Answer:
(a) P-value = 0.044
(b) P-value = 0.0022
(c) P-value = 0.4402
(d) P-value = 0.022
Step-by-step explanation:
The complete question is: An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the p-value for the given set of hypotheses and t-test statistics. Also, determine if the null hypothesis would be rejected at α = 0.05.
a) HA : μ > μ0, n = 11, T = 1.91
b) HA : μ < μ0, n = 17, T = -3.45
c) HA : μ [tex]\neq[/tex] μ0, n = 7, T = 0.83
d) HA : μ > μ0, n = 28, T = 2.13
(a) We are given the right-tailed test with sample size (n) of 11 and the test statistics of 1.91.
Now, the P-value of the test statistics is given by;
P-value = P([tex]t_n_-_1[/tex] > 1.91)
= P([tex]t_1_0[/tex] > 1.91) = 0.044
Since the P-value of the test statistics is less than the level of significance as 0.044 < 0.05, so we have sufficient evidence to reject our null hypothesis.
(b) We are given the left-tailed test with sample size (n) of 17 and the test statistics of -3.45.
Now, the P-value of the test statistics is given by;
P-value = P([tex]t_n_-_1[/tex] < -3.45)
= P([tex]t_1_6[/tex] < -3.45) = 0.0022
Since the P-value of the test statistics is less than the level of significance as 0.0022 < 0.05, so we have sufficient evidence to reject our null hypothesis.
(c) We are given the two-tailed test with sample size (n) of 7 and the test statistics of 0.83.
Now, the P-value of the test statistics is given by;
P-value = P([tex]t_n_-_1[/tex] > 0.83)
= P([tex]t_6[/tex] > 0.83) = 0.2201
For the two-tailed test, the P-value is calculated as = 2 [tex]\times[/tex] 0.2201 = 0.4402.
Since the P-value of the test statistics is less than the level of significance as 0.044 < 0.05, so we have sufficient evidence to reject our null hypothesis.
(d) We are given the right-tailed test with sample size (n) of 28 and the test statistics of 2.13.
Now, the P-value of the test statistics is given by;
P-value = P([tex]t_n_-_1[/tex] > 2.13)
= P([tex]t_2_7[/tex] > 2.13) = 0.022
Since the P-value of the test statistics is less than the level of significance as 0.022 < 0.05, so we have sufficient evidence to reject our null hypothesis.
Suppose that computer literacy among people ages 40 and older is being studied and that the accompanying tables describes the probability distribution for four randomly selected people, where x is the number that are computer literate. Is it unusual (using P(x) less than 0.05) to find four computer literates among four randomly selected people?
Answer:
Step-by-step explanation:
The complete question is given thus:
Suppose that computer literacy among people ages 40 and older is being studied and that the accompanying tables describes the probability distribution for four randomly selected people, where x is the number that are computer literate. Is it unusual to find four computer literates among four randomly selected people?
x P(x)
0 0.16
1 0.25
2 0.36
3 0.15
4 0.08
Yes NoANSWER:
The odds that this will occur according to the chart are 0.08, or 8%, so although this is unlikely, it's not terribly unusual.
⇒ NO
So from the following we can say it is not unusual to find four (4) computer literates among four randomly selected people.
ok, so P(1) + P(2) + P(3) + P(4) + P(0) = 0.16+0.25+0.36+0.15+0.08 = 1
Whereas the chance of finding four (4) out of four (4) computer iteration is low when compared to other factors.
cheers i hope this helped !!
A first number plus twice a second number is 4. Twice the first number plus the second totals 17. Find the numbers
Answer:
10; -3
Step-by-step explanation:
Let's represent the first number with x, and the second number with y. Now let's write these two equations to find the numbers.
x + 2y = 4
2x + y = 17
We can solve using the substitution method:
x = 4 - 2y
2x + y = 17
2 (4 - 2y) + y = 17
8 - 4y + y = 17
-3y = 9
y = -3
Now plug the value of y in to find x:
x + 2y = 4
x + 2(-3) = 4
x + -6 = 4
x = 10
So, the first number is 10, and the second number is -3.
