Bob has a bulb factory that produces two types of bulbs: white light (x) and color light (y). It is known that the standard deviation of service life for the population of white light bulbs is hours and hours for color bulbs, both are normally distributed. He tested the mean service life of those two types of bulbs by randomly drawing a sample of 20 bulbs from each type. The estimated mean service life are hours and hours. Assume that . What is the absolute value of the t-statistic if the null hypothesis is that both types of bulbs have the same service life?
Answers
Answer:
The answer is "3.51".
Step-by-step explanation:
[tex]\to t=\frac{\bar{x}-\bar{y}}{\sqrt{\frac{\sigma_x^2}{n_x}+\frac{\sigma_y^2}{n_y}}}\\\\[/tex]
[tex]=\frac{960-945}{\sqrt{\frac{14^2}{20}+\frac{13^2}{20}}}\\\\=\frac{15}{\sqrt{\frac{196}{20}+\frac{169}{20}}}\\\\=\frac{15}{\sqrt{\frac{196+169}{20}}}\\=\frac{15}{\sqrt{\frac{365}{20}}}\\\\=\frac{15}{\sqrt{18.25}}\\\\=\frac{15}{4.27}\\\\=3.51[/tex]
Related Questions
What is the area of a square that has 2/4 units on each side
Answers
Answer:
1/4 of 0.25
Step-by-step explanation:
2/4 x 2/4 = 1/4
Verify the following identity and show steps
(Cos2 θ)/(1+sin2 θ)= (cot θ-1)/(cot θ+1)
Answers
Answer:
Verified below
Step-by-step explanation:
We want to show that (Cos2θ)/(1 + sin2θ) = (cot θ - 1)/(cot θ + 1)
In trigonometric identities;
Cot θ = cos θ/sin θ
Thus;
(cot θ - 1)/(cot θ + 1) gives;
((cos θ/sin θ) - 1)/((cos θ/sin θ) + 1)
Simplifying numerator and denominator gives;
((cos θ - sin θ)/sin θ)/((cos θ + sin θ)/sin θ)
This reduces to;
>> (cos θ - sin θ)/(cos θ + sin θ)
Multiply top and bottom by ((cos θ + sin θ) to get;
>> (cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ)
In trigonometric identities, we know that;
cos 2θ = (cos² θ - sin²θ)
cos²θ + sin²θ = 1
sin 2θ = 2sinθcosθ
Thus;
(cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ) gives us:
>> cos 2θ/(1 + sin 2θ)
This is equal to the left hand side.
Thus, it is verified.
Canadians who visit the United States often buy liquor and cigarettes, which are much cheaper in the United States. However, there are limitations. Canadians visiting in the United States for more than 2 days are allowed to bring into Canada one bottle of liquor and one carton of cigarettes. A Canada Customs agent has produced the following joint probability distribution of the number of bottles of liquor and the number of cartons of cigarettes imported by Canadians who have visited the United States for 2 or more days.
a. Find the marginal probability distribution of the number of bottles imported.
P(0 Bottles) =
P(1 Bottle) =
b. Find the marginal probability distribution of the number of cigarette cartons imported.
P(0 Cartons) =
P(1 Carton) =
c. Compute the mean and variance of the number of bottles of liquor imported.
Mean =
Variance =
d. Compute the mean and variance of the number of cigarette cartons imported.
Mean =
Variance =
e. Compute the covariance and the coefficient of correlation.
