A sprinkler system is being installed in a newly renovated building on campus. The average activation time is supposed to be at most 20 seconds. A series of 12 fire alarm/sprinkler system tests results in an average activation time of 21.5 seconds. Do these data indicate that the design specifications have not been met? The hypotheses to be tested are H0: m = 20 versus Ha: m > 20, where m = the true average activation time of the sprinkler system. Assume that activation times for this system are Normally distributed with s = 3 seconds.
(a) What is the value of the observed test statistic?
(b) What is the value of the P-value?
(c) Are the data statistically significant at the 5% significance level? Explain briefly.
(d) What does the decision you made mean with respect to the question "Do these data indicate that the design specifications have not been met?"
(e) If the true average activation time of the sprinkler system is, in fact, equal to 20 seconds, what type of error would you have made?
Answers
Answer:
A) t = 1.73
B) p-value = 0.0558
C) Data is not statistically significant because the p-value of 0.0558 is more than the significance value of 0.05
D) The decision means that the design specifications are not met.
E) Type II error
Step-by-step explanation:
The hypotheses are:
H₀: μ = 20
H₁: μ > 20
A) Formula for the test statistic is;
t = (x' - μ)/(s/√n)
Now, we are given;
x' = 21.5
μ = 20
s = 3
n = 12
Thus;
t = (21.5 - 20)/(3/√12)
t = 1.73
B) we have our t-value as 1.73
Now, Degree of freedom(DF) = n - 1
So,DF = 12 - 1 = 11
Using significance level of α = 0.05, t-value = 1.73 and DF = 11, one tailed hypothesis, from online P-value calculator attached, we have;
p-value = 0.0558
C) Data is not statistically significant because the p-value of 0.0558 is more than the significance value of 0.05
D) We will not reject the null hypothesis. The decision means that the design specifications are not met.
E) If the true average activation time of the sprinkler system is, in fact, equal to 20 seconds, then the null hypothesis is false.
Since we did not reject the null hypothesis even though it is false, the error that was committed was therefore a type II error.
Related Questions
and is in group 38 Rock she can put them into groups of 10 rocks or as single rocks what are the different ways Ann can group the rocks?
and is grouping 38 rocks she can put them into groups of 10 rocks or has single rocks what are the different ways and can group The Rocks
Answers
Answer:
She can put the rocks into groups of 19.
That would give her 2 groups.
Step-by-step explanation:
Let f(x)=x^3-6x+3 i. find the domain of the function and f’(x) in the domain.
Answers
Domain of a any cubic function [tex]f(x)=ax^3+bx^2+cx+d[/tex] is defined to be always [tex]\mathbb{R}[/tex].
The derivative with respect to x of your cubic function is,
[tex]\dfrac{d}{dx}f(x)=f'(x)[/tex]
to find the derivative of a polynomial function, simply take a derivative of each factor and sum them up,
[tex]\dfrac{d}{dx}x^3=3x^2[/tex] by the rule [tex]\dfrac{d}{dx}x^m=mx^{m-1}[/tex] where [tex]m\in\mathbb{R}[/tex]
[tex]\dfrac{d}{dx}-6x=-6[/tex]
[tex]\dfrac{d}{dx}3=0[/tex]
So the derivative is,
[tex]f'(x)=3x^2-6[/tex]
both derivative and the original function have equal domain.
Hope this helps :)
Step-by-step explanation:
[tex]thank \: you[/tex]
PLEASE HELP!!
Solve for y
a) 8
b) 12
c) 3V7
d) 4V7
Answers
Answer:
C. [tex] y = 3\sqrt{7} [/tex]
Step-by-step explanation:
Based on the right triangle altitude theorem, the altitude, y, in the diagram above, equals the geometric mean of 9 and 7.
This implies => [tex] y = \sqrt{9*7} [/tex]
Thus, solve for y.
