Answer:
Hospital A is less likely to record an average birth weight of at least 3400 g.
Step-by-step explanation:
Applying the Central Limit Theorem and the normal probability distribution.
Normal probability distribution
Problems of normally distributed samples are solved using 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 [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Applying the Central Limit Theorem to find the z-score.
[tex]Z = \frac{X - \mu}{\sigma} = \frac{X - \mu}{\frac{s}{\sqrt{n}}[/tex]
Probability of an average birth weight of at least 3400 g?
This probability is 1 subtracted by the pvalue of Z when X = 3400.
Mean is 3100, so [tex]\mu = 3100[/tex]
Suppose s is the same for both.
Hospital A:
n = 50. So
[tex]Z = \frac{X - \mu}{\frac{s}{\sqrt{n}}[/tex]
[tex]Z = \frac{3400 - 3100}{\frac{s}{\sqrt{50}}[/tex]
[tex]Z = \frac{300\sqrt{50}}{s}[/tex]
Hospital B:
n = 10. So
[tex]Z = \frac{X - \mu}{\frac{s}{\sqrt{n}}[/tex]
[tex]Z = \frac{3400 - 3100}{\frac{s}{\sqrt{10}}[/tex]
[tex]Z = \frac{300\sqrt{10}}{s}[/tex]
Comparasion:
[tex]\frac{300\sqrt{50}}{s} > \frac{300\sqrt{10}}{s}[/tex]
This means that hospital A has the higher z-score.
The higher the z-score, the higher the pvalue.
So, for A, 1 subtracted by the pvalue of Z when give a lower value than the 1 subtracted by the pvalue of Z in b. This means that hospital A is less likely to record an average birth weight of at least 3400 g.
A firm’s marketing manager believes that total sales for next year will follow the normal distribution, with a mean of $3.2 million and a standard deviation of $250,000. Determine the sales level that has only a 3% chance of being exceeded next year.
Answer:
The sales level that has only a 3% chance of being exceeded next year is $3.67 million.
Step-by-step explanation:
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.
In this question, we have that:
In millions of dollars,
[tex]\mu = 3.2, \sigma = 0.25[/tex]
Determine the sales level that has only a 3% chance of being exceeded next year.
This is the 100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So X when Z = 1.88.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.88 = \frac{X - 3.2}{0.25}[/tex]
[tex]X - 3.2 = 0.25*1.88[/tex]
[tex]X = 3.67[/tex]
The sales level that has only a 3% chance of being exceeded next year is $3.67 million.
Answer: $3,670,198
Step-by-step explanation:
Here, the mean, μ, is 3.2 million =3,200,000 and the standard deviation, σ, is 250,000. Let x be sales for next year. To determine the sales level that has only a 3% chance of being exceeded next year, the area to the right of x is 0.03. So the area to the left of x is 1−0.03=0.97.
Open Excel. Click on an empty cell. Type =NORM.INV(0.97,3200000,250000) and press ENTER.
Round the answer to the nearest dollar, is x≈3,670,198. Thus, the sales level that has only a 3% chance of being exceeded next year is $3,670,198.
Please answer this correctly without making mistakes
Answer:
140.4 yards squared
Step-by-step explanation:
Given the sequence rn defined recursively below, find r4.
r1=2
rn=4rn−1−3
Answer:
[tex]r_4 = 65[/tex]
Step-by-step explanation:
Given
[tex]r_1 = 2[/tex]
[tex]r_n = 4r_{n-1} - 3[/tex]
Required
Find [tex]r_4[/tex]
Calculating the value of [tex]r_4[/tex]
This means n = 4;
Hence,
[tex]r_n = 4r_{n-1} - 3[/tex]
[tex]r_4 = 4r_{4-1} - 3[/tex]
[tex]r_4 = 4r_3 - 3[/tex]
At this point, we need to solve for [tex]r_3[/tex];
Taking n as 3
[tex]r_n = 4r_{n-1} - 3[/tex]
[tex]r_3 = 4r_{3-1} - 3[/tex]
[tex]r_3 = 4r_2 - 3[/tex]
At this point, we need to solve for [tex]r_2[/tex];
Taking n as 2
[tex]r_n = 4r_{n-1} - 3[/tex]
[tex]r_2 = 4r_{2-1} - 3[/tex]
[tex]r_2 = 4r_1 - 3[/tex]
Substitute 2 for [tex]r_1[/tex]
[tex]r_2 = 4 * 2 - 3[/tex]
[tex]r_2 = 8 - 3[/tex]
[tex]r_2 = 5[/tex]
Solving for [tex]r_3[/tex]
Substitute 5 for [tex]r_2[/tex]
[tex]r_3 = 4 * 5 - 3[/tex]
[tex]r_3 = 20 - 3[/tex]
[tex]r_3 = 17[/tex]
Solving for [tex]r_4[/tex]
Substitute 17 for [tex]r_3[/tex]
[tex]r_4 = 4 * 17 - 3[/tex]
[tex]r_4 = 68 - 3[/tex]
[tex]r_4 = 65[/tex]
Hence, [tex]r_4 = 65[/tex]
Use the quadratic formula to solve the equation.