Covariance =
Coefficient of Correlation =
Answers
Answer:
(a): Marginal pmf of x
[tex]P(0) = 0.72[/tex]
[tex]P(1) = 0.28[/tex]
(b): Marginal pmf of y
[tex]P(0) = 0.81[/tex]
[tex]P(1) = 0.19[/tex]
(c): Mean and Variance of x
[tex]E(x) = 0.28[/tex]
[tex]Var(x) = 0.2016[/tex]
(d): Mean and Variance of y
[tex]E(y) = 0.19[/tex]
[tex]Var(y) = 0.1539[/tex]
(e): The covariance and the coefficient of correlation
[tex]Cov(x,y) = 0.0468[/tex]
[tex]r \approx 0.2657[/tex]
Step-by-step explanation:
Given
x = bottles
y = carton
See attachment for complete question
Solving (a): Marginal pmf of x
This is calculated as:
[tex]P(x) = \sum\limits^{}_y\ P(x,y)[/tex]
So:
[tex]P(0) = P(0,0) + P(0,1)[/tex]
[tex]P(0) = 0.63 + 0.09[/tex]
[tex]P(0) = 0.72[/tex]
[tex]P(1) = P(1,0) + P(1,1)[/tex]
[tex]P(1) = 0.18 + 0.10[/tex]
[tex]P(1) = 0.28[/tex]
Solving (b): Marginal pmf of y
This is calculated as:
[tex]P(y) = \sum\limits^{}_x\ P(x,y)[/tex]
So:
[tex]P(0) = P(0,0) + P(1,0)[/tex]
[tex]P(0) = 0.63 + 0.18[/tex]
[tex]P(0) = 0.81[/tex]
[tex]P(1) = P(0,1) + P(1,1)[/tex]
[tex]P(1) = 0.09 + 0.10[/tex]
[tex]P(1) = 0.19[/tex]
Solving (c): Mean and Variance of x
Mean is calculated as:
[tex]E(x) = \sum( x * P(x))[/tex]
So, we have:
[tex]E(x) = 0 * P(0) + 1 * P(1)[/tex]
[tex]E(x) = 0 * 0.72 + 1 * 0.28[/tex]
[tex]E(x) = 0 + 0.28[/tex]
[tex]E(x) = 0.28[/tex]
Variance is calculated as:
[tex]Var(x) = E(x^2) - (E(x))^2[/tex]
Calculate [tex]E(x^2)[/tex]
[tex]E(x^2) = \sum( x^2 * P(x))[/tex]
[tex]E(x^2) = 0^2 * 0.72 + 1^2 * 0.28[/tex]
[tex]E(x^2) = 0 + 0.28[/tex]
[tex]E(x^2) = 0.28[/tex]
So:
[tex]Var(x) = E(x^2) - (E(x))^2[/tex]
[tex]Var(x) = 0.28 - 0.28^2[/tex]
[tex]Var(x) = 0.28 - 0.0784[/tex]
[tex]Var(x) = 0.2016[/tex]
Solving (d): Mean and Variance of y
Mean is calculated as:
[tex]E(y) = \sum(y * P(y))[/tex]
So, we have:
[tex]E(y) = 0 * P(0) + 1 * P(1)[/tex]
[tex]E(y) = 0 * 0.81 + 1 * 0.19[/tex]
[tex]E(y) = 0+0.19[/tex]
[tex]E(y) = 0.19[/tex]
Variance is calculated as:
[tex]Var(y) = E(y^2) - (E(y))^2[/tex]
Calculate [tex]E(y^2)[/tex]
[tex]E(y^2) = \sum(y^2 * P(y))[/tex]
[tex]E(y^2) = 0^2 * 0.81 + 1^2 * 0.19[/tex]
[tex]E(y^2) = 0 + 0.19[/tex]
[tex]E(y^2) = 0.19[/tex]
So:
[tex]Var(y) = E(y^2) - (E(y))^2[/tex]
[tex]Var(y) = 0.19 - 0.19^2[/tex]
[tex]Var(y) = 0.19 - 0.0361[/tex]
[tex]Var(y) = 0.1539[/tex]
Solving (e): The covariance and the coefficient of correlation
Covariance is calculated as:
[tex]COV(x,y) = E(xy) - E(x) * E(y)[/tex]
Calculate E(xy)
[tex]E(xy) = \sum (xy * P(xy))[/tex]
This gives:
[tex]E(xy) = x_0y_0 * P(0,0) + x_1y_0 * P(1,0) +x_0y_1 * P(0,1) + x_1y_1 * P(1,1)[/tex]
[tex]E(xy) = 0*0 * 0.63 + 1*0 * 0.18 +0*1 * 0.09 + 1*1 * 0.1[/tex]
[tex]E(xy) = 0+0+0 + 0.1[/tex]
[tex]E(xy) = 0.1[/tex]
So:
[tex]COV(x,y) = E(xy) - E(x) * E(y)[/tex]
[tex]Cov(x,y) = 0.1 - 0.28 * 0.19[/tex]
[tex]Cov(x,y) = 0.1 - 0.0532[/tex]
[tex]Cov(x,y) = 0.0468[/tex]
The coefficient of correlation is then calculated as:
[tex]r = \frac{Cov(x,y)}{\sqrt{Var(x) * Var(y)}}[/tex]
[tex]r = \frac{0.0468}{\sqrt{0.2016 * 0.1539}}[/tex]
[tex]r = \frac{0.0468}{\sqrt{0.03102624}}[/tex]
[tex]r = \frac{0.0468}{0.17614266944}[/tex]
[tex]r = 0.26569371378[/tex]
[tex]r \approx 0.2657[/tex] --- approximated
A decimal that stops (like 2.48) is which type of number?