Cheers.
Use the confidence interval to find the margin of error and the sample mean. (1.71, 2.05)
Answer:
Margin of error = 0.17Sample mean = 1.88Step-by-step explanation:
Given:
Sample 1.71 , 2.05
Find:
Margin of error
Sample mean
Computation:
1. Margin of error = (2.05 - 1.71) / 2
Margin of error = 0.34 / 2
Margin of error = 0.17
2. Sample mean = (2.05 + 1.71) / 2
Sample mean = 3.76 / 2
Sample mean = 1.88
Which location has the least elevation
Answer:
the Dead Sea has the least elevation.
Solve the equation [tex]\frac{x}{3} -5=15[/tex]
Answer:
The answer is
x = 60Step-by-step explanation:
[tex] \frac{x}{3} - 5 = 15[/tex]Send 5 to the right side of the equation
That's
[tex] \frac{x}{3} = 15 + 5[/tex][tex] \frac{x}{3} = 20[/tex]Multiply both sides of the equation by 3
We have
[tex]3 \times \frac{x}{3} = 20 \times 3[/tex]x = 20 × 3
We have the final answer as
x = 60Hope this helps you
4 OT
Which of the following are exterior angles? Check all that apply.
4
6
5
3
2
O A. 26
B. 25
C. <3
O D. 24
O E. 22
O F. 21
Answer:
A. <6
Step-by-step explanation:
Exterior angle of this geometric shape is 6
The exterior angle in the given figure is ∠6.
Option A is the correct answer.
What is an angle?The angles between two lines are the angles formed by two intersecting lines, measured in degrees or radians.
Several different types of angles can be formed between two lines, including acute angles, right angles, and obtuse angles.
We have,
From the diagram,
We see that the exterior angle is ∠6.
Now,
The exterior angle is the sum of its two nonadjacent interior angles.
So,
∠6 = ∠1 + ∠3
Thus,
The exterior angle is ∠6.
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translation to an equation and solve. Let x be the unknown number. 120% of what number is 60? Type an integer or a decimal.
Answer:
72
Step-by-step explanation:
120% × 60 =
(120 ÷ 100) × 60 =
(120 × 60) ÷ 100 =
7,200 ÷ 100 =
hopefully this helped
If $(x + y)^2 = 1$ and $xy = -4$, what is the value of $x^2 + y^2$? Please Help!!
Expanding the first expression gives
[tex](x+y)^2=x^2+2xy+y^2=1[/tex]
Since [tex]xy=-4[/tex], we have
[tex]x^2+2(-4)+y^2=1\implies\boxed{x^2+y^2=9}[/tex]
what is a histogram?
Answer:
A histogram is a graph that organizes a group of data points. A histogram graphically summarize the distribution of a univariate data set.
Solve
x2+ 4x = 4 for x by completing the square.
Answer:
x = -2 +/- √8 or 0.828.... and -4.828....
Step-by-step explanation:
x² + 4x + 4 = 4 + 4
(x + 2)² = 8
x + 2 = +/-√8
x = -2 +/- √8
The time for service call follows a uniform distribution over the interval 20 to 60 minutes.
1. What is the probability that the service call takes longer than 30 minutes?
2. What is the interquartile range?
3. What is the 90th percentile?
Answer:
(1) 0.75
(2) 30
(3) 56
Step-by-step explanation:
Let X represent the time for service call.
It is provided that: [tex]X\sim Uni(20, 60)[/tex]
The probability density function of X is:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b[/tex]
(1)
Compute the probability that the service call takes longer than 30 minutes as follows:
[tex]P(X>30)=\int\limits^{60}_{30} {\frac{1}{60-20}} \, dx[/tex]
[tex]=\frac{1}{40}\times |x|^{60}_{30}\\\\=\frac{60-30}{40}\\\\=\frac{3}{4}\\\\=0.75[/tex]
Thus, the probability that the service call takes longer than 30 minutes is 0.75.