4x^2−10x+5=0
Quadratic formula:
[tex]x=\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]
What do we have:
a=4
b=-10
c=5
Substitude:
[tex]x=\frac{10±\sqrt{b^{2}-4(4)(5)}}{2(a)}[/tex]
Solve:
[tex]x=\frac{10±\sqrt{(-10)^{2}-4(4)(5)}}{2(4)}\\\\x=\frac{10±\sqrt{100-4(20)}}{8}\\\\x=\frac{10±\sqrt{100-4(20)}}{8}\\\\x=\frac{10±\sqrt{100-80}}{8}\\\\x=\frac{10±\sqrt{20}}{8}\\\\x=\frac{10±2\sqrt{5 }}{8}\\\\x=\frac{2(±5\sqrt{5) }}{2(4)}[/tex]
Cancel the common terms:
[tex]x=\frac{5±\sqrt{5} }{4}[/tex]
A town has a population of 18000 and grows at 2% every year. What will be the population after 12 years, to the nearest whole number?
Answer:
Step-by-step explanation:
A=18000(1+0.02)^11
A=22,380.74
Answer:
y≈22828
Step-by-step explanation:
If AD= 2 and DC= 8, find BD 8 6 4
Answer:
[tex]BD= 4[/tex]
Answer:
BD would equal 4
Step-by-step explanation:
A rectangle on a coordinate plane has vertices L(0.6), M3, 6), N80), and O(0, 0) What are the dimensions of the
rectangle?
O
• The base is 6 and the height is 8
• The base is 8 and the height is 6
• The base is 6 and the height is 6
• The base is 8 and the height is 8
Answer:
• The base is 8 and the height is 6
Step-by-step explanation:
A rectangle has two dimensions:
The base, which is the distance between the points who have the same value of y.
The height, which is the distance between the points who have the same value of x.
Distance between 2 points:
Points (a,b) and (c,d).
[tex]D = \sqrt{(c-a)^{2} + (d-b)^{2}}[/tex]
I suppose there was a small typing mistake, as these points do not make a rectangle.
I will say that we have these following points:
L(0,6), M(8,6), N(8,0), O(0,0).
Base:
Same value of y.
L(0,6), M(8,6), or N(8,0) and O(0,0).
They will have the same result, will use the second.
[tex]D = \sqrt{(8-0)^{2} + (0-0)^{2}} = \sqrt{64} = 8[/tex]
The base is 8.
Height:
Same value of x.
L(0,6), O(0,0) or M(8,6) and N(8,0).
[tex]D = \sqrt{(8-8)^{2} + (6-0)^{2}} = \sqrt{36} = 6[/tex]
The height is 6.
So the correct answer is:
• The base is 8 and the height is 6
find the 4th term (x-y)^12
Answer:
The fourth term of the expansion is -220 * x^9 * y^3
Step-by-step explanation:
Question:
Find the fourth term in (x-y)^12
Solution:
Notation: "n choose k", or combination of k objects from n objects,
C(n,k) = n! / ( k! (n-k)! )
For example, C(12,4) = 12! / (4! 8!) = 495
Using the binomial expansion formula
(a+b)^n
= C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + C(n,3)a^(n-3)b^3 + C(n,4)a^(n-4)b^4 +....+C(n,n)b^n
For (x-y)^12, n=12, k=3, a=x, b=-y, and the fourth term is
C(n,3)a^(n-3)b^3
=C(12,3) * x^(12-3) * (-y)^(3)
= 220*x^9*(-y)^3
= -220 * x^9 * y^3
The fourth term in the binomial expansion of ( x - y )¹² is given by the equation A₄ = -220 x⁹y³
What is Binomial Expansion?The general term of the binomial expansion is Tr+1 = nCr x^n-r y^r . Here the coefficient values are found from the pascals triangle or using the combinations formula, and the sum of the exponents of both the terms in the general term is equal to n.
( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ
Given data ,
Let the binomial expansion be represented as A
Now , the value of A is
A = ( x - y )¹² be equation (1)
On simplifying the equation , we get
The fourth term of the binomial expansion is calculated by
A₄ = ⁿC₃ a⁽ⁿ⁻³⁾ b³
Substituting the values in the equation , we get
A₄ = ¹²C₃ x⁽¹²⁻³⁾ ( -y )³
On further simplification , we get
A₄ = ( 12 )! / ( 9 )! 3! x⁹ ( -y )³
A₄ = 12 x 11 x 10 / 2 x 3 x⁹ ( -y) ³
A₄ = -220 x⁹y³
Hence , the fourth term of binomial expansion is -220 x⁹y³
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The statement the sum of x and 7% of x is at least 30"
Answer:
x + 0.07x ≥ 30
Step-by-step explanation:
A sum is terms separated by a plus sign.
"Is at least" means "is greater than or equal to."
7% as a decimal fraction is 0.07.
"Of" means "times."
__
In consideration of the above, you have ...
x plus 7% of x is at least 30
x + 0.07x ≥ 30 . . . . . using math symbols
find the value of x in 3x=3
Answer:
the value of x is x=1
Step-by-step explanation:
3x=3
x=3÷3
x=1
1.
Step-by-step explanation:
Which expression is equivalent to 3 sqrt x^10
Answer:
its D on ed
Step-by-step explanation:
3 sqrt x^9 * x
The expression is [tex]x^{10/3}[/tex]
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
∛[tex]x^{10}[/tex]
This can be written as,
= [tex]x^{10/3}[/tex]
Thus,
The expression is [tex]x^{10/3}[/tex]
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f (x) = (x - 6)2(x + 2)2
Answer:
Step-by-step explana[tex]f(x) = (x^{2} - 6x + 36) . (x^{2} + 2x + 4)\\f (x) = (x^{4} + 2x^{3} + 4x^{2} - 6x^{3} - 12x^{2} - 24x + 36x^{2} + 72x + 144)\\f(x) = (x^{4} - 4x^{3} + 28x^{2} + 48x + 144)[/tex]
x=6 and x=-2 are the roots of the equation f(x)= (x - 6)²(x + 2)².
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
We need to find the roots of f(x) = (x - 6)²(x + 2)²
f(x)= (x - 6)²(x + 2)²
f of x equal to x minus six whole power six into x plus two whole square
=(x²+36-12x)(x²+4+4x)
Apply distributive law.
=x⁴+4x²+4x³+36x²+144+144x-12x³-48x-48x²
=x⁴-8x³-8x²+96x+144
Hence, x=6 and x=-2 are the roots of the equation f(x)= (x - 6)²(x + 2)².
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Find the values of a b and c in the table
Answer: use google calculator It’s reliable
Step-by-step explanation:
Answer: a=1, b=2, c=below x
Step-by-step explanation:
A farmer needs to put in a fence in their rectangular field. If we look at the field from above, the cost of the west and east sides are $10/ft, the cost of the south side is $2/ft and the cost of the north side is $7/ft. If we have $700, use optimization to determine the dimensions of the field that will maximize the enclosed area.
Answer:
north and south sides are 38 8/9 ft longeast and west sides are 17.5 ft longStep-by-step explanation:
Short answer: area is maximized when half the cost is spent in each of the orthogonal directions. This means the east and west sides will total $350 at $20 per foot, so will be 17.5 feet. The north and south sides will total $350 at $9 per foot, so will be 38 8/9 feet.
The dimensions that maximize the area are 17.5 ft in the north-south direction by 38 8/9 ft in the east-west direction.
__
Long answer: If x represents the length of the north and south sides, and y represents the length of the east and west sides, then the total cost is ...
10y +10y +2x +7x = 700
9x +20y = 700
y = (700 -9x)/20
We want to maximize the area:
A = xy = x(700 -9x)/20
We can do this by differentiating and setting the derivative to zero:
dA/dx = 700/20 -9x/10 = 0
350 -9x = 0 . . . . multiply by 10
x = 350/9 = 38 8/9
y = (700 -9(350/9))/20 = 350/20 = 17.5
The north and south sides are 38 8/9 ft long; the east and west sides are 17.5 ft long to maximize the area for the given cost.