[tex] y = \sqrt{9} * \sqrt{7} [/tex]
[tex] y = 3\sqrt{7} [/tex]
The answer is C. [tex] y = 3\sqrt{7} [/tex]
The work shows how to use long division to find?
Answers
Answer:
remainder = [tex]\frac{1}{x-2}[/tex]
Step-by-step explanation:
The remainder is the value of the subtraction of the last 2 lines in the procedure.
5x - 9
- (5x - 10)
That is
5x - 5x = 0 and - 9 - (- 10) = - 9 + 10 = 1
over the divisor x- 2 , gives
remainder = [tex]\frac{1}{x-2}[/tex]
After a 75% reduction, you purchase a new clothes dryer for $200. What was the original price of the clothes dryer?
Answers
Answer:
$800
Step-by-step explanation:
Let the original price be $x.
75% reduction ----- 100% -75%= 25%
25%x= 200
[tex] \frac{25}{100} x = 200 \\ x = 200 \div \frac{25}{100} \\ x = 200 \times \frac{100}{25} \\ x = 800[/tex]
Thus, the original price of the clothes dryer is $800.
Answer:
$800
Step-by-step explanation:
Let the original price be x.
Final price=100%-75%
=25%
x-75%=200
x=200 x 100/75
x=8 x 100
x=800
Thank you!
In the figure, ∆BAT ≅ ∆CAT. Which statement is not true by CPCTC? ∠BTA ≅ ∠CTA ∠BAT ≅ ∠CAT
Answers
Answer:
The two choices are true by CPCTC. Are there other choices that were not posted?
Question 1: A triangle has sides with lengths 5, 6, and 7. Is the triangle right, acute, or obtuse?
A)Right
B)Obtuse
C)Can't be determined
D) Acute
Question 2: A 15-foot statue casts a 20-foot shadow. How tall is a person who casts a 4-foot-long shadow?
A)0.33 feet
B)3.75 feet
C)3 feet
D)5 feet
Question 3: A triangle has sides with lengths 17, 12, and 9. Is the triangle right, acute, or obtuse?
A)Acute
B)Right
C)Can't be determined
D)Obtuse
Question 4: Two friends are standing at opposite corners of a rectangular courtyard. The dimensions of the courtyard are 12 ft. by 25 ft. How far apart are the friends?
A)21.34 ft.
B)21.93 ft.
C)27.73 ft.
D)19.21 ft.
Answers
Answer:
Question 1 = D) Acute
Question 2 = C)3 feet
Question 3 = D) Obtuse
Question 4 = C)27.73 ft.
Step-by-step explanation:
Question 1: A triangle has sides with lengths 5, 6, and 7. Is the triangle right, acute, or obtuse?
In order to be able to accurately classify that a triangle with 3 given sides is either a right , acute or obtuse angle, we use the Pythagoras Theorem
Where:
If a² + b² = c² = Right angle triangle
If a² +b² > c² = Acute triangle.
If a² +b² < c² = Obtuse triangle.
It is important to note that the length ‘‘c′′ is always the longest.
Therefore, for the above question, we have lengths
5 = a, 6 = b and c = 7
a² + b² = c²
5² + 6² = 7²
25 + 36 = 49
61 = 49
61 ≠ 49, Hence 61 > 49
Therefore, this is an Acute Triangle
Question 2: A 15-foot statue casts a 20-foot shadow. How tall is a person who casts a 4-foot-long shadow?
This is question that deals with proportion.
The formula to solve for this:
Height of the statue/ Length of the shadow of the person = Height of the person/ Length of the shadow of the person
Height of the statue = 15 feet
Length of the shadow of the person = 20 feet
Height of the person = unknown
Length of the shadow of the person = 4
15/ 20 = Height of the person/4
Cross Multiply
15 × 4 = 20 × Height of the person
Height of the person = 15 × 4/20
= 60/20
Height of the person = 3 feet
Therefore, the person is 3 feet tall.