A.rational
B.whole number
C.irrational
D.integer
Answers
Answer: B rational
Step-by-step explanation:
if y=12 and x=89, then what is the value of z?
Answers
Answer:
z = 166°
Step-by-step explanation:
Given:
x = 89
y = 12
An angle with its vertex in a circle = ½(intercepted arcs)
Thus:
x = ½(y + z)
Substitute
89 = ½(12 + z)
Multiply both sides by 2
2(89) = 12 + z
178 = 12 + z
178 - 12 = z
z = 166°
WILL GIVE BRAINLIEST!!! No LINKS or REPORT!!!
Answers
The formula is:
V= (3.14)π⋅ (radius)r^2⋅(height)h/3
(^2 is a exponent)
How to solve:
π ·2^2· 9/3= 37.69911
(Round to the nearest tenth)
37.7I just did this one and i got it right
Quick answers please!!!!!!
I literally have no idea
Answers
Answer:
The solution to this question is 104.25cm²
Step-by-step explanation:
u
Answer:
hi
Step-by-step explanation:
i think so
A=
[tex] = \pi \times {r}^{2} [/tex]
=3,14×5,76²=104,177
hope it helps
have a nice day
Find the area of the shaded region in the figure below, if the radius of the outer circle is 8 and the radius of the inner circle is 4. Keep your answer in terms of π.
Answers
Answer:
48 π
Step-by-step explanation:
Area of Circle =πr∧2
Big Circle Area = π(8)∧2 = 64π
Small Circle Area =π(4)∧2= 16π
Shaded Region = 64π - 16π = 48π
A circle with a diameter of 10 has its center in the first quadrant. The lines y = -3 and x = -1 are tangent to the circle. Write an equation of the circle.
Answers
Answer:
34
Step-by-step explanation:
Answer:
(h,k)=(-1,-3)
radius =10/2=5 unit
equation of the circle
(x-h)² +(y-k)²=r²
(x+1)²+(y+3)²=25 is a required equation..
A race is 6.75 kilometers long. What is the distance of this race in meters?
Answers
Answer:
6750 meters
Step-by-step explanation:
1 kilometer = 1000 meters
1000*6.75=6750
Answer:
6750 meters
Step-by-step explanation:
Kilometers are equal to 1000 meters, so we can just multiply 6.75 x 1000 to get 6750 meters
at first an athlete jogs at 4 miles per hr and then jogs at 6 miles per hour, traveling 8 miles in 1.5 hours. how long does the athlete jogs at each speed? the athlete jogged ? hours at a speed of 4 miles per hr and ? hour(s) at a speed of 6 miles per hour?
Answers
Answer:
The athlete jogged at 4 miles per hour for 30 minutes, and jogged at 6 miles per hour for 1 hour.
Step-by-step explanation:
Given that at first an athlete jogs at 4 miles per hour and then jogs at 6 miles per hour, traveling 8 miles in 1.5 hours, to determine how long does the athlete jogs at each speed the following calculation must be performed:
4 x 1.5 + 6 x 0 = 6
4 x 1 + 6 x 0.5 = 7
4 x 0.75 + 6 x 0.75 = 7.5
4 x 0.5 + 6 x 1 = 8
Therefore, the athlete jogged at 4 miles per hour for 30 minutes, and jogged at 6 miles per hour for 1 hour.
The irrational number square root 67 is less than [blank]
Answers
Answer:
The square root of 67 is less than the whole number of 9
Step-by-step explanation:
8 squared is 64
9 squared is 81
67 is in between them
Solve by substitution: y=3x and x+y=-32
Answers
Answer:
X=-8, y=-24
Step-by-step explanation:
Y=3x
x+y=-32
substitute value of y (3x) from first equation to the second equation
x+3x=-32
4x=-32
x=-8
solve for y by putting value of x (-8) into either equation
y=3x
y=3(-8)
y=-24
0r
x+y=32
-8+y=-32
y=-24
Without solving, tell what is true of the product of 3 and 2/3 =?
Answers
Answer:
3 is a whole number while 2/3 is less than 3
Step-by-step explanation:
whats 1girl + 1 girl=
Answers
Answer:
(whats 1girl + 1 girl=) uhh ima go with 2girl ;)
Step-by-step explanation:
whats 1girl + 1 girl=?
well 1+1=2 so 1girl + 1 girl= 2girl
If you wanted to put a fence around your garden, would you find the perimeter or the area of the garden??
Answers
Answer:
U would find the perimeter.
Step-by-step explanation:
A circle passes through the points (3,2) and (7,2) and has radius 2√2. Find the two possible equations for this circle
Answers
Answer:
18 because of its addition
Step-by-step explanation:
πr²=3+2+7+2+2+2
=5+9+4
=18
Giving Brainlest !!!!! If your bank offered you 3% interest on $5,000 in your savings account , how much money would you have in your account at the end of the year after interest ?
Answers
Answer: $5,150
Step-by-step explanation:
5000x0.03=150+5000=5,150
The correct expression for a number which is 9 times as big as the number obtained after p has been increased
by 4
Answers
Answer:
9(p + 4)
Step-by-step explanation:
One of the unknown variable is p.
First of all, we know that the number is 9 times as big (multiplication) as the new number obtained through the addition of four to p i.e (p + 4).
Translating the word problem into an algebraic expression, we have;
9 * (p + 4) = 9(p + 4)
Simplifying further, we have;
9p + 36
Helppp plssssssssssss
Answers
Answer:
The answer is C
Step-by-step explanation:
If you plot them carefully.
PLS HELP FAST ITS THE LAST DAY TO DO THIS TEST NO LINKSSSS
An electrician charges $40 per hour plus an initial service fee of $75. He charges a customer $195 for 3 hours of work.
When this linear relationship is graphed, which value represents the slope?
A. 3
B. 40
C. 75
D. 195
Answers
Answer:
40 because every hour he charges 40 dollas so its 40x+75=y
Step-by-step explanation:
The slope is 40 because every hour he charges 40 dollars so its 40x+75=y
We have given that,
An electrician charges $40 per hour plus an initial service fee of $75. He charges a customer $195 for 3 hours of work.
We have to determine,
When this linear relationship is graphed, which value represents the slope.
What is the slope?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as a rising overrun.
The slope is 40 because every hour he charges 40 dollars so its 40x+75=y
To learn more about slope visit:
https://brainly.com/question/3493733
#SPJ2
PLSS HELPPPPPPPPPPPP
Answers
Answer:
c Melindas account will have about 5.40 more than olivia's account
Step-by-step explanation:
Sofia asked 50 students at her school whether they prefer music class or art class as an
elective. This table shows the relative frequencies from the survey.
Answers
Answer:
1 and 4
or say it as
More seventh graders prefer art class to music class as an elective
There is no association between a student's grade level and the electives they prefer
24. ZABC and ZDEF are linear pairs. Which of the following is true?
a. If m ABC = 2m DEF, then m ABC = 120 and m DEF = 60.
b. If m ABC = m DEF + 40, then m ABC = 140 and m DEF = 40.
c. If m ABC = m DEF - 30, then m ABC = 30 and m DEF = 150.
d. If m ABC = 3m DEF, then m ABC = 130 and m DEF = 60.
Answers
4. What number comes next. Whats my rule?
34,41,. 55,63,
Whats my rule?
(2 Points)
Enter your answer
Answers
The function g is defined by g(x) = x² +4.
Find g(5n)
Answers
Answer:
g(5n)=5n^2+4
Step-by-step explanation:
Substitute 5n for x
5n^2+4
You can't really do much with this so that is the answer
someone anwser this please
Answers
Square root 81 = one side length = 9m volume = 9^3 = 729
Dominic is going to invest $1,800 and leave it in an account for 17 years. Assuming the interest is compounded annually, what interest rate, to the nearest tenth of a percent, would be required in order for Dominic to end up with $4,700?
Answers
Answer: 5.8%
Step-by-step explanation: got it right lol
Name 4 points that would form a square with the origin at is center.
Answers
9514 1404 393
Answer:
(2, 3), (-3, 2), (-2, -3), (3, -2)
Step-by-step explanation:
You can pick any point you like, then rotate it around the origin to the four quadrants (or axes) by the transformation ...
(x, y) ⇒ (-y, x) . . . . . . . . . 90° rotation CCW
That is a rotation 90° CCW. Of course a rotation CW can do the same thing for you.
__
One possible square is ...
(2, 3), (-3, 2), (-2, -3), (3, -2)
Acellus
Find Y.
Round to the nearest tenth.
20 ft/
\22 ft
Y
Х 18 ft
Y= [? ]°
Law of Cosines: c2 = a2 + b2 - 2ab cos C
Enter
Answers
Answer:
58.9
Step-by-step explanation:
y²=x²+z²-2×z cos(y)
20²=22²+18²-2(22)(18) cos (y)
400=484+324-792 cos(y)
-408=-772 cos (y)
408/792=cos y
y=cos⁻¹(408/792)=58.9
hope it helps...
have a great day!!