth of its conclusion-it's impossible for the premises to be true and the conclusion to be false at the same time.
If you can construct a scenario where the premises are true but the conclusion is false, then that argument is invalid. Understanding this concept is fundamental to the evaluation of arguments in logic, for it plays a critical role in ensuring coherent, reasonable and valid reasoning.
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Plot a rectangle with vertices (–1, –4), (–1, 6), (3, 6), and (3, –4).
What is the length of the base of the rectangle?
Answer: 4 units.
Step-by-step explanation:
Once each point is plotted, you get the rectangle attached.
You can observe in the figure that the base of the rectangle is its longer side.
Since the length of the base of the rectangle goes from [tex]x=-1[/tex] to [tex]x=3[/tex], you can say that the lenght of the base is the difference between 3 and -1.
So, you need to subtract this two coordinates, getting that the lenght of the base of the rectangle attached is:
[tex]lenght_{(base)}=3-(-1)\\\\lenght_{(base)}=3+1\\\\lenght_{(base)}=4\ units[/tex]
Answer: 4 units
Step-by-step explanation:
The distribution of scores in a exam has a normal distribution with a mean of 82 and a standard deviation of 13. What is the probability that a randomly selected score was less than 80? Enter your answer using decimal notation (and not percentages), and round your result to 2 significant places after the decimal (for example the probability of 0.1877 should be entered as 0.19)
Answer: 0.07
Step-by-step explanation:
Given: Mean : [tex]\mu = 82[/tex]
Standard deviation : [tex]\sigma = 13[/tex]
The formula to calculate z is given by :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 80
[tex]z=\dfrac{80-82}{13}=−0.15384615384\approx-1.5[/tex]
The P Value =[tex]P(z<-1.5)=0.0668072\approx0.07[/tex]
Hence, the probability that a randomly selected score was less than 80 =0.07
Peter applied to an accounting firm and a consulting firm. He knows that 30% of similarly qualified applicants receive job offers from the accounting firm, while only 20% of similarly qualified applicants receive job offers from the consulting firm. Assume that receiving an offer from one firm is independent of receiving an offer from the other. What is the probability that both firms offer Peter a job?
The probability that both firms offer Peter a job is 6%.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
let X be the probability that Peter would receive offer from the accounting firm.
and, Y be the probability that Peter would receive offer from the consulting firm.
We have P(X) = 30% and P(Y) = 20%.
Now we want to find P(X∪Y) = ?
We know that
P(A∩B) = P(A) × P(B
= 30% x 20%
= 0.30 x 0.20
= 0.06
= 6%
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To find the probability that both an accounting firm and a consulting firm offer Peter a job, we multiply the individual probabilities of him receiving an offer from each firm. This results in a 6% chance that Peter will receive job offers from both firms.
Explanation:The question asks about calculating the probability that Peter receives job offers from both an accounting firm and a consulting firm. Since the events are independent, the probability that both events occur is the product of their individual probabilities.
To compute the probability that both firms offer him a job, we multiply the probability of receiving an offer from the accounting firm (30%) by the probability of receiving an offer from the consulting firm (20%):
Probability(Both offers) = Probability(Accounting offer) times Probability(Consulting offer)
Probability(Both offers) = 0.30 times 0.20
Probability(Both offers) = 0.06 or 6%
Therefore, the probability that both firms offer Peter a job is 6%.
Is a product of two positive decimals, each less than 1, always less than each of the original decimals?
Answer with explanation:
Let me answer this question by taking two decimals less than 1.
A= 0.50
B= 0.25
→A × B
= 0.50 × 0.25
=0.125
It is less than both A and B.
→→A=0.99
B= 0.1
→C=A × B
= 0.99 × 0.1
=0.099
It is less than both A and B.
So, We can say with surety, that if take two decimals ,both less than 1, the product of these two decimals will be less than each of the original decimals.
General Rule
→A =0. p ,
→ B=0. 0 q,
Product of , A × B, gives a number in which there will be three digits after decimal which will be always less than both A and B as in A, there is one digit after decimal, and in B there are two digits after decimal.
Which of the following is NOT a property of the sampling distribution of the sample mean? Choose the correct answer below. A. The sample means target the value of the population mean. B. The expected value of the sample mean is equal to the population mean. C. The distribution of the sample mean tends to be skewed to the right or left. D. The mean of the sample means is the population mean.
Answer:
B. The expected value of the sample mean is equal to the population mean.
Step-by-step explanation:
The expected value of the sample mean is equal to the population mean is NOT a property of the sampling distribution of the sample.
This is about understanding properties of sampling distribution of sample mean.
Option A is not a Property of Sampling distribution of Sample mean.