Question 3: A triangle has sides with lengths 17, 12, and 9. Is the triangle right, acute, or obtuse?
In order to be able to accurately classify that a triangle with 3 given sides is either a right , acute or obtuse angle, we use the Pythagoras Theorem
Where:
If a² + b² = c² = Right angle triangle
If a² +b² > c² = Acute triangle.
If a² +b² < c² = Obtuse triangle.
It is important to note that the length ‘‘c′′ is always the longest.
Therefore, for the above question, we have lengths 17, 12, 9
9 = a, 12 = b and c = 17
a² + b² = c²
9² + 12² = 17²
81 + 144 = 289
225 = 289
225 ≠ 289
225 < 289
Hence, This is an Obtuse Triangle.
Question 4: Two friends are standing at opposite corners of a rectangular courtyard. The dimensions of the courtyard are 12 ft. by 25 ft. How far apart are the friends?
To calculate how far apart the two friends are we use the formula
Distance = √ ( Length² + Breadth²)
We are given dimensions: 12ft by 25ft
Length = 12ft
Breadth = 25ft
Distance = √(12ft)² + (25ft)²
Distance = √144ft²+ 625ft²
Distance = √769ft²
Distance = 27.730849248ft
Approximately ≈27.73ft
Therefore, the friends are 27.73ft apart.
I need help on this question :(
Answers
Explanation:
FT bisect angle EFD dividing it into 2 equal angles (EFT and DFT)
And EFD = 80
We get :
EFT = 80/2
EFT = 40
And EFT + DFT = EFD = 80 degree
Therefore EFT = 40 degrees
Rhombus J K L M is shown. The length of J K is 2 x + 4 and the length of J M is 3 x. What is the length of a side of rhombus JKLM? 4 units 8 units 12 units 16 units
Answers
Answer:
12 units
Step-by-step explanation:
Since all of the sides of a rhombus are congruent, JK = JM which means:
2x + 4 = 3x
-x = -4
x = 4 so 3x = 3 * 4 = 12
What's 955 ÷ 35 ?
[tex]955 \div 35[/tex]
Answers
Answer:
Hello
Step-by-step explanation:
955÷35
27.2857142857
Or
35/955
35)955(27
-945
________
10
I hope this works♥️
Evaluate cosA/2 given cosA=-1/3 and tanA >0
Answers
Answer:
[tex]\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}[/tex]
Step-by-step explanation:
Given that:
[tex]cosA=-\dfrac{1}3[/tex]
and
[tex]tanA > 0[/tex]
To find:
[tex]cos\dfrac{A}{2} = ?[/tex]
Solution:
First of all,we have cos value as negative and tan value as positive.
It is possible in the 3rd quadrant only.
[tex]\dfrac{A}{2}[/tex] will lie in the 2nd quadrant so [tex]cos\dfrac{A}{2}[/tex] will be negative again.
Because Cosine is positive in 1st and 4th quadrant.
Formula:
[tex]cos2\theta =2cos^2(\theta) - 1[/tex]
Here [tex]\theta = \frac{A}{2}[/tex]
[tex]cosA =2cos^2(\dfrac{A}{2}) - 1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =cosA+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =-\dfrac{1}3+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =\dfrac{2}3\\\Rightarrow cos(\dfrac{A}{2}) = \pm \dfrac{1}{\sqrt3}[/tex]
But as we have discussed, [tex]cos\dfrac{A}{2}[/tex] will be negative.