(2)
The Inter quartile range is the difference between the 75th and 25th percentile.
From part (1), we know that P (X > 30) = 0.75.
⇒ 1 - P (X > 30) = 0.75
⇒ P (X < 30) = 0.25
The 25th percentile is 30.
Compute the 75th percentile as follows:
[tex]P(X<x)=0.75\\\\\int\limits^{x}_{20} {\frac{1}{60-20}} \, dx=0.75\\\\\frac{1}{40}\times |x|^{x}_{20}=0.75\\\\x-20=40\times 0.75\\\\x=30+20\\\\x=50[/tex]
The 75th percentile is 50.
Then the inter quartile range is:
[tex]IQR=P_{75}-P_{25}[/tex]
[tex]=50-20\\=30[/tex]
Thus, the inter quartile range is 30.
(3)
Compute the 90th percentile as follows:
[tex]P(X<x)=0.90\\\\\int\limits^{x}_{20} {\frac{1}{60-20}} \, dx=0.90\\\\\frac{1}{40}\times |x|^{x}_{20}=0.90\\\\x-20=40\times 0.90\\\\x=36+20\\\\x=56[/tex]
The 90th percentile is 56.
PLEASE HELP ASAP it is my homework
Answer:
0.4
Step-by-step explanation:
The number of ways to select 3 points out of 5 points:
N1 = 5C3 = (5 x 4 x 3)/(1 x 2 x3) = 10
The number of ways to select 3 points out of 4 points that are already collinear:
N2 = 4C3 = (4 x 3 x 2)/(1 x 2 x 3) = 4
=> The probability of selecting 3 points that are collinear:
P = N2/N1 = 4/10 = 0.4
Good day, Harry!
Larry and Donna bought a sofa at the sale price of $1,536. The original price of the sofa was $1,920.
Answer: $384
Step-by-step explanation:
1000- 1000=0
900-500=400
20-36=-16
400+-16=384
Lisa built a rectangular flower garden that is 4 meters wide and has a perimeter of 26 meters.
What is the length of Lisa's flower garden?
Given that :-
Width of garden is 4 meters Perimeter of garden is 26 metersTo Find :-
Length of rectangular garden.Solution :-
→ Perimeter = 2( Length + breadth)
→ 26 = 2 ( Length+ 4 )
→ 26/2 = Length + 4
→ 13 = Length + 4
→ Length = 13 -4
→ Length = 9 meters.
So the Length of Lisa's garden is 9 meters .
Answer:
9
Step-by-step explanation:
In a polynomial do you identify how many terms are in a problem before or after you solve it?
Answer:
All you have to do to identify the number of terms in a polynomial is to count the number of separate parts in the polynomial separated by a plus or minus (terms)
Step-by-step explanation:
What is the relationship between the linear correlation coefficient r and the slope of a regression line?
Answer:
The relationship is that the value of the linear correlation coefficient will always have the same sign as the value of the slope of a regression line.
Step-by-step explanation:
The slope of regression is simply the covariance between X and Y divided by the variance of X i.e Cov(X, Y)/Var X. Whereas, the correlation is the covariance divided by the product of the standard deviation. Thus, we can say that the correlation is the product of the gradient of the regression line and the ratio of the standard deviations.
Thus, it means when the correlation is positive, the slope is also positive and vice versa.
The sign of the correlation coefficient, r, is always the same as that of the slope of the regression line.
Linear Correlation Coefficient and Slope of A Regression LineSlope of a regression line is gotten by dividing the covariance of between X and Y by the variance of X.On the other hand, linear correlation coefficient is gotten by dividing the covariance by the standard deviation.Thus, if the slope of regression line is positive, the correlation coefficient will be positive too and vice versa.Therefore, the sign of the correlation coefficient, r, is always the same as that of the slope of the regression line.
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What is the slope of the graph ? Leave your answer as a reduced fraction .
What is the coefficient of determination for two variables that have perfect positive linear correlation or perfect negative linear correlation? Interpret your answer.