Dr. Kora borrowed $8000 to purchase new medical equipment for her new office . If she paid 7.5% simple interest for 10 years. How much interest will she pay?
Answer:
Dr. Kora will pay an interest of $6,000
Step-by-step explanation:
Simple interest = P × R × T
Where:
P = Principal = $8000
R = Rate = 7.5% = 0.075
T = Time = 10 years
∴ Simple interest = 8000 × 0.075 × 10 = $6,000
Therefore Dr. Kora will pay an interest of $6,000
Verizon Wireless would like to estimate the proportion of households that use cell phones for their phone service without a land line. A random sample of 150 households was selected and 48 relied strictly on cell phones for their service. The margin of error for a 90% confidence interval for the proportion based on this sample is ________.
Answer:
[tex] ME = 1.64 \sqrt{\frac{0.32 (1-0.32)}{150}}= 0.0625[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] n = 150[/tex] represent the sampel size selected
[tex] X = 48[/tex] represent the number of households who relied strictly on cell phones for their service
The estimated proportion of households who relied strictly on cell phones for their service is given by:
[tex] \hat p =\frac{X}{n}= \frac{48}{150}= 0.32[/tex]
And the margin of error would be given by:
[tex] ME = z_{\alpha/2} \sqrt{\hat p(1-\hat p)}{n}[/tex]
The confidence is 90% so then the significance is [tex]\alpha=1-0.9=0.1[/tex] and [tex] \alpha/2 =0.05[/tex] the critical value for this case from the normal standard distribution is:
[tex] z_{\alpha/2}= 1.64[/tex]
And the margin of error would be:
[tex] ME = 1.64 \sqrt{\frac{0.32 (1-0.32)}{150}}= 0.0625[/tex]
What is the median of the following set of data? 21, 4, 18, 9, 25, 16, 27, 30,
33, 15, 31
The median is the middle number in the data set when
the data set is written from least to greatest.
So let's write our data set from least to greatest.
4, 9, 15, 16, 18, 21, 25, 27, 30, 31, 33
Now, we identify the middle number.
4, 9, 15, 16, 18, 21, 25, 27, 30, 31, 33
Notice that 21 appears in the middle.
So the median of the data set is 21.
Answer:
Median: 21
Step-by-step explanation:
arrange all the numbers from least to greatest:
4, 9, 15, 16, 18, 21, 25, 27, 30, 31, 33
median = is the middle number in the data set/listed numbers.
Since there are eleven numbers in the set of data, we divide it equally, to find the median.
{4, 9, 15, 16, 18} 21 {25, 27, 30, 31, 33}
Help me please !!
In the spring you decide to start cleaning your room on a weekly basis. The first cleaning takes you 135 minutes. You notice for watch cleaning after that, you decrease the time it takes from the week before by 20%. After 4 weeks, how long will it take you to clean your room? Round your answer to the nearest minute.
Answer:
69
Step-by-step explanation:
first 135
second 135 - 20% = 135 - 27 = 108
third 108 - 20% = 108 - 21.6 = 86.4
fourth 86.4 -20% = 86.4 -17.28= 69.12
rounded 69
Roberto finishes a triathlon in 63.2 minutes. Among all men in the race, the mean finishing time was 69.4 minutes with a standard deviation of 8.9 minutes. Zandra finishes the same triathlon in 79.3 minutes. Among allwomen in the race, the mean finishing time was 84.7 minutes with a standard deviation of 7.4 minutes. Who did better inrelation to their gender?
Answer:
Due to the lower z-score of the finishing time, Zandra was faster, that is, doing better in relation to her gender.
Step-by-step explanation:
Z-score:
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.
In this question:
Whoever had the lower z-score was faster, that is, did better in relation to their gender.
Roberto:
63.2 minutes. Mean finishing time was 69.4 minutes with a standard deviation of 8.9 minutes. So [tex]X = 63.2, \mu = 69.4, \sigma = 8.9[/tex]
Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{63.2 - 69.4}{8.9}[/tex]
[tex]Z = -0.7[/tex]
Zandra:
79.3 minutes. Mean finishing time was 84.7 minutes with a standard deviation of 7.4 minutes. So [tex]X = 79.3, \mu = 84.7, \sigma = 7.4[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{79.3 - 84.7}{7.4}[/tex]
[tex]Z = -0.73[/tex]
Due to the lower z-score of the finishing time, Zandra was faster, that is, doing better in relation to her gender.
