The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7 comma 539 hours. The population standard deviation is 840 hours. A random sample of 49 light bulbs indicates a sample mean life of 7 comma 359 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 7 comma 539 hours question mark b. Compute the p-value and interpret its meaning. c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. d. Compare the results of (a) and (c). What conclusions do you reach?
Answers
Answer:
a) Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 7539
b) \(t=\frac{7359-7539}{\frac{840}{\sqrt{49}}}=-1.5\)
The degrees of freedom are given by:
\(df=n-1=49-1=48\)
The p value is given by:
\(p_v =P(t_{(48)}<-1.5)=0.07\)
c) \(7359-2.01\frac{840}{\sqrt{49}}=7117.8\)
\(7359+2.01\frac{840}{\sqrt{49}}=7600.2\)
d) For this case since the confidence interval contains the value of 7539 we don't have enough evidence to reject the null hypothesis at the significance level given of 5%. same conclusion using the hypothesis test and with the confidence interval
Step-by-step explanation:
Part a and b
Data given
\(\bar X=7359\) represent the sample mean
\(\sigma=840\) represent the population standard deviation
\(n=49\) sample size
\(\mu_o =7539\) represent the value to test
t would represent the statistic
\(p_v\) represent the p value
Hypothesis to verify
We want to verify if the mean life is different from 7539 hours, the system of hypothesis would be:
Null hypothesis:\(\mu \geq 7539\)
Alternative hypothesis:\(\mu < 7539\)
The statistic for this case would be given by:
\(t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}\) (1)
Replacing the info given we got:
\(t=\frac{7359-7539}{\frac{840}{\sqrt{49}}}=-1.5\)
The degrees of freedom are given by:
\(df=n-1=49-1=48\)
The p value is given by:
\(p_v =P(t_{(48)}<-1.5)=0.07\)
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 7539
Part c
The confidence interval for the mean is given by the following formula:
\(\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}\) (1)
We can find the critical value using the confidence level given of 95% and using the t distribution with 48 degrees of freedom we got \(t_{\alpha/2}=\pm 2.01\)
Now we have everything in order to replace into formula (1):
\(7359-2.01\frac{840}{\sqrt{49}}=7117.8\)
\(7359+2.01\frac{840}{\sqrt{49}}=7600.2\)
Part d
For this case since the confidence interval contains the value of 7539 we don't have enough evidence to reject the null hypothesis at the significance level given of 5%. same conclusion using the hypothesis test and with the confidence interval
Related Questions
Computer programs are sold for $20 each if 300 people buy them. For every $5.00 increase increase in price, 30 fewer people buy them
Answers
Given that the cost of a computer program is $20 if 300 people buy them. For every $5.00 increase in price, 30 fewer people buy them. We need to find the relation between the price of computer programs and the number of people who will buy them.Relation between the price of computer programs and the number of people who will buy them can be represented in a table:Price per program .
Number of people who buy them$20 300$25 270$30 240$35 210$40 180$45 150$50 120Note that with each $5.00 increase in price, 30 fewer people buy the computer program.
Hence, the number of people who will buy the computer program will reduce by 30 with each $5.00 increase in price.
For instance, if the price increases from $20 to $25, the number of people who will buy it will reduce by 30 and be 270.
In conclusion, we can say that with every $5.00 increase in price, the number of people buying computer programs reduces by 30.
The relation between the price of computer programs and the number of people who will buy them can be represented in a table.
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Simple Random Sample of Size 25:
Chances are, since you are studying AP Statistics, you plan to earn at least a bachelor's degree from college. According to the U.S. Census Bureau, 29% of Americans age 25 years or older have already earned a bachelor's or more advanced degree. You decide to randomly select 58 adults over the age of 25 to ask if they have earned at least a bachelor's degree. Describe the sampling distribution of the proportion of respondents who have earned at least a bachelor's degree.
Answers
Answer:
By the Central Limit Theorem, it is approximately normal with mean 0.29 and standard deviation 0.0596
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
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 \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)
According to the U.S. Census Bureau, 29% of Americans age 25 years or older have already earned a bachelor's or more advanced degree.
This means that \(p = 0.29\)
You decide to randomly select 58 adults over the age of 25 to ask if they have earned at least a bachelor's degree.
This means that \(n = 58\)
Describe the sampling distribution of the proportion of respondents who have earned at least a bachelor's degree.