So, answer is:
[tex]\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}[/tex]
1.1.3 what is the the perimeter of a swimming pool if the length is 4,5m and the breadth is 3m? 1.1.4 Define the following concepts :a. Ratio. b. Rate
Answers
The perimeter of the swimming pool is 15m
A swimming pool is rectangular in nature. The perimeter of the rectangular pool is expressed using the formula;
[tex]P=2(L+W)[/tex]
Given that
Length L = 4.5m
Width W = 3m
Get the perimeter
[tex]Perimeter = 2(4.5+3)\\Perimeter = 2(7.5)\\Perimeter = 15m[/tex]
Hence the perimeter of the pool is 15m
1.1.4 Rate is defined as the ratio between two quantities with a different unit. Examples of rates are;
meter per second, miles per hourcalories per serving etcThe ratio is simply defined as the ordered pair between two variables x and y, For instance,
The ratio of x to y is x:y.If there are 5 pencils and 2 pens in a carton, then the ratio of the pencil to pen is 5:2.Learn more on ratio and rate here: https://brainly.com/question/24325733
Apply the square root principle to solve (x-5)^2-40=0
Answers
Answer: {5 ± 2√10, 5 - 2√10}
Step-by-step explanation: First isolate the binomial squared by adding 40 to both sides to get (x - 5)² = 40.
Next, square root both sides to get x - 5 = ± √40.
Notice that root of 40 can be broken down to 2√10.
So we have x - 5 = ± 2√10.
To get x by itself, add 5 to both sides to get x = 5 ± 2√10.
So our answer is just {5 ± 2√10, 5 - 2√10}.
As a matter of form, the number will always come before the
radical term in your answer to these types of problems.
In other words, we use 5 ± 2√10 instead of ± 2√10 + 5.
I am performing a before and after evaluation on 30 students who have taken a keyboarding class. I want to see if the course improved their words per minute keyed.
Required:
a. State the Null and Alternate Hypothesis.
b. The statistic that I would use is:_________
c. What would my t critical be for this calculation at a 0.10 level of significance?
d. If my t calculated = 1.62, would I reject or fail to reject the null hypothesis?
Answers
Answer:
a)
H₀ : µd = 0
H₁ : µd < 0
b)
The test statistic is
tₙ₋₁ = α / s√n
c)
at 0.10 level of significance,
tₙ₋₁ , ₐ
t₃₀₋₁ , ₀.₁₀ = t₂₉, ₀.₁₀ = 1.311
d)
given that T(critical) = 1.62
∴ T(critical) = 1.62 > t₂₉, ₀.₁₀ = 1.311
at 10% level of significance,
REJECT H₀
Since 1.62 > 1.311, we can reject the null hypothesis.
1. In the past, Sam cashed his paycheck each month at Ready Cash, a check cashing service that
charges a 5% fee. He recently opened a checking account at Bank of America so he can now
deposit and/or cash his paycheck without a fee. If Sam is making $28,500 per year, how much will
he save by not going to Ready Cash anymore?
Answers
Step-by-step explanation:
28000 ÷ 100
=280
280 × 5
=1400
Find the length of GV¯¯¯¯¯¯¯¯ A. 43.92 B. 33.1 C. 41.45 D. 68.87
Answers
Answer:
The answer is option AStep-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find GV
To find GV we use cosine
cos∅ = adjacent / hypotenuse
From the question
GV is the adjacent
GC is the hypotenuse
So we have
[tex] \cos(37) = \frac{GV}{GC} [/tex]GC = 55°
GV[tex] \cos(37) = \frac{GV}{55} [/tex]GV = 55 cos 37
GV = 43.92495
We have the final answer as
GV = 43.92Hope this helps you
What should be added to p to get p+q?
Answers
Answer:
Step-by-step explanation:
The correct answer is q
Because we have been given the equation p + q already so if we observe the equation carefully we see that if we add the variable q to the variable p we get the answer p + q
What is the percentage of 204 over 1015, 1 over 8120, 1 over 5832, and 1 over 6?
Answers
Answer:
204/1015 (irreducible) = 20.1%
1/8120 (irreducible) = 0.01232%
1/5832 (irreducible) = 0.01715%
1/6 (irreducible) = 16.67%
Step-by-step explanation:
For the following graph, state the polar coordinate with a positive r and positive q (in radians). Explain your steps as to how you determined the coordinate (in your own words). I'm looking for answers that involve π, not degrees for your angles. State the polar coordinate with (r, -q). Explain how you found the new angle. State the polar coordinate with (-r, q). Explain how you found the new angle. State the polar coordinate with (-r, -q). Explain how you found the new angle.