Answer:
r^2 = 1
Step-by-step explanation:
The computation of the coefficient of determination for the two variables is shown below:
here the perfect positive linear correlation is r = 1
And, the negative linear correlation is r = -1
Based on this, the coefficient of determination is equivalent to the linear correlation coefficient square
[tex]r^2 = (\pm)^2 \\\\ = 1[/tex]
This above describes that variation that lies between the variables as explained by the linear regression line
The coefficient of determination for two variables that have perfect positive linear correlation or perfect negative linear correlation is denoted by; r² = (±1)² = 1
The mathematical computation of the coefficient of determination for two variables that have perfect positive linear correlation can be in two forms and is as follows;
The perfect positive linear correlation is denoted, r = 1The negative linear correlation is denoted, r = -1In lieu of this, the coefficient of determination is equivalent to the square of linear correlation coefficient.
r² = (±1)²r² = 1The computation above describes that variation that lies between the variables as explained by the linear regression line.
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Which of the following rewrites shows the correct process for completing the square? A. 4x^2+9x+5=0 rewritten as 4x^2+9x+81/4=-5+81/4 B. 4x^2+12x+7=0 rewritten as x^2+3x+9/4=-7/4+9/4 C. 3x^2-6x-4=0 rewritten as x^2-2x+1=4+1 D. 2x^2-8x-9=0 rewritten as 2x^2-8x+16=9+16
Answer: B
Step-by-step explanation:
ax² + bx + c = 0 is rewritten as x² + (b/a)x + (b/2a)² = -c/a + (b/2a)²
A) 4x² + 9x + 5 = 0 --> x² + (9/4)x + (9/8)² = -5/4 + (9/8)²
= x² + (9/4)x + 81/64 = -5/4 + 81/64
B) 4x² + 12x + 7 = 0 --> x² + (12/4)x + (12/8)² = -7/4 + (12/8)²
= x² + 3x + 9/4 = -7/4 + 9/4 <---- this works!
C) 3x² - 6x - 4 = 0 --> x² + (-6/3)x + (-6/6)² = 4/3 + (-6/6)²
= x² - 2x + 1 = 4/3 + 1
D) 2x² - 8x - 9 = 0 --> x² + (-8/2)x + (-8/4)² = 9/2 + (-8/4)²
= x² - 4x + 4 = 9/2 + 4
Answer:
B
Step-by-step explanation:
its the correct answer :)
The region bounded by y = e−x2, y = 0, x = 0, and x = b (b > 0) is revolved about the y-axis. (Round your answers to three decimal places.) (a) Find the volume of the solid generated when b = 2.
Answer:
0.982 * [tex]\pi[/tex] = 3.085 cubic units
Step-by-step explanation:
To find the volume of the solid generated by a region that is bounded by lines where x = 0 , x (b) = 2 we apply the formula given in the attachment below
the required region boundaries are
y = e^-x2 , y = 0 , x = 0, x = b ( b >0)
attached below is a detailed solution of the problem
A trapezoid has sides of length 5 millimeters, 2 millimeters, 5 millimeters, and 6 millimeters.
What is the perimeter?
millimeters
Answer:
18 millimeters
Step-by-step explanation:
The perimeter of any shape is the sum of the sides. A trapezoid has four sides, so the perimeter is found by adding the four side lengths together.
The trapezoid in this problem has side lengths of 5 mm, 2 mm, 5 mm, and 6 mm.
Add the sides together.
5 mm + 2 mm + 5 mm + 6 mm
7 mm + 5 mm + 6mm
12 mm + 6 mm
18 mm
The perimeter of the trapezoid is 18 millimeters.
The hypotheses relating to the discoveries of radium and Neptune may be classified as empirical hypotheses.
a) true
b) false
Answer:
a) true
Step-by-step explanation:
Empirical hypothesis is the type of hypothesis used to try and explain a phenomenon which leads to a theory been developed and put to the test, using observation and experiment.
Radium was discovered due to a discrepancy in pitchblende's radiation. It was noted by the Curies that Polonium alone could not suffice for that amount of radiation, leading to the theory that another element could be present. After further testing, Radium was discovered as the culprit element.
