The scientist performs additional analyses and observes that the number of major earthquakes does appear to be decreasing but wonders whether the relationship is statistically significant. Based on the partial regression output below and a 5% significance level, is the year statistically significant in determining the number of earthquakes above magnitude 7.0?Dependent Variable: Earthquakes above Magnitude 7.0 Coefficients Standard t Stat P-value Lower 95% Upper 95% ErrorIntercept 64.67 38.08 4.32 89.22 240.12Year -0.07 0.02 -3.82 -0.11 -0.04
Answers
Answer:
Step-by-step explanation:
Hello!
A regression model was determined in order to predict the number of earthquakes above magnitude 7.0 regarding the year.
^Y= 164.67 - 0.07Xi
Y: earthquake above magnitude 7.0
X: year
The researcher wants to test the claim that the regression is statistically significant, i.e. if the year is a good predictor of the number of earthquakes with magnitude above 7.0 If he is correct, you'd expect the slope to be different from zero: β ≠ 0, if the claim is not correct, then the slope will be equal to zero: β = 0
The hypotheses are:
H₀: β = 0
H₁: β ≠ 0
α: 0.05
The statistic for this test is a student's t: [tex]t= \frac{b - \beta }{Sb} ~~t_{n-2}[/tex]
The calculated value is in the regression output [tex]t_{H_0}= -3.82[/tex]
This test is two-tailed, meaning that the rejection region is divided in two and you'll reject the null hypothesis to small values of t or to high values of t, the p-value for this test will also be divided in two.
The p-value is the probability of obtaining a value as extreme as the one calculated under the null hypothesis:
p-value: [tex]P(t_{n-2}\leq -3.82) + P(t_{n-2}\geq 3.82)[/tex]
As you can see to calculate it you need the information of the sample size to determine the degrees of freedom of the distribution.
If you want to use the rejection region approach, the sample size is also needed to determine the critical values.
But since this test is two tailed at α: 0.05 and there was a confidence interval with confidence level 0.95 (which is complementary to the level of significance) you can use it to decide whether to reject the null hypothesis.
Using the CI, the decision rule is as follows:
If the CI includes the "zero", do not reject the null hypothesis.
If the CI doesn't include the "zero", reject the null hypothesis.
The calculated interval for the slope is: [-0.11; -0.04]
As you can see, both limits of the interval are negative and do not include the zero, so the decision is to reject the null hypothesis.
At a 5% significance level, you can conclude that the relationship between the year and the number of earthquakes above magnitude 7.0 is statistically significant.
I hope this helps!
(full output in attachment)
Related Questions
How many x-intercepts does the graph of y = 2x2 + 4x - 3 have?
Answers
Answer:
3
Step-by-step explanation:
Given
y
=
2
x
2
−
4
x
+
3
The y-intercept is the value of
y
when
x
=
0
XXX
y
=
2
(
0
)
2
−
4
(
0
)
+
3
=
3
For a quadratic in the general form:
XXX
y
=
a
x
2
+
b
x
+
c
the determinant
Δ
=
b
2
−
4
a
c
indicates the number of zeros.
Δ
⎧
⎪
⎨
⎪
⎩
<
0
==⇒
no solutions
=
0
==⇒
one solution
>
0
==⇒
two solutions
In this case
XXX
Δ
=
(
−
4
)
2
−
4
(
2
)
(
3
)
<
0
so there are no solutions (i.e. no values for which the expression is equal to zero).
This can also be seen from a graph of this equation:
graph{2x^2-4x+3 [-6.66, 13.34, -0.64, 9.36]}
Answer link
Vinícius Ferraz
Nov 13, 2015
(
0
,
3
)
Explanation:
x
=
0
⇒
y
=
0
−
0
+
3
y
=
0
⇒
x
=
−
b
±
√
b
2
−
4
a
c
2
a
a
=
2
,
b
=
−
4
,
c
=
3
But
Δ
< 0, then there is no real root
(
x
0
,
0
)
.
Answer:
it has 2
Step-by-step explanation:
I hope this helps!
For the functions f(x)=3x−1 and g(x)=4x−3, find (f∘g)(x) and (g∘f)(x)
Answers
(g°f)(x)= 12x-7
Hope this helps
Question 15 A party rental company has chairs and tables for rent. The total cost to rent 8 chairs and 3 tables is $38 . The total cost to rent 2 chairs and 5 tables is $35 . What is the cost to rent each chair and each table?