Answers
Answer:
Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )
Step-by-step explanation:
For the first two cases, ( r, θ ) r would be > 0, where r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.
So when r is positive, we can tell that this point is 8 units from the pole, so r is going to be 8 in either case,
( 8, 240° ) - because r is positive, theta would have to be an angle with which it's terminal side passes through this point. As you can see that would be 2 / 3rd of 90 degrees more than a 180 degree angle,or 60 + 180 = 240 degrees.
( 8, - 120° ) - now theta will be the negative side of 360 - 240, or in other words - 120
Now let's consider the second two cases, where r is < 0. Of course the point will still be 8 units from the pole. Again for r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.
( - 8, 60° ) - theta will now be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Thus our second point for - r will be ( - 8, - 300° )
_________________________________
So we have the points ( 8, 240° ), ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). However we only want 3 cases, so we have points ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). Let's convert the degrees into radians,
Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )
Sharon tried to solve an equation step by step.
9
9
15
5
=−3(e−2)
=−3e+6
=3e
=e
Step 1
Step 2
Step 3
Find Sharon's mistake.
Choose 1 answer:
Choose 1 answer:
Answers
Answer:
step 2
Step-by-step explanation:
9 = -3(e - 2)
9 = -3e + 6
9-6 = -3e
3 = -3e
divide both sides by -3
-1 = e
Solve the right triangle.
a = 3.3 cm, b = 1.7 cm, C = 90°
Round values to one decimal place.
Answers
Answer:
A = 62.7°B = 27.3°c = 3.7Step-by-step explanation:
tan(A) = a/b = 3.3/1.7
A = arctan(33/17) ≈ 62.7°
B = 90° -A = 27.3°
c = √(a²+b²) = √(3.3² +1.7²) = √13.78
c ≈ 3.7
1/3 is part of which set of numbers?
Answers
Answer:
[tex] \frac{1}{3} [/tex]Rational number as denominator is not equal to zero and numerator is a integer.
Rational numbers. denoted by [tex] \mathbb Q[/tex]
1/3 is clearly not a natural number or integer.
it is a fraction, =0.333 , it fits the definition of rational number ([tex] \frac pq [/tex]).
For the functions f(x)=4x+5 and g(x)=6x+4, find (f∘g)(0) and (g∘f)(0).
Answers
Answer:
Step-by-step explanation:
f(g(0))=
g(0)= 6(0) + 4 = 0 + 4 = 4
f(4)= 4(4)+5 = 16 + 5 = 21
g(f(0))=
f(0)= 4(0)+5 = 0+5 = 5
g(5)= 6(5)+4 = 30+4= 34
Estimate the mean exam score for the 50 students in Prof. Burke's class.
Score
f
40 but less than 50
21
50 but less than 60
39
60 but less than 70
40
70 but less than 80
34
80 but less than 90
28
Total
162
Group of answer choices
65.56
63.78
64.89
62.34
Answers
The mean of the exam score is 65.56
The given exam data is as follows;
Possible Score range ----------- frequency (f) -------- score (x) -----------(fx)
40 - 50 ------------------------- 21 ------------------- -----45 -------------- 945
50 - 60 --------------------------- 39------------------------55 ---------------2145
60 - 70 ----------------------------- 40---------------------- 65 ---------------- 2600
70 - 80 ------------------------------ 34 --------------------- 75 ----------------- 2550
80 - 90 ------------------------------ 28 --------------------- 85 ---------------- 2380
Note:[tex]score (x) = \frac{sum \ of \ the \ range }{2} , \ example \ \frac{40+49.99}{2} \approx 45[/tex]
The sum of the frequency (f) = 162
The sum of fx, ∑fx = 10620
The mean of the exam score:
[tex]\bar x = \frac{\Sigma fx }{\Sigma f} = \frac{10620}{162} = 65.56[/tex]
Therefore, the mean of the exam score is 65.56
To learn more about grouped mean calculation please visit: https://brainly.in/question/20735794
Which geometric sequence has a first term equal to 55 and a common ratio of -5? {-55, 11, -2.2, 0.44, …} {55; 275; 1,375; 6,875; …} {55, 11, 2.2, 0.44, …} {55; -275; 1,375; -6,875; …}
Answers
Answer:
The answer is 55, -275, 1375, -6875......