Also, the presence pf another planet, later discovered to be Neptune was theorized to explain the phenomenon that could cause the irregularities in the motion pattern of the planet Uranus. After much experimentation, observations and calculations, Neptune was discovered.
An account executive
earns $400 per month
plus a 4% commission
on sales. The executive's
goal is to earn $2800
this month. How much must she sell to achieve this goal?
Answer:
She must sell $60,000
Step-by-step explanation:
4 percent of 60,000 is 2,400 and you add the $400 that she automatically makes every month and you get $2800 as the total amount she makes.
the difference of two number is 28. if one number is 11, find the other number
Answer:
39
Step-by-step explanation:
difference=28
other number=11
so:
11+28=39
39 is your other number
Answer:
Just simply add the given two numbers and you ll get the answer 39 now to check whether its right or wrong subtract 11 from 39 and you ll get 28 which proves that its correct
Step-by-step explanation:
A cohort study was conducted to examine the relationship between smoking and risk of lung cancer. Among 4000 smokers, 800 were eventually diagnosed with lung cancer and among 6000 non-smokers, 500 were eventually diagnosed with lung cancer. (Use this information to answer questions below)What was the relative risk of being diagnosed with lung cancer in this study?a. 0.08b. 0.13c. 0.20d. 0.40e. 2.40
Answer:
2.4
Step-by-step explanation:
Given that segment AB is tangent to the circle shown in the diagram centered at point C, determine the value of x
Answer:
x= 37Step-by-step explanation:
This problem can be solved by applying Pythagoras theorem, since the segment AB is tangent to the circle(meaning that the point A is at 90 degree to the circle)
According to Pythagoras theorem "It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides".
given (as seen from the diagram)
x, hypotenuse= ?
opposite= 12
adjacent= 35
Applying Pythagoras theorem
[tex]hyp^2= opp^2+adj^2\\\\hpy=\sqrt{opp^2+adj^2}[/tex]
Substituting our given data and solving for hpy we have
[tex]hyp=\sqrt{12^2+35^2} \\\\hyp=\sqrt{144+1225}\\\\hyp=\sqrt{1369}\\\\hyp= 37[/tex]
hence x= 37
A bag contains 4 red, 6 blue, 4 yellow and 2 green marbles. Once a marble is selected, it is not replaced. What is the probability that in 3 successive draws you will get exactly one blue, one red and no green
Answer:
0.0857
Step-by-step explanation:
What we need is, B R -G, successively. We do not add each probability, but multiply them.
P(1st marble is B) = 6 / 16
P(2nd marble is R) = 4 / 15
*your sample space decreases because you took one marble already before, the Blue one
P(3rd marble is not Green) = 12/14
** it's 12 because you took 2 non-Green marbles before
*** it's 14 because you took 2 marbles before
To arrive at the final answer, just multiply all probability.
What is 72x32 Please help.
Answer:
72
32 x
________
144
2160 +
________
2304
Step-by-step explanation:
Solve F(x) for the given domain.
F(x) = x² + 3x - 2
F(3)=____
a. 13
b. 16
C. 40
Answer:
B. 16
Step-by-step explanation:
F(3) means we must plug the number "3" into the equation for each x.
(3)^2 + 3(3) -2
9 + 9 - 2
16
Answer:
16
Step-by-step explanation:
F(x) = x² + 3x - 2
Let x=3
F(3)= 3^2 +3*3 -2
= 9+9-2
= 18-2
=16
Find the slope of the line (3,14) and (6,10)
Answer:
The slope is
[tex] - \frac{4}{3} [/tex]
Step-by-step explanation:
To find the slope given two points we use the formula
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
where
m is the slope
(x1 , y1) and (x2 , y2) are the points
From the question
The points are (3,14) and (6,10)
The slope of the line (3,14) and (6,10) is
[tex]m = \frac{10 - 14}{6 - 3} = \frac{ - 4}{ 3} [/tex]
[tex]m = - \frac{4}{3} [/tex]
Hope this helps you