Last month, Carla's neighbors paid her to take care of their cat when they went on
vacation. She spent $4 of her earnings on an afternoon snack and $12 on a new book. Afterward,
she had at least $5 left. How can you best describe how much Carla's neighbors paid her?
Select the correct choice below and fill in the answer box to complete your choice.
OA. They paid her exactly $
OB. They paid her at least $
. C. They paid her at most $
Answer:
She had at least 21
Step-by-step explanation:
She had at least 4+ 12 +5
She had at least 21
She spent 4 and 12 so she had 16 dollars
She had at least 5 left
so at the very least she had 16+5 which is 21, she may have had more
Answer:
21
Step-by-step explanation:
she spent 4 and 12 so she had 16 dollars so she have at least she have $5 left
Puji paid $7.50 for three pounds of gummy candy.
Part A
Assuming the cost per pound of gummy candy is proportional, complete the table of values representing the cost of gummy candy in pounds.
(Please look at the graph uptop)
Answer:
1: 2.5, 2: 5.0 , 3:7.5 , 4:10 , 5: 12.5
Step-by-step explanation:
asumming it is proportional, you divide 7.5 by 3 which will give you the cost per pound which is $2.5, then you multiply this number by the amount of pounds you want
Answer:
1: 2.5 , 2: 5.0 , 3:7.5 , 4:10 , 5: 12.5
Step-by-step explanation:
Choose the correct interpretation of the above confidence interval. Note: 2 submissions allowed.
1) Since 0 is not in the confidence interval, the surveys provide evidence that the proportion of teens that text while driving is greater than the proportion of adults that text while driving.
2) Since the confidence interval is entirely positive, the surveys provide evidence that the proportion of teens that text while driving is greater than the proportion of adults that text while driving.
3) Since the confidence interval is entirely positive, the surveys provide evidence that the proportion of adults that text while driving is greater than the proportion of teens that text while driving.
4) Since 0 is not in the confidence interval, the surveys provide evidence that there is no significant difference between the proportions of adults and teens that text while driving.
Answer:
Step-by-step explanation:
Hello!
Full Text:
As part of its "It Can Wait" campaign to discourage texting while driving, AT&T recently released the results of separate surveys concerning the extent of texting while driving among adults twd_commutor_survey and among teens att_teen_survey_executive . In the survey of the adults, 496 of n1 = 1,011 adult drivers (49.06%) said they text while driving. In the survey of the teens, 516 of n2 = 1,200 (43%) said they text while driving.
Question 1. Calculate a 98% confidence interval for the difference padult - pteen in the proportions of adults that text while driving and the proportion of teens that text while driving. (use 4 decimal places in your answers) lower bound upper bound
Be:
X₁: Number of adult drivers that text while driving, out of 1011.
n₁= 1011
x₁= 496
p₁'= 496/1011= 0.4906
X₂: Number of teen drivers that text while driving, out of 1200.
n₂= 1200
x₂= 516
p₂'= 516/1200= 0.43
For the 98% CI for p₁-p₂
[tex]Z_{1-\alpha /2}= Z_{0.99}= 2.326[/tex]
(p₁'-p₂')±[tex]Z_{1-\alpha /2}[/tex] * [tex]\sqrt{\frac{p'_1(1-p'_1)}{n_1} +\frac{p'_2(1-p'_2)}{n_2} }[/tex]
(0.4906-0.43)±2.326*[tex]\sqrt{\frac{0.4906(1-0.4906)}{1011} +\frac{0.43(1-0.43)}{1200} }[/tex]
0.0606±2.326*0.0212
[0.011; 0.11]
Using a 98% confidence level, you'd expect that the interval [0.011; 0.11] contains the difference between the population proportion of adults that text while driving and the population proportion of teens that ext while driving.
Question 2. Choose the correct interpretation of the above confidence interval. Note: 2 submissions allowed.
To decide over a hypothesis test using a confidence interval there are several conditions that should be met:
1) The hypotheses should be two-tailed:
H₀: p₁ - p₂= 0
H₁: p₁ - p₂≠ 0
2) The confidence level of the interval and the significance level of the test should be complementary, this means that if the interval was constructed with a level 1 - α: 0.98 then the test should be made using α: 0.02.
Naturally, the hypotheses and the CI should be made for the same parameters.