Answers
Answer:
Each table is $6 and each chair is $2.50
Step-by-step explanation:
HELP!! Im not sure what i did wrong!!
Answers
I'm not sure what exactly you did wrong, but I agree with you that the sample size is too small, so the correct answer will probably be the fourth options. Hope that this gives you some confidence, and 'm sorry not to be able to help you any further...
HELP! will give brainlest or whatever its called... Triangle ABC has vertices A(–2, 3), B(0, 3), and C(–1, –1). Find the coordinates of the image after a reflection over the x-axis. A’ B’ C’
Answers
Answers:
A ' = (-2, -3)
B ' = (0, -3)
C ' = (-1, 1)
=======================================================
Explanation:
To apply an x axis reflection, we simply change the sign of the y coordinate from positive to negative, or vice versa. The x coordinate stays as is.
Algebraically, the reflection rule used can be written as [tex](x,y) \to (x,-y)[/tex]
Applying this rule to the three given points will mean....
Point A = (-2, 3) becomes A ' = (-2, -3)Point B = (0, 3) becomes B ' = (0, -3)Point C = (-1, -1) becomes C ' = (-1, 1)The diagram is provided below.
Side note: Any points on the x axis will stay where they are. That isn't the case here, but its for any future problem where it may come up. This only applies to x axis reflections.
Answer:
(-2,-3)...(0,-3)...(-1,1)
Step-by-step explanation:
Please answer this correctly
Answers
Step-by-step explanation:
pnotgrt8rthan4 = 3 ÷ 7 × 100
= 42.8571428571 / 43%
What is the measure of PSQ?
Answers
Answer:
Do you have an image because I'm a bit confused with you just asking the measure of PSQ.
Step-by-step explanation:
7
х
45
Find x.
x=
V(14)
7
07/2
Answers
Answer:
7
Step-by-step explanation:
This a special 90° 45° 45° triangle and is an Isosceles triangle at the same time
Of one of the equal side is 7 than the other one too must be 7
The length of the rectangle is described by the function y = 3x + 6, where x is the width of the rectangle. Find the domain in this situation.
Answers
Answer:2/3
Step-by-step explanation:
Given that the length of the rectangle is described by the function y = 3x + 6, where x is the width of the rectangle. The domain of the function is (0, ∞).
What is domain of a function?The domain of a function is the set of all possible inputs for the function. In other words, domain is the set of all possible values of x. In this question, x is the width of the rectangle. Width of a rectangle existing in two dimensional space, cannot be negative or zero. Thus it is the set of all positive real numbers, or we say, (0, ∞).
Learn more about domain of a function here
https://brainly.com/question/13113489
#SPJ2
Given the equation 4x - 3y = 12
1. Write the equation in slope-intercept form.
2. Identify the slope and y-intercept.
3. Graph the line.
4. Identify if it is a positive or negative slope.
Answers
Answer:
see below
Step-by-step explanation:
Slope intercept form is y = mx+b where m is the slope and b is the y intercept
4x - 3y = 12
Solve for y
Subtract 4x from each side
4x-4x - 3y =-4x+ 12
-3y = -4x+12
Divide by -3
-3y/-3 = -4x/-3 + 12/-3
y = 4/3x -4
The slope is 4/3 and the y intercept is -4
The slope is Positive
Of 41 bank customers depositing a check, 22 received some cash back. Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back. (Round your answers to 4 decimal places.)
Answers
Answer:
CI: {0.4085; 0.6647}
Step-by-step explanation:
The confidence interval for a proportion (p) is given by:
[tex]p \pm z*\sqrt{\frac{(1-p)*p}{n} }[/tex]
Where n is the sample size, and z is the z-score for the desired confidence interval. The score for a 90% confidence interval is 1.645. The proportion of depositors who ask for cash back is:
[tex]p=\frac{22}{41}=0.536585[/tex]
Thus the confidence interval is:
[tex]0.536585 \pm 1.645*\sqrt{\frac{(1-0.536585)*0.536585}{41}}\\0.536585 \pm 0.128109\\L=0.4085\\U=0.6647[/tex]
The confidence interval for the proportion of all depositors who ask for cash back is CI: {0.4085; 0.6647}
A child is 2 -1/2 feet tall. The child’s mother is twice as tall as the child. How tall is the child’s mother
Answers
Answer:
5 feet
Step-by-step explanation:
"Twice as tall" means "2 times as tall".