Step-by-step explanation:
find the circle through (-4,sqrt(5) with center (0,0)
Answers
Answer:
Circle Equation : x² + y² = 21
Step-by-step explanation:
So we know that this circle goes through the point ( - 4, √5 ), with a center being the origin. Therefore, this makes the circle equation a bit simpler.
The first step in determining the circle equation is the length of the radius. Applying the distance formula, the radius would be the length between the given points. Another approach would be creating a right triangle such that the radius is the hypotenuse. Knowing the length of the legs as √5 and 4, we can calculate the radius,
( √5 )² + ( 4 )² = r²,
5 + 16 = r²,
r = √21
In general, a circle equation is represented by the formula ( x - a )² + ( y - b )² = r², with radius r centered at point ( a, b ). Therefore our circle equation will be represented by the following -
( x - 0 )² + ( y - 0 )² = (√21 )²
Circle Equation : x² + y² = 21
The weight of an object on moon is 1/6 of its weight on Earth. If an object weighs 1535 kg on Earth. How much would it weigh on the moon?
Answers
Answer:
255.8
Step-by-step explanation:
first
1/6*1535
=255.8
(x+y)^2 where x= 4 and y= -3
Answers
(4-3)^2
1*1
answer is 1
7th grade math!!! Please help!! will mark brainlist
Answers
The answer is the first choice. If every 2 cm. is 4 cm., that means that the dimensions' values are doubled. Then, you can just double the dimensions. Preferably, in my opinion, this is the easier way to go. By your preference, though, you can do it the longer way as well.
There are 4 2s in the number 8.
There are 3 2s in the number 6.
If each of the 2s are 4s,
So, therefore,
Transforming the 2s to 4s,
4x4=16 cm.
3x4=12 cm.
So, this means that the final answer is the first choice. I hoped that this helped answer your question. Enjoy your day, and take care!
Answer:
`Length=16 feet, width=12 feet
Image result for how to use scale model step by step'
Divide the real life dimension of either length or width by that of the model. So the real life object had a length of 32m, and the model had a length of 8, then do 8(4). This is equal to 32, then divide by 2.
Hope this helps love <3
A city is holding a referendum on increasing property taxes to pay for a new high school. In a survey of 434 likely voters, 202 said that they would vote "yes" on the referendum. Create a 95% confidence interval for the proportion of likely voters who would vote "yes" on the referendum. Use a TI-83, TI-83 plus, or TI-84 calculator, rounding your answers to three decimal places.
Answers
Answer: 0.418 < p < 0.512
Step-by-step explanation: A 95% conifdence interval for a population proportion is given by:
[tex]p + z\sqrt{\frac{p(1-p)}{n} }[/tex]
where:
p is the proportion
z is score in z-table
n is sample size
The proportion for people who said "yes" is
[tex]p=\frac{202}{434}[/tex] = 0.465
For a 95% confidence interval, z = 1.96.
Calculating
[tex]0.465 + 1.96*\sqrt{\frac{0.465(0.535)}{434} }[/tex]
[tex]0.465 + 1.96*\sqrt{0.00057}[/tex]
0.465 ± 1.96*0.024
0.465 ± 0.047
Interval is between:
0.465 - 0.047 = 0.418
0.465 + 0.047 = 0.512
The interval with 95% of confidence is between 0.418 and 0.512.