If all conditions are met, the decision criteria is as follows:
If the CI contains the value stated in the null hypothesis, the decision is to not reject the null hypothesis.
If the CI doesn't contain the value stated in the null hypothesis, the decision is to reject the null hypothesis.
In this case, the value stated in the null hypothesis is "zero" and is not included in the interval, so the decision is to reject the null hypothesis. You can conclude that the population proportions of adults and teens that text while driving are different.
Considering that the CI is positive, we can think that the proportion of adults that text while driving is grater than the proportion of teens that text while driving.
Options:
1) Since 0 is not in the confidence interval, the surveys provide evidence that the proportion of teens that text while driving is greater than the proportion of adults that text while driving.
2) Since the confidence interval is entirely positive, the surveys provide evidence that the proportion of teens that text while driving is greater than the proportion of adults that text while driving.
3) Since the confidence interval is entirely positive, the surveys provide evidence that the proportion of adults that text while driving is greater than the proportion of teens that text while driving.
4) Since 0 is not in the confidence interval, the surveys provide evidence that there is no significant difference between the proportions of adults and teens that text while driving.
The correct option is: "3"
I hope this helps!
A hyperbola in the form (x ^ 2)/(a ^ 2) - (y ^ 2)/(b ^ 2) = 1 has a center, vertices, and foci that fall along a horizontal. Please select the best answer from the choices provided. True or false
Answer:
True
Step-by-step explanation:
Explanation:-
The equation of the standard hyperbola is
[tex]\frac{x^{2} }{a^{2} } - \frac{y^{2} }{b^{2} } =1[/tex]
Center is (0,0) Hyperbola is symmetric with respective to both the axes, since if (x, y) is a point on the hyperbola, then (-x, y), (-x,-y), (x,-y) are also lie on the parabola. The relation of between focus and transverse and conjugate axes c²=a²+b² The transverse axis is along x-axis The conjugate axis is along y-axis The length of transverse axis is 2 a The length of conjugate axis is 2 b The foci is (±c,0) and the equation of foci is x=±a e) The length of Latus rectum is [tex]\frac{2b^{2} }{a}[/tex]Answer:
It is True!
Step-by-step explanation:
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Answer:
1) This is because some has their own shape and the commonly used loop is the clothoid loop, e.t.c.
2) This is because researchers found out that it helps ease the passage of the kidney stones.
Step-by-step explanation:
Hope it helps
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Answer:
1) Roller coaster loops are never circular...why do you think that is?:
This force is called the Centripetal Force.
Newton's first Law of Motion of motion tells us that, without this force, the coaster would like to travel in a straight line and at constant speed. The centripetal force is pushing the coaster around in a circle. It is your body's (equal and opposite) reaction to this force, often referred to as the Centrifugal Force, that explains the feeling you get .There is a force (provided by the rails), that is pushing the trucks of the coaster towards the centre of the loop. t of being squashed into your seat (Newton's third Law of Motion)
2. Riding Big Thunder Mountain Railroad at Disney World could help dislodge kidney stones....why do you think that is?:
Riding the Big Thunder Mountain Railroad roller coaster at Disney World could help ease the passage of small kidney stones. Kidney stones are hard masses of minerals that form in the kidneys. They can range in size, from a tiny grain of sand to, in extreme cases, the size of a golf ball. Patients with kidney stones don't always need treatment, because the stones can pass out of the body on their own, but the process of passing them can be quite painful. Riding the Big Thunder Mountain Railroad roller coaster at Disney World could help ease the passage of small kidney stones, according to the new study because of 'The intense ride helps get rid of them'.
(a) Find the size of each of two samples (assume that they are of equal size) needed to estimate the difference between the proportions of boys and girls under 10 years old who are afraid of spiders. Assume the "worst case" scenario for the value of both sample proportions. We want a 98% confidence level and for the error to be smaller than 0.02.
b) Again find the sample size required, as in part (a), but with the knowledge that a similar student last year found that the proportion of boys afraid of spiders is 0.45 and the proportion of girls afraid of spiders was 0.58.
Answer:
(a) The sample sizes are 6787.
(b) The sample sizes are 6666.