2 × (2 1/2 ft) = (2 × 2 ft) +(2 × (1/2 ft)) = 4 ft + 1 ft = 5 ft
The child's mother is 5 feet tall.
Answer:
The mother is 5ft tall
Step-by-step explanation:
2 1/2 + 2 1/2 = 5ft
2ft+2ft = 4ft
1/2+1/2= 1ft
4ft+1ft = 5ft
An athletics coach states that the distribution of player run times (in seconds) for a 100-meter dash is normally distributed with a mean equal to 13.00 and a standard deviation equal to 0.2 seconds. What percentage of players on the team run the 100-meter dash in 13.36 seconds or faster
Answers
Answer:
96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster
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:
[tex]\mu = 13, \sigma = 0.2[/tex]
What percentage of players on the team run the 100-meter dash in 13.36 seconds or faster
We have to find the pvalue of Z when X = 13.36.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{13.36 - 13}{0.2}[/tex]
[tex]Z = 1.8[/tex]
[tex]Z = 1.8[/tex] has a pvalue of 0.9641
96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster
Simplify 4 + (−3 − 8)
Answers
Answer:
-7
Step-by-step explanation:
4 + (−3 − 8)
PEMDAS
Parentheses first
4 + (-11)
Add and subtract next
-7
Answer:
first I'm using BODMAS
4+(-11)
= -7
hope it helps
CAN SOMEONE PLEASE HELP ME THIS IS DUE SOON!!
Answers
Answer:
95 ft²
Step-by-step explanation:
Given:
regular pyramid with,
Square base of side length (s) = 5 ft
Slant height (l) = 7 ft
Required:
Surface area
Solution:
Surface area of a regular pyramid = ½*P*l + B
Where,
P = perimeter of the square base = 4(s) = 4(5) = 20 ft
l = slant height = 7 ft
B = area of base = s² = 5² = 25 ft²
Surface area = ½*20*7 + 25
= 10*7 + 25
= 70 + 25
Surface area of regular pyramid = 95 ft²
The tens digit in a two digit number is 4 greater than one’s digit. If we interchange the digits in the number, we obtain a new number that, when added to the original number, results in the sum of 88. Find this number
Answers
Answer:
The original digit is 62
Step-by-step explanation:
Let the Tens be represented with T
Let the Units be represented with U
Given:
Unknown Two digit number
Required:
Determine the number
Since, it's a two digit number, then the number can be represented as;
[tex]T * 10 + U[/tex]
From the first sentence, we have that;
[tex]T = 4 + U[/tex]
[tex]T = 4+U[/tex]
Interchanging the digit, we have the new digit to be [tex]U * 10 + T[/tex]
So;
[tex](U * 10 + T) + (T * 10+ U) = 88[/tex]
[tex]10U + T + 10T + U= 88[/tex]
Collect Like Terms
[tex]10U + U + T + 10T = 88[/tex]
[tex]11U + 11T = 88[/tex]
Divide through by 11
[tex]U + T = 8[/tex]
Recall that [tex]T = 4+U[/tex]
[tex]U + T = 8[/tex] becomes
[tex]U + 4 + U = 8[/tex]
Collect like terms
[tex]U + U = 8 - 4[/tex]
[tex]2U = 4[/tex]
Divide both sides by 2
[tex]U = 2[/tex]
Substitute 2 for U in [tex]T = 4+U[/tex]
[tex]T = 4 + 2[/tex]
[tex]T = 6[/tex]
Recall that the original digit is [tex]T * 10 + U[/tex]
Substitute 6 for T and 2 for U
[tex]T * 10 + U[/tex]
[tex]6 * 10 + 2[/tex]
[tex]60 + 2[/tex]
[tex]62[/tex]
Hence, the original digit is 62
Please answer this correctly
Answers
Answer:
1/7
Step-by-step explanation:
There are 7 cards, 1 of which is less than 2. Therefore, P (less then 2) = 1/7
Answer:
1/7
Step-by-step explanation:
The number from the list that is less than 2 is 1.
1 number out of a total of 7 numbers.
= 1/7
Please answer this correctly
Answers
Answer:
2/3
Step-by-step explanation:
There are 2 numbers out of 3 that fit the rule, 1 and 3. There is a 2/3 chance picking one of them.
Answer:
2/3Step-by-step explanation:
This is the answer because one number that is select is one. A number greater than 2 is 3. SO it is 2/3.