Option A; The sample mean does not target the population mean because it is just an independent mean gotten from a sample of the population. This statement is not true.Option B; This statement is true because when we carry out sampling distribution of sample mean, the mean of all sample means is called expected value and this is equal to the population mean.Option C; This statement is true because there are two major skewness in distribution either to the left which is negative or the right which is positive.Option D; This statement is true for the same reason given in Option B above.Read more at; https://brainly.com/question/15201212
olve the equation of exponential decay. A company's value decreased by 11.2% from 2009 to 2010. Assume this continues. If the company had a value of $9,220,000 in 2009, write an equation for the value of the company t years after 2009.
Answer:
f(t)=9,220,000(0.888)^t
Step-by-step explanation:
We use 9,220,000 as our base because this is where the decay begins. To get the correct amount of decay, we need to subtract 11.2% from 1, or 100%. We get 88.8% so we turn this into a decimal by dividing by 100 and getting 0.888. We put this to the power of t to represent the decay because it has to be an exponent to be exponential decay, not linear decay. f(t) is not necessary, you could also use y. Hope this helps :)
A basketball player has two foul shots (free throw), if he is a 90% free throw shooter. What is the probability that he will make 2 of 2?
Step-by-step explanation:
The probability he makes both shots is:
P = (0.90)^2
P = 0.81
There's a 81% probability he makes both shots.
Atool set has been discounted down to a price of R412.00. If the discount given was 3) 21%, how much was the toolset before the discount was applied?
The cost of toolset before the discount was applied is:
Rs. 521.5189
Step-by-step explanation:It is given that:
A tool set has been discounted down to a price of Rs 412.00.
The percent discount that is provided to us is: 21%
Let the actual price of toolset be: Rs. x
This means that:
[tex]x-21\%\ of x=412\\\\i.e.\\\\x-0.21x=412\\\\i.e.\\\\(1-0.21)x=412\\\\i.e.\\\\0.79x=412\\\\i.e.\\\\x=\dfrac{412}{0.79}\\\\x=521.5189[/tex]
Hence, the actual price of toolset i.e. cost before discount is:
Rs. 521.5189
To find the original price of the toolset before the discount was applied, we can set up an equation and solve for the original price. The original price of the toolset was R520.89.
Explanation:To find the original price of the toolbox, we need to first calculate the amount of the discount. The discount given is 21%. Let's say the original price of the toolbox is P. We can calculate the amount of the discount by multiplying the original price by the discount percentage:
Discount = P * 21% = P * 0.21
The discounted price is given as R412.00. So we can set up the equation:
Original price - Discount = Discounted price
P - P * 0.21 = R412.00
We can now solve for P:
P(1 - 0.21) = R412.00
0.79P = R412.00
P = R412.00 / 0.79
P = R520.89
Therefore, the original price of the toolset before the discount was applied was R520.89.
f. A fair coin is thrown in the air four times. If the coin lands with the head up on the first three tosses, what is the probability that the coin will land with the head up on the fourth toss? a. 0 b. 1/16 c. 1/8 d. 1/2
Answer:
D. 1/2
Step-by-step explanation:
Coin tosses are independent. Past results don't affect future probabilities. So the probability of getting heads on the fourth toss is still 1/2.
Answer:
D. 1/2
Step-by-step explanation:
Flipping coin is an INDEPENDENT event, meaning that if you flip a coin before, it is NOT going to affect the outcome of the next coin flipping
Since a coin has 2 sides, so the probability is 1/2
A study studied the birth weights of 1,600 babies born in the United States. The mean weight was 3234 grams with a standard deviation of 871 grams. Assume that birth weight data are approximately bell-shaped. Estimate the number of newborns who weighed between 1492 grams and 4976 grams. Write only a number as your answer. Round your answer to the nearest whole number. Hint: Use the empirical rule. Answer:
Answer: 1527
Step-by-step explanation:
Given: Mean : [tex]\mu = 3234\text{ grams}[/tex]
Standard deviation : [tex]\sigma=871\text{ grams}/tex]
Sample size : [tex]n=1600[/tex]
The formula to calculate the z score is given by :-
[tex]z=\dfrac{X-\mu}{\sigma}[/tex]
For X=1492
[tex]z=\dfrac{1492-3234}{871}=-2[/tex]
The p-value of z =[tex]P(z<-2)=0.0227501[/tex]
For X=4976
[tex]z=\dfrac{4976-3234}{871}=2[/tex]
The p-value of z =[tex]P(z<2)=0.9772498[/tex]
Now, the probability of the newborns weighed between 1492 grams and 4976 grams is given by :-
[tex]P(1492<X<4976)=P(X<4976)-P(X<1492)\\\\=P(z<2)-P(z<-2)\\\\=0.9772498-0.0227501\\\\=0.9544997[/tex]
Now, the number newborns who weighed between 1492 grams and 4976 grams will be :-
[tex]1600\times0.9544997=1527.19952\approx1527[/tex]
15. A certain guy has six shirts, 7 pairs of pants, and 5 pairs of shoes. All of these are color coordinated, meaning any shirts goes with any shoes and pants. If decides to wear a different outfit consisting of the three items each day, how many days will go by before he repeats the same outfit
[tex]6\cdot7\cdot5=210[/tex]
210 days
Suppose that events E and F are independent, P(E)equals=0.40.4, and P(F)equals=0.90.9. What is the Upper P left parenthesis Upper E and Upper F right parenthesisP(E and F)?
Answer:
The probability of E and F is 0.367236 ≅ 0.367
Step-by-step explanation:
* Lets study the meaning independent probability
- Two events are independent if the result of the second event is not
affected by the result of the first event
- If A and B are independent events, the probability of both events
is the product of the probabilities of the both events
- P (A and B) = P(A) · P(B)
* Lets solve the question
- There are two events E and F
- E and F are independent
- P(E) = 0.404
- P(F) = 0.909
∵ Events E and F are independent
- To find P(E and F) find the product of P(E) and P(F)
∴ P (E and F) = P(E) · P(F)
∵ P(E) = 0.404
∵ P(F) = 0.909
∴ P(E and F) = (0.404) · (0.909) = 0.367236 ≅ 0.367
* The probability of E and F is 0.367236 ≅ 0.367
the probability that both event E and event F occur is 0.36.
When dealing with independent events, the probability of both events E and F occurring, denoted as P(E and F), is determined by multiplying the probability of event E by the probability of event F. In this case, since P(E)=0.4 and P(F)=0.9 and the events are independent, you calculate P(E and F) as follows:
P(E and F) = P(E) × P(F) = 0.4 × 0.9 = 0.36.
Therefore, the probability that both event E and event F occur is 0.36.
For which function is the domain -6 ≤ x ≤ -1 not appropriate?
Answer it right pls, thanks
Answer:
The last option is correct
Step-by-step explanation:
Hope this helps!
A single card is drawn form a standard 52 card deck. Let D be the event that the card drawn is red., and let F be the event that the card drawn is a face card. Find the indicated probabilities 1. P (D' U F')
Hence, the probability is:
0.8846
Step-by-step explanation:D be the event that the card drawn is red.
and F denote the event that the card drawn is a face card.
We are asked to find:
P(D'∪F')
We know that D' denote the complement of event D
and F' denote the complement of event F.
Hence, we have:
[tex]P(D'\bigcup F')=(P(D\bigcap F))'\\\\i.e.\\\\P(D'\bigcup F')=1-P(D\bigcap F)[/tex]
D∩F denote the event that the card is a red card and is a face card as well
Since there are 6 cards which are face as well as red cards out of a total of 52 cards.
Hence, we get:
[tex]P(D'\bigcup F')=1-\dfrac{6}{52}\\\\i.e.\\\\P(D'\bigcup F')=\dfrac{52-6}{52}\\\\i.e.\\\\P(D'\bigcup F')=\dfrac{46}{52}\\\\P(D'\bigcup F')=0.8846[/tex]
There are 11 candidates for three postions at a restaraunt. One postion is for a cook. The second position is for a food server The third position is for a cashier If all 11 candidates are equally qualfied for the theee positions, in how many diflerent ways can the three postions be Sted? diferent ways to fil the three posilions There ate 19 pm Emer your anwer in the atcwer box Cameten Netecr Desitu La-rie Kensington 8 c 5 3 Eng PuD Eter
Answer:
165 combinations possible
Step-by-step explanation:
This is a combination problem as opposed to a permutation, because the order in which we fill these positions is not important. We are merely looking for how many ways each of these 11 people can be rearranged and matched up with different candidates, each in a different position each time. The formula can be filled in as follows:
₁₁C₃ = [tex]\frac{11!}{3!(11-3)!}[/tex]
which simplifies to
₁₁C₃ = [tex]\frac{11*10*9*8!}{3*2*1(8!)}[/tex]
The factorial of 8 will cancel out in the numerator and the denominator, leaving you with
₁₁C₃ = [tex]\frac{990}{6}[/tex]
which is 165
In the figure, AB∥CD. Find x and y.
Answer:
y=131°
x=53°
Step-by-step explanation:
∠ ABD and ∠ BDC are supplementary.
The sum of the supplementary angles =180 °
thus y-4+x=180...........i
x and 37° are complementary, that is, they add up to 90°
Thus, x=90-37=53°
Using this value in equation 1 we obtain:
y-4°+53° =180°
y= 180°-53°+4°
y=131°
Answer:
x = 53°
y = 131°
Step-by-step explanation:
From the figure we can see a right angled triangle.