Step-by-step explanation:
(a)
The information provided is:
Confidence level = 98%
MOE = 0.02
n₁ = n₂ = n
[tex]\hat p_{1} = \hat p_{2} = \hat p = 0.50\ (\text{Assume})[/tex]
Compute the sample sizes as follows:
[tex]MOE=z_{\alpha/2}\times\sqrt{\frac{2\times\hat p(1-\hat p)}{n}[/tex]
[tex]n=\frac{2\times\hat p(1-\hat p)\times (z_{\alpha/2})^{2}}{MOE^{2}}[/tex]
[tex]=\frac{2\times0.50(1-0.50)\times (2.33)^{2}}{0.02^{2}}\\\\=6786.125\\\\\approx 6787[/tex]
Thus, the sample sizes are 6787.
(b)
Now it is provided that:
[tex]\hat p_{1}=0.45\\\hat p_{2}=0.58[/tex]
Compute the sample size as follows:
[tex]MOE=z_{\alpha/2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})}{n}[/tex]
[tex]n=\frac{(z_{\alpha/2})^{2}\times [\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})]}{MOE^{2}}[/tex]
[tex]=\frac{2.33^{2}\times [0.45(1-0.45)+0.58(1-0.58)]}{0.02^{2}}\\\\=6665.331975\\\\\approx 6666[/tex]
Thus, the sample sizes are 6666.
A researcher uses a matched-samples design to investigate whether single people who own pets are generally happier than single people without pets. A mood inventory questionnaire is administered to a group of 20- to 29-year old non-pet owners and a similar age group of pet owners. The pet owners are matched one-to-one with the non-pet owners for income, number of close friendships and general health. The data are as follows. Matched-Pair Non-pet Pet A 11 13 B 9 8 C 11 14 D 13 13 E 6 12 F 9 11 Calculate and report below the value of the appropriate test statistic to determine if there is evidence for this researcher's hypothesis.
Answer:
There is not enough evidence to support the claim that single people who own pets are generally happier than single people without pets. (P-value=0.0509).
Step-by-step explanation:
We have to calculate the difference for every pair, and applied the hypothesis test to this sample of differences.
Non-pet Pet --> Difference (d)
A 11 13 --> 2
B 9 8 --> -1
C 11 14 --> 3
D 13 13 --> 0
E 6 12 --> 6
F 9 11 --> 2
The claim is that single people who own pets are generally happier than single people without pets. In the context of the sample, it means that the difference between the metric of happiness between the pet and the non-pet subjects is bigger than 0.
The mean and standard deviation of the sample of differences is:
[tex]M=\dfrac{1}{6}\sum_{i=1}^{6}(2+(-1)+3+0+6+2)\\\\\\ M=\dfrac{12}{6}=2[/tex]
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{6}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{5}\cdot [(2-(2))^2+(-1-(2))^2+(3-(2))^2+(0-(2))^2+(6-(2))^2+(2-(2))^2]}\\\\\\ s=\sqrt{\dfrac{1}{5}\cdot [(0)+(9)+(1)+(4)+(16)+(0)]}\\\\\\ s=\sqrt{\dfrac{30}{5}}=\sqrt{6}\\\\\\s=2.449[/tex]
Then we perform an hypothesis test for the population mean.
The claim is that single people who own pets are generally happier than single people without pets.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_d=0\\\\H_a:\mu_d> 0[/tex]
The significance level is 0.05.
The sample has a size n=6.
The sample mean is M=2.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.449.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2.449}{\sqrt{6}}=0.9998[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2-0}{0.9998}=\dfrac{2}{0.9998}=2.0004[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=6-1=5[/tex]
This test is a right-tailed test, with 5 degrees of freedom and t=2.0004, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t>2.0004)=0.0509[/tex]
As the P-value (0.0509) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that single people who own pets are generally happier than single people without pets.
Answer:
Step-by-step explanation:
Null hypothesis : [tex]H_0:\mu_d=0[/tex]
Alternative hypothesis: [tex]H_0:\mu_d>0[/tex]
Level pf significance [tex]\alpha =0.05[/tex]
Test statistic [tex]t = \frac{\bar d- \mu}{s_d/\sqrt{n} }[/tex]
Mean of difference
[tex]\bar d = \frac{\sum d_i}{n} = 12/6 = 2[/tex]
Standard deviation of difference
[tex]s_d=\sqrt{\frac{\sum (d_i- \bar d)}{n-1} } \\\\=\sqrt{\frac{30}{6.1} } \\\\=2.441[/tex]
Test statistic
[tex]t = \frac{\bar d- \mu}{s_d/\sqrt{n} }[/tex]
[tex]=\frac{2-0}{2.449/\sqrt{6} } \\\\=2.00[/tex]
Degree of freedom
df = n - 1
6-1 = 5
This test is a right-tailed test, with 5 degrees of freedom and t=2.0004, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t>2.0004)=0.0509[/tex]
As the P-value (0.0509) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that single people who own pets are generally happier than single people without pets.