Mexican currency is the peso. One Mexican peso is currently equal to 0.055 U.S. dollars. If a traveler exchanges $400 for Mexican pesos, how many pesos will he receive? Round to the nearest peso.
Answers
Answer:
7,273 Pesos
Step-by-step explanation:
1 Peso = $0.055
The formula below converts pesos to dollars:
1 Peso x 0.055 = $1
The formula below converts dollars to pesos:
$1/0.055= 1 Pesos
We use the second formula because we are coverting
from dollars to pesos.
$400/0.055=7,273 Pesos
Answer:
22
Step-by-step explanation:
If one Mexican peso is .055 U.S dollars that means it has a greater value than the dollar so we can make the following ratio 1:.055. But if the .055 is a 400 1:400 we just multiply to get 22.
Will give brainliest answer
Answers
Answer:
[tex]153.86 \: {units}^{2} [/tex]
Step-by-step explanation:
[tex]area = \pi {r}^{2} \\ = 3.14 \times 7 \times 7 \\ = 3.14 \times 49 \\ = 153.86 \: {units}^{2} [/tex]
Answer:
153.86 [tex]units^{2}[/tex]
Step-by-step explanation:
Areaof a circle = πr^2
[tex]\pi = 3.14[/tex](in this case)
[tex]r^{2} =7[/tex]
A = πr^2
= 49(3.14)
= 153.86
Someone please answer this emergency pleaseee
Answers
Answer:
7). y = 140
8). x = 9
Step-by-step explanation:
Question (7).
All-right pencil factory will produce the graphite pencils, table formed will represent a linear graph.
Three points on the graph are (12, 42) and (18, 63), (40, y)
Slope of the line passing through these points = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{63-42}{18-12}[/tex] = [tex]\frac{y-42}{40-12}[/tex]
[tex]\frac{21}{6}[/tex] = [tex]\frac{y-42}{40-12}[/tex]
3.5 = [tex]\frac{y-42}{40-12}[/tex]
98 = y - 42
y = 140
Question (8),
If a bicyclist rides at a constant rate, table formed will represent a linear graph.
Slope of a line passing through three points (2, 25), (5, 62.5) and (x, 112.5) given in the table,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{62.5-25}{5-2}=\frac{112.5-62.5}{x-5}[/tex]
[tex]\frac{37.5}{3}=\frac{50}{x-5}[/tex]
37.5x - 187.5 = 150
37.5x = 337.5
x = 9
Which expression is equivalent to [tex]4^7*4^{-5}[/tex]? A. [tex]4^{12}[/tex] B. [tex]4^2[/tex] C. [tex]4^{-2}[/tex] D. [tex]4^{-35}[/tex]
Answers
Answer:
B. [tex]4^2[/tex]
Step-by-step explanation:
[tex]4^7 \times 4^{-5}[/tex]
Apply rule (if bases are same) : [tex]a^b \times a^c = a^{b + c}[/tex]
[tex]4^{7 + -5}[/tex]
Add exponents.
[tex]=4^2[/tex]
Answer:
[tex] {4}^{2} [/tex]Step by step explanation
[tex] {4}^{7} \times {4}^{ - 5} [/tex]
Use product law of indices
i.e
[tex] {x}^{m} \times {x}^{n} = {x}^{m + n} [/tex]
( powers are added in multiplication of same base)
[tex] = {4}^{7 + ( - 5)} [/tex]
[tex] = {4}^{7 - 5} [/tex]
[tex] = {4}^{2} [/tex]
Hope this helps...
Best regards!
find the solution set x^2+2x-15=0
Answers
Answer:
x = 3 or x = -5
Step-by-step explanation:
x² + 2x - 15 = 0
Factor left side of equation.
(x - 3)(x + 5) = 0
Set factors equal to 0
x - 3 = 0
x = 3
x + 5 = 0
x = -5
About ____% of the area is between z= -2 and z= 2 (or within 2 standard deviations of the mean)
Answers
Answer:
The percentage of area is between Z =-2 and Z=2
P( -2 ≤Z ≤2) = 0.9544 or 95%
Step-by-step explanation:
Explanation:-
Given data Z = -2 and Z =2
The probability that
P( -2 ≤Z ≤2) = P( Z≤2) - P(Z≤-2)
= 0.5 + A(2) - ( 0.5 - A(-2))
= A (2) + A(-2)
= 2 × A(2) (∵ A(-2) = A(2)
= 2×0.4772
= 0.9544
The percentage of area is between Z =-2 and Z=2
P( -2 ≤Z ≤2) = 0.9544 or 95%
find the third angle in a triangle when the other two angles are (2a-32)° and (3a+22)°
Answers
Answer:
(190-5a)°
Step-by-step explanation:
Sum of internal angles of a triangle equals to 180°
If the third angle is x, then we have:
(2a-32)°+(3a+22)° +x = 180°(5a- 10)° +x= 180°x= (180+10-5a)°x= (190-5a)°The third angle is: (190-5a)°
Find the fourth term in the expansion of the binomial
(4x + y)^4
a) 16xy^3
b) 256x^4
c) 64y^4
d) 4xy^3
Answers
Answer:
a) 16xy³
Step-by-step explanation:
For a binomial expansion (a + b)ⁿ, the r+1 term is:
nCr aⁿ⁻ʳ bʳ
Here, a = 4x, b = y, and n = 4.
For the fourth term, r = 3.
₄C₃ (4x)⁴⁻³ (y)³
4 (4x) (y)³
16xy³
A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.050.05. If 212212 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.030.03
Answers
Answer:
95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.
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 [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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.05, n = 212, \mu = 0.05, s = \sqrt{\frac{0.05*0.95}{212}} = 0.015[/tex]
What is the probability that the sample proportion will differ from the population proportion by less than 0.03?
This is the pvalue of Z when X = 0.03 + 0.05 = 0.08 subtracted by the pvalue of Z when X = 0.05 - 0.03 = 0.02. So
X = 0.08
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.08 - 0.05}{0.015}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 0.02
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.02 - 0.05}{0.015}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.
PLEASE HELP!!!! Find the common difference
Answers
Answer:
The common difference is 1/2
Step-by-step explanation:
Data obtained from the question include:
3rd term (a3) = 0
Common difference (d) =.?
From the question given, we were told that the 7th term (a7) and the 4th term (a4) are related by the following equation:
a7 – 2a4 = 1
Recall:
a7 = a + 6d
a4 = a + 3d
a3 = a + 2d
Note: 'a' is the first term, 'd' is the common difference. a3, a4 and a7 are the 3rd, 4th and 7th term respectively.
But, a3 = 0
a3 = a + 2d
0 = a + 2d
Rearrange
a = – 2d
Now:
a7 – 2a4 = 1
Substituting the value of a7 and a4, we have
a + 6d – 2(a + 3d) = 1
Sustitute the value of 'a' i.e –2d into the above equation, we have:
–2d + 6d – 2(–2d + 3d) = 1
4d –2(d) = 1
4d –2d = 1
2d = 1
Divide both side by 2
d = 1/2
Therefore, the common difference is 1/2
***Check:
d = 1/2
a = –2d = –2 x 1/2 = –1
a3 = 0
a3 = a + 2d
0 = –1 + 2(1/2)
0 = –1 + 1
0 = 0
a7 = a + 6d = –1 + 6(1/2) = –1 + 3 = 2
a4 = a + 3d = –1 + 3(1/2) = –1 + 3/2
= (–2 + 3)/2 = 1/2
a7 – 2a4 = 1
2 – 2(1/2 = 1
2 – 1 = 1
1 = 1
What is the equation of the line which passes through (-0.5,-5) and (2,5)
Answers
Answer:
by using distance formula
d=[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
by putting the values of coordinates
[tex]d=\sqrt{(2-(-0.5))^2+(5-(-5))^2}[/tex]
[tex]d=\sqrt{(2+0.5)^2+(5+5)^2}[/tex]
[tex]d=\sqrt{(2.5)^2+(10)^2}[/tex]
[tex]d=\sqrt{6.25+100}[/tex]
[tex]d=\sqrt{106.25}[/tex]
[tex]d=10.3[/tex]
Step-by-step explanation:
i hope this will help you :)
Rebecca collected data from a random sample of 500 homeowners in her state asking whether or not they use electric heat. Based on the results, she reports that 51% of the homeowners in the nation use electric heat. Why is this statistic misleading?
Answers
Answer:
She makes conclusion about a population that is not well represented by the sample.
Step-by-step explanation:
The conclusion she is making is about a population that is not well represented by her sample: the population is the homeowners in the nation, but the sample is made of homeowners or only her state.
The population about which she can make conclusions with this sample is the homeowners of her state, given that the sampling is done right.
Answer: The sample is biased