AB∥CD
To find the value of x and y
Consider the large triangle, by using angle sum property we can write,
90 + 37 + x = 180
127 + x = 180
x = 180 - 127
x = 53°
Since AB∥CD and BD is a traversal on these parallel lines.
Therefore <ABD and < CDB are supplementary
we have x = 53°,
x + (y - 4) = 180
53 + y - 4 = 180
y = 180 - 49 = 131°
y = 131°
Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation 0.070 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g. What percentage of legal quarters will be rejected? Round your answer to two decimal places.
Answer:
1.94%
Step-by-step explanation:
The desired percentage can be found using an appropriate calculator or spreadsheet. A nice on-line calculator is shown in the attachment.
Application 11. Dasha took out a loan of $500 in oeder to buy the # 1 selling book in the world, "Math, What is it Good For?" by Smart E. Pants. She plans to pay back this loanin 30 months. The loan will collect simple interest at 6.5% per year. How much will Dasha have to pay back at the end of this time? What is the accumulated interest? [3 marks]
Answer:
[tex]\boxed{\text{\$581.25; \$81.25}}[/tex]
Step-by-step explanation:
The formula for the total accrued amount is
A = P(1 + rt)
Data:
P = $500
r = 6.5 % = 0.065
t = 30 mo
Calculations:
(a) Convert months to years
t = 30 mo × (1 yr/12 mo) = 2.5 yr
(b) Calculate the accrued amount
A = 500(1 + 0.065 × 2.5)
= 500(1 + 0.1625)
= 500 × 1.1625
= 581.25
[tex]\text{Dasha will have to pay back }\boxed{\textbf{\$581.25}}[/tex]
(c) Calculate the accumulated interest
[tex]\begin{array}{rcl}A & = & P + I\\581.25 & = & 500 + I\\I & = & 81.25\\\end{array}\\\text{The accumulated interest is }\boxed{\textbf{\$81.25}}[/tex]
In a survey, 11 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $46 and standard deviation of $14. Construct a confidence interval at a 90% confidence level.
Answer:
The population standard deviation is not known.
90% Confidence interval by T₁₀-distribution: (38.3, 53.7).
Step-by-step explanation:
The "standard deviation" of $14 comes from a survey. In other words, the true population standard deviation is not known, and the $14 here is an estimate. Thus, find the confidence interval with the Student t-distribution. The sample size is 11. The degree of freedom is thus [tex]11 - 1 = 10[/tex].
Start by finding 1/2 the width of this confidence interval. The confidence level of this interval is 90%. In other words, the area under the bell curve within this interval is 0.90. However, this curve is symmetric. As a result,
The area to the left of the lower end of the interval shall be [tex]1/2 \cdot (1 - 0.90)= 0.05[/tex].The area to the left of the upper end of the interval shall be [tex]0.05 + 0.90 = 0.95[/tex].Look up the t-score of the upper end on an inverse t-table. Focus on the entry with
a degree of freedom of 10, and a cumulative probability of 0.95.[tex]t \approx 1.812[/tex].
This value can also be found with technology.
The formula for 1/2 the width of a confidence interval where standard deviation is unknown (only an estimate) is:
[tex]\displaystyle t \cdot \frac{s_{n-1}}{\sqrt{n}}[/tex],
where
[tex]t[/tex] is the t-score at the upper end of the interval, [tex]s_{n-1}[/tex] is the unbiased estimate for the standard deviation, and[tex]n[/tex] is the sample size.For this confidence interval:
[tex]t \approx 1.812[/tex],[tex]s_{n-1} = 14[/tex], and[tex]n = 11[/tex].Hence the width of the 90% confidence interval is
[tex]\displaystyle 1.812 \times \frac{14}{\sqrt{10}} \approx 7.65[/tex].
The confidence interval is centered at the unbiased estimate of the population mean. The 90% confidence interval will be approximately:
[tex](38.3, 53.7)[/tex].
Which choice correctly compares four-sevenths and six-ninths?
Answer:
4/7 < 6/9. Hope this helps
Kobe has collected 750 football cards and 660 baseball cards. He wants to divide them into piles so that each pile has only one type of card, there is the same number of cards in each pile, and each pile has the greatest possible number of cards. How many cards will be in each pile?
Answer: 30 cards
Step-by-step explanation:
To find the greatest possible number of cards in each pile such that there is the same number of cards in each pile we need to find the greatest common factor of 750 and 660.
Using Euclid division method , we have
[tex]750=1(660)+90\\\\660=7(90)+30\\\\90=3(30)+0[/tex]
Hence, the greatest common factor of 750 and 660 = 30
Thus, there will be 30 cards in each pile.