By the Central Limit Theorem, it is approximately normal with mean \(\mu = p = 0.29\) and the standard deviation is \(s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.29*0.71}{58}} = 0.0596\)
PLEASE HELP IN THE NEXT 15 MINUTES!!!!!!!!!!
The Cross Bayou Bridge in Shreveport, Louisiana has trusses that form triangles. The exterior angle of one triangle has a measure of (5 - 3)°. If the two nonadiacent interior angles of the triangle are 43° and (3x)°, what is the value of the exterior angle, in degrees?
Answers
The exterior angle of the triangle is 62°.
What is triangle?
A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.
Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.
Let us take the triangle as ABC.
Here \(m\angle C\)= 180-(5x-3)° [Because straight line angle is 180°].
We know that sum of all angles in triangle is add upto 180° Then,
=> \(m\angle A+m\angle B+m\angle C\)=180
=> 43°+3x°+180-5x+3=180°
=> -2x=180-180-43-3
=> -2x=-46
=> x=13°
Now exterior angle ,
=> 5x-3
=> 5*13-3
=> 65-3
=> 62°
Hence the exterior angle of the triangle is 62°.
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Ten posts were used to secure the fence. A hole was dug for each post and a total of 23.5 pounds of concrete were poured into the holes. An equal amount of concrete was poured into each hole. How much concrete was poured into each hole?
Answers
The amount of concrete poured into each hole is given by A = 2.35 pounds
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the amount of concrete poured into each hole be A
Now , the total amount of concrete = 23.5 pounds
Ten posts were used to secure the fence. A hole was dug for each post.
So , the total number of holes = 10 holes
Now , the amount of concrete poured into 10 holes = total amount of concrete / 10
On simplifying the equation , we get
The amount of concrete poured into each hole is A = 23.5 / 10
The amount of concrete poured into each hole is A = 2.35 pounds
Hence , the equation is A = 2.35 pounds
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i need help with this question
Answers
Answer:(2I3O-9247)
Step-by-step explanation:
The parabola y=√x-4 (principal square root) opens: down left Right up
Answers
The parabola \(y = √(x - 4)\) opens upward.
The parabola y = √(x - 4) represents the square root function of x minus 4. To determine the direction in which the parabola opens, we examine the behavior of the square root function.
The square root function (√x) returns non-negative values for non-negative inputs. Since the expression inside the square root, (x - 4), must be non-negative for real solutions, we have x - 4 ≥ 0. Solving this inequality, we find x ≥ 4.
This means that the parabola is defined for x values greater than or equal to 4. As we increase x from 4, the value of √(x - 4) will also increase. Therefore, the graph of the parabola opens upward.
The parabola \(y = √(x - 4)\) opens upward.
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5) Choose which postulate proves the triangles congruent.
Answers
Answer:
AAS
Step-by-step explanation:
HEHE
ΔBAC and ΔDAC are the congruent triangles by ASA postulate of the congruence of two triangles.
In ΔBAC and ΔDAC,
Given properties are,
AC bisects ∠BADAC bisects ∠BCDBy using these properties,
∠BAD ≅ ∠DAC (Given)
∠BCA ≅ ∠DCB (Given)
AC ≅ AC (Reflexive property)
ΔBAC ≅ ΔDAC (ASA postulate of congruence of two triangles)
Therefore, ΔBAC and ΔDAC will be congruent by ASA postulate for the congruence of two triangles.
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Marco can paddle his canoe at a rate of 6 miles per hour on unmoving water. However, today Marco is canoeing down (with the current), and then back up (against the current), a river that's moving at a rate of 1 mile per hour, so the current affects his rate of speed. If it takes Marco 6 total hours to go x miles downstream and then return to his starting point, how far downstream does he travel?
A) 1.25 miles
B) 2.5 miles
C) 5 miles
D) 17.5 miles
Answers
Answer:
S = v1 t1 = 7 t1 traveling downstream
S = v2 t2 = 5 t2 traveling upstream
7 t1 = 5 t2
7 (6 - t2) = 5 t2 since t1 + t2 = 6
42 - 7 t2 = 5 t2
t2 = 42 / 12 = 3.5 hrs so t1 = 2.5 hrs
S = 7 t1 = 7 * 2.5 = 17.5 mi
Also, S = 5 t2 = 5 * 3.5 = 17.5 mi
100 POINTS PLEASE HELP
Answers
Answer:
The correct answer is (d) 1900.
Step-by-step explanation:
here's a step-by-step explanation of how to arrive at the correct answer:
Step 1: Identify the total expenses for the month of November
From the given ledger, we can see that there are two entries for expenses in the month of November: $1,000 on November 5 and $900 on November 15. To find the total expenses for the month, we add these two amounts: $1,000 + $900 = $1,900.
Step 2: Determine the balance of the expenses account
In the ledger, both entries for expenses are listed as debits. Since debits increase the balance of expense accounts, the balance of the expenses account is the total of the debits, which is $1,900.
Step 3: Create the closing entry
The purpose of the closing entry is to transfer the balance of the expenses account to the income summary account. Since the expenses account has a debit balance of $1,900, we need to credit the expenses account for this amount and debit the income summary account for the same amount. This will reduce the balance of the expenses account to zero and transfer the total expenses for the month to the income summary account. The closing entry is:
Expenses 1,900 (credit)
Income Summary 1,900 (debit)
Step 4: Check the options to find the correct answer
From the given options, we can see that option (d) 1900 is the correct answer, as it matches the amount of the closing entry we calculated in Step 3.
Therefore, the correct answer is (d) 1900.
Question 3 of 10
Which of the following shows the polynomial below written in descending
order?
5x3x+9x7+4+3x11
OA. 9x² + 5x³+4+3x¹¹ - x
OB. 3x¹¹ +9x7 + 5x³ − x + 4
OC. 3x¹1 +9x7-x+4+5x³
D. 4+ 3x¹¹+
D. 4+ 3x¹1 +9x7 + 5x³ - x
Answers
Answer:
B. 3x¹¹ +9x⁷ +5x³ −x +4
Step-by-step explanation:
You want to identify the polynomial that has terms written in descending order of their degree.
DegreeThe degree of a term is the exponent of x in that term. In the given polynomial, the term degrees are 3, 1, 7, 0, 11.
When these are put into descending order, that order is ...
11, 7, 3, 1, 0
Standard formThe answer to this question will be the polynomial with terms written in the order of their degree as shown above:
3x¹¹ +9x⁷ +5x³ −x +4
__
Additional comment
When the exponent of x is 0, the value of the term x^0 is 1. That is why we can say the constant term is a term that has the variable to degree 0.
<95141404393>
What’s the following sum?
Answers
\( \huge{ \orange{ \boxed{ \bold{6 \sqrt{5} }}}}\)
EXPLAINATION :
By following the rule in finding the sum or difference of similar radicals
\( \green{a \sqrt{c} \: + \: b \sqrt{c} \: = (a + b) \sqrt{c} }\)
Answer:
3.73
Step-by-step explanation:
LA and ZB are vertical angles. If m_A = (8x – 20) and m B = (3x – 5)º,
then find the value of x.
Answers
Answer:
52
Step-by-step explanation:
Angle A equals 4x+8
Angle B equals 5x-b
and they are vertical angles.
If so, vertical angels are equal. You can set the expressions equal to each other, solve for x, and plug that value back in to solve for A.
4x+8=5x-b
add 3 to both sides
4x+11=5x
subtract 4x from both sides
11=x
Then plug x=11 into 4x+8.
4(11)+8
44+8
52
A closet in Shivani's house is 2 yards by 1 yard. How much would it cost to put a new floor in the closet if the flooring costs $38.00 per square yard?
Answers
The amount it would cost to put a new floor in the closet is $76.00
Calculating how much it would cost to put a new floor in the closetFrom the question, we are to calculate how much it would cost to put a new floor in the closet
From the given information,
A closet in the house is 2 yards by 1 yard.
To determine how much it would cost to put a new floor in the closet,
First,
We calculate the area of the closet
Area of the closet = 2 yard × 1 yard
Area of the closet = 2 square yards
Now,
From the given information,
The flooring costs $38.00 per square yard
Thus,
The amount it would cost to put a new floor in the closet is
2 × $38.00
= $76.00
Hence,
The amount it would cost is $76.00
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What is the total weight of the bags that weighed /8 pound each?
Answers
The total weight of Rice that Mark buys is given as follows:
2.5 pounds.
How to obtain the total weight?The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.
The weight of each bag is given as follows:
5/8 pounds = 0.625 pounds.
The number of bags is given as follows:
4 bags.
Hence the total weight of Rice that Mark buys is given as follows:
4 x 0.625 = 2.5 pounds.
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Can someone help me with this please?
Answers
Answer:
The triangles are similar.
Explanation:
Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.
The vector w=ai+bj is perpendicular to the line ax+by=c and parallel to the line bx−ay=c. It is also true that the acute angle between intersecting lines that do not cross at right angles is the same as the angle determined by vectors that are either normal to the lines or parallel to the lines. Use this information to find the acute angle between the lines below.
2x+5y=4, 7x+3y=8
Answers
Answer:
The angle between the liens is 135 degree.
Step-by-step explanation:
Equation of first line
2 x + 5 y = 4 ...... (1)
Equation of second line
7 x + 3 y = 8 ..... (2)
The slope of a line is given by
\(m = \frac{- coefficient of x}{coefficient of y}\)
Slope of first line
\(m = -\frac {2}{5}\)
Slope of second line
\(m'= - \frac{7}{3}\)
The angle between the two lines is given by
\(tan\theta = \frac{m- m'}{1 + m m'}\\\\tan\theta = \frac{-\frac{2}{5}+\frac{7}{3}}{1+\frac{2}{5}\times \frac{7}{3}}\\\\tan\theta = -1 \\\\\theta = 135^o\)
Plzzzz help The variables p, q, and r are rational numbers with the following properties:
p>0, q<0, and r < 0.
Based upon the given information, select the option below where both expressions have a negative value.
A Op.p and s.r
B O qr and pa
C O qr and 7pr
D O pq and 7pr
Answers
Answer:
qr and pq
Step-by-step explanation:
find the 6th term of the geometric progressive (go) -108,-36,-12...
Answers
Answer:
-108, -36, -12, -3, -1, -.333333
Step-by-step explanation:
I need questions 10 , 13 , 15 , and 16 solved with steps and graph
Answers
10. |x - 4| - 4 = 1/2x
⇒ Multiplying by 2,
2 |x - 4| - 8 = x
So, x - 4 = (x + 8)/2
= -(x + 8)/2
When,
x - 4 = (x + 8)/2
2x - 8 = x + 8 (Multiplying by 2)
2x - x = 8 + 8 (Adding 8 and subtracting x to both sides)
x = 16
When,
x - 4 = - (x + 8)/2
2x - 8 = -x - 8 (Multiplying by 2)
2x + x = -8 + 8 (Adding 8 and x to both sides)
3x = 0
x = 0
Hence, the solution is x = 16 and x = 0.
13. (3/4)x = 2x - 10
⇒ Subtract 2x from both sides.
-5x/4 = -10
Multiply both sides by 4/(-5).
(-5x/4)×4/(-5) = -10 × 4/(-5).
x = 8 is the solution of the equation.
15. x² - 7x - 8 > 0
⇒ Solve the quadratic equation by splitting the middle term,
x² - 8x + x - 8 > 0
x(x - 8) + 1(x -8) > 0
(x + 1)(x- 8) > 0
-1 and 8 are the critical points of the inequality.
x < -1 and x > 8 are the solutions of the inequality which are represented by the shaded red region in the graph.
16. x - 5 > - 2x + 4
⇒ Adding 2x to both sides.
3x - 5 > 4
Adding 5 to both sides.
3x > 9
Divide both sides by 3.
x > 3 is the required solution represented by blue shade region in the graph.
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A rectangle is removed from the middle of a larger shaped board. What is the area of the remaining board?
Answers
Answer:
Step-by-step explanation:
Step 1: Find the area of the larger shaped board
Step 2: Find the area of the rectangle
Step 3: Subtract the area of the rectangle from the area of the larger shaped board
The result is the area of the larger shaped board minus the rectangle
The table shows the total distance of four trails. You want to complete a trail in 1 1/2 hours with an absolute deviation of at most 15 minutes. you hike at a rate of 3 miles per hour. CREATE AN ABSOLUTE VALUE INEQUALITY
Answers
Answer:
The answer would be: A = 5 1/4
Mike has $75 to spend at a local model car show. The entrance price for the show is $20. At one seller’s stand, Mike finds some model cars that he likes that are $7.50 each. What is the maximum number of model cars that Mike can buy at that stand?
Answers
Answer:
Mike can buy 7 model cars
Step-by-step explanation:
The equation for this word problem would be
7.5x+20=75
subract 20 from both sides
7.5x=55
divide both sides by 7.5
x= 7.33 or 7 1/3 or 22/3
but since you cant buy a third of a car the answer would be 7
Please help me with 15 & 16. Step by Step!!!!
15. The length of a rectangle is four times its width. If its width is x^5 units, what is the area of the rectangle?
16. The width of a rectangular prism is six times its length. The height is five times its length. If its length is m units, what is the volume of the prism?
Answers
Answer:
15. 4x¹⁰
16. 30m³
Step-by-step explanation:
15. Area of Rectangle is given by A=LW
since W=x⁵ and L is 4 times W, L=4x⁵
therefore, A = x⁵(4x⁵) = 4x¹⁰
16. Volume of Rectangular Prism is V=LWH
W=6L=6m and H=5L=5m and L=m
so V = m(6m)(5m) = 30m³
3. The fuel economy of a car, measured in miles per gallon, is modeled by the function f(s) = -0.009s² +0.699s +12 where s represents the speed of the car, measured in miles per hour. What's the fuel economy of the car when it
travels at an average of 20 miles an hour?
O A. 20 miles per gallon
O B. 26.63 miles per gallon
4
O C.-10.02 miles per gallon"
O D. 22.38 miles per gallon
O Mark for review (Will be highlighted on the review page)
Answers
Answer:
The Answer Will Be D
Step-by-step explanation:
The fuel economy of a car is modeled by the function f(s) = -0.009s² +0.699s +12 where s represents the speed of the car, measured in miles per hour.We need to find the fuel economy of the car when it travels at an average of 20 miles an hour.f(20) = -0.009(20)² +0.699(20) +12f(20) = -0.009(400) +13.98f(20) = 9.6The fuel economy of the car when it travels at an average of 20 miles an hour is 9.6 miles per gallon.Therefore, the answer is option D. 22.38 miles per gallon.
70 POINTS
Select the correct answer.
Here are four decimal numbers:
0.39, 0.85, 0.731, 0.773
Choose the list that shows the numbers in order from smallest to largest.
A.
0.773, 0.39, 0.85, 0.731
B.
0.773, 0.85, 0.39, 0.731
C.
0.39, 0.731, 0.773, 0.85
D.
0.85, 0.773, 0.731, 0.39
Answers
Answer: A
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Two parallel lines are crossed by a transversal.
What is the value of d?
Answers
The value of d in the image that shows the two parallel lines that are crossed by the transversal is determined as: 125°.
What is a Transversal?In geometry, a transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects a pair of parallel lines, it creates various angles and relationships between those angles.
The image attached below shows the two parallel lines which are crossed by the transversal, where angle d and 125° are vertical angles.
Since they are vertical angles, they will be equal or congruent to each other. Therefore, the value of d = 125°
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helpppppppppppppppppp
Answers
Answer:
38 m²Step-by-step explanation:
Area of the trapezoid:
A = 1/2(b1 + b2)hA = 1/2(4 + 15)*4 = 38 m²Area of trapizoid:-
\(\blue{A=\dfrac{1}{2}(b_1 +b_2)×h }\)
According to the question,
\(\bold{\dfrac{1}{2}×(4+15)×4 }\)
\(\bold{\dfrac{1}{2}×(19)×4 }\)
\(\bold{\dfrac{1}{\cancel{2}}×(19)×\cancel{4}}\)
\(\bold{19×2 ~m^2 }\)
\(\bold{ 38~m^2 }\)
Find the height of the tower using the information given in the illustration.
Answers
using SOH CAH TOA
Tan 85.144 =h/130
h=tan 85.144*130
h=1530.19 fr
To the nearest whole number, what is the mean of the
number of stamps for these four friends?
F. 92
G. 124
H. 203
J. 217
K. 234
Answers
To find the mean of the number of stamps for these four friends, we need to add up the total number of stamps and divide by 4 (the number of friends).
Samir has 60 stamps. Lisa has 2 1/2 times as many stamps as Samir, which can be calculated as follows: 2 1/2 * 60 = 150
Kwame has 443 stamps.
Jake has 159 fewer stamps than Kwame, which can be calculated as follows: 443 - 159 = 284 To find the total number of stamps, we add up the number of stamps each friend has: 60 + 150 + 443 + 284 = 937
To find the mean, we divide by 4: 937 / 4 = 234.25
Therefore, to the nearest whole number, the mean of the number of stamps for these four friends is 234.
Therefore, the answer is K. 234.
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PLEASE HELPPP!!!!!!!!
Answers
Answer:
A
Step-by-step explanation:
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