Franco made a dozen muffins for his party. Upon taking them out of the oven he noticed that 2 of the muffins were badly burnt. Franco served 7/10 of the remaining muffins. Which equation shows the fraction of the non burned muffins that remains?
Answer:
(B)[tex]\frac{10}{10}-\frac{7}{10}=\frac{3}{10}[/tex]
Step-by-step explanation:
The question is Incomplete. Find the complete question in the attachment.
Number of muffins made by Franco =12
Number of Badly Burnt Muffins =2
Number of non burned muffins =12-2=10
Franco served [tex]\frac{7}{10} $ of the non burned muffins = $ \frac{7}{10}*10=7$ muffins[/tex]
Therefore, the number of non burned muffins that remains =10-7 =3
We can then say the fraction of the non-burned muffins that remains[tex]=\frac{3}{10}[/tex]
Therefore, the correct equation is in Option B:
[tex]\frac{10}{10}-\frac{7}{10}=\frac{3}{10}[/tex]
Suppose you have a sample of 40 16-year-old children with antisocial tendencies and you are particularly interested in the emotion of disgust. The average 16-year-old has a score on the emotion recognition scale of 11.80. (The higher the score on this scale, the more strongly an emotion has to be displayed to be correctly identified. Therefore, higher scores indicate greater difficulty recognizing the emotion). Assume that scores on the emotion recognition scale are normally distributed.
Here is the complete question.
A one-tailed hypothesis test with the t statistic Antisocial personality disorder (ASPD) is characterized by deceitfulness, reckless disregard for the well-being of others, a diminished capacity for remorse, superficial charm, thrill seeking, and poor behavioral control. ASPD is not normally diagnosed in children or adolescents, but antisocial tendencies can sometimes be recognized in childhood or early adolescence. James Blair and his colleagues have studied the ability of children with antisocial tendencies to recognize facial expressions that depict sadness, happiness, anger, disgust, fear, and surprise. They have found that children with antisocial tendencies have selective impairments, with significantly more difficulty recognizing fearful and sad expressions. Suppose you have a sample of 40 16-year-old children with antisocial tendencies and you are particularly interested in the emotion of fear. The average 16-year-old has a score on the emotion recognition scale of 11.80. (The higher the score on this scale, the more strongly an emotion has to be displayed to be correctly identified. Therefore, higher scores indicate greater difficulty recognizing the emotion). Assume that scores on the emotion recognition scale are normally distributed. You believe that children with antisocial tendencies will have a harder time recognizing the emotion of fear in other words, they will have higher scores on the emotion recognition test).
What is your null hypothesis stated using symbols?
What is your alternative hypothesis stated using symbols?
This is a tailed test. Given what you know, you will evaluate this hypothesis using a statistic.
Answer:
Step-by-step explanation:
Given that :
the population mean = 11.80
Thus;
The null hypothesis stated using symbols is :
[tex]\mathbf{H_o = \mu = 11.80}[/tex]
The alternative hypothesis stated using symbols is:
[tex]\mathbf{H_i = \mu > 11.80}[/tex]
However, Since the alternative hypothesis looks somewhat greater than the null hypothesis, then the test is based one right - tailed test
Thus;
This is a one tailed test and the hypothesis uses a t statistic
Brainliest to whoever gets this correct The graph of g(x), shown below, resembles the graph of f(x) = x4 - x2, but it has been changed somewhat. Which of the following could be the equation of g(x)?
Why is this?
We start with x^4 - x^2, which is the original f(x) function. Adding some number to this result will increase the y coordinate of any point on the f(x) function. This is because y = f(x). The only thing that matches is choice C, where we shift the graph up 0.5 units. We say that g(x) = f(x) + 0.5
Choice D goes in the opposite direction, and shifts the graph down 0.5 units.
Choices A and B shift the graph horizontally to the right 0.5 units and to the left 0.5 units respectively.
3 5/5
Simplify the expression
2
+
and write the result in the form a+bi.
2
a.
2147
.
23/
2
b.
5
-231
d!
4
Please select the best answer from the choices provided
A
Answer:
4
Step-by-step explanation: