Suppose you are the manager of Speedy Oil Change which claims that it will change the oil in customers’ cars in less than 30 minutes on average. Further suppose that several complaints have been filed from customers stating that their oil change took longer than 30 minutes. Upper-level management at Speedy Oil Change headquarters has requested that you investigate the complaints. To begin your investigation, you randomly audit 36 oil changes performed by Speedy Oil Change and record the time each customer waited for the oil change. The number of minutes to complete each of the 36 oil changes is reported below.
Suppose you are the manager of Speedy Oil Change which claims that it will change the oil in customers’ cars in less than 30 minutes on average. Further suppose that several complaints have been filed from customers stating that their oil change took longer than 30 minutes. Upper-level management at Speedy Oil Change headquarters has requested that you investigate the complaints. To begin your investigation, you randomly audit 36 oil changes performed by Speedy Oil Change and record the time each customer waited for the oil change. The number of minutes to complete each of the 36 oil changes is reported below.
42
29
19
11
10
27
41
27
22
26
28
32
17
15
25
35
31
22
13
31
17
37
33
25
18
24
28
21
40
19
33
30
14
23
22
10
1. Write the null and alternative hypothesis. Label each accordingly.
2. Calculate the Test Statistic and the P-value. Label each accordingly, and report the P-value to 4 decimal places.
3. Using the P-value calculated in #2, explain why you would or would not reject the null hypothesis? Answer using a complete sentence, proper grammar and correct spelling. Do NOT write a conclusion.
4. Based on your answer to #3, write a final conclusion for the test of hypotheses, and explain if the company is fulfilling its promise to “change the oil in customers’ cars in less than 30 minutes on average?” Answer using a complete sentence, proper grammar and correct spelling.
Answers
Answer:
Explained below.
Step-by-step explanation:
(1)
The hypothesis can be defined as follows:
H₀: The Speedy Oil Change will change the oil in customers’ cars in more than 30 minutes on average, i.e. μ > 30.
Hₐ: The Speedy Oil Change will change the oil in customers’ cars in less than 30 minutes on average, i.e. μ ≤ 30.
(2)
Use Excel to compute the sample mean and standard deviation as follows:
[tex]\bar x=\text{AVERAGE(array)}=24.917\\\\s=\text{STDEV.S(array)}=8.683[/tex]
Compute the test statistic as follows:
[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{24.917-30}{8.683/\sqrt{36}}=-3.51[/tex]
The degrees of freedom is:
df = n - 1
= 36 - 1
= 35
Compute the p-value as follows:
[tex]p-value=P(t_{35}<3.51)=0.0006[/tex]
(3)
The p-value = 0.0006 is very small.
The null hypothesis will be rejected at any of the commonly used significance level.
(4)
There is sufficient evidence to support the claim that the Speedy Oil Change will change the oil in customers’ cars in less than 30 minutes on average.
Using the t-distribution, we have that:
1.
The null hypothesis is [tex]H_0: \mu \geq 30[/tex]
The alternative hypothesis is [tex]H_1: \mu < 30[/tex]
2. The test statistic is t = 3.51.
3. The p-value is of 0.0063.
4. Since the p-value is of less than the standard significance level of 0.05, we reject the null hypothesis, and can conclude that the company is fulfilling its promise.
Item 1:
At the null hypothesis, we test if the mean is of at least 30 minutes, that is:
[tex]H_0: \mu \geq 30[/tex]
At the alternative hypothesis, we test if the mean is of less than 30, that is:
[tex]H_1: \mu < 30[/tex]
Item 2:
We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. s is the standard deviation of the sample. n is the sample size.For this problem:
[tex]\mu = 30, n = 36[/tex]Using a calculator, [tex]\overline{x} = 24.92, s = 8.68[/tex]The test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{24.92 - 30}{\frac{8.68}{\sqrt{36}}}[/tex]
[tx]t = 3.51[/tex]
The test statistic is t = 3.51.
Item 3:
The p-value is found using a left-tailed test, as we are testing if the mean is less than a value, with t = 3.51 and 36 - 1 = 35 df.
Using a calculator, this p-value is of 0.0063.
Item 4:
Since the p-value is of less than the standard significance level of 0.05, we reject the null hypothesis, and can conclude that the company is fulfilling its promise.
A similar problem is given at https://brainly.com/question/16194574
Related Questions
Write an equation that passes through the point (1, 3) and is perpendicular to x – 2y = -8.
Answers
Answer:
y = -2x + 5
Step-by-step explanation:
Given:
Passes through point (1, 3)
Perpendicular to x – 2y = -8
Solve:
x – 2y = -8
y = 1/2x + 4
The slope is m = 1/2
The slope of the perpendicular line is the inverse of the slope of the original equation.
The slope of the inverse equation is m = -2.
Making an inverse equation of y = -2x + a
Find a:
Use point, (1, 3) where (x, y):
3 = (-2)*(1) + a
a = 5
y = -2x + 5
Answer:
y=½x+5
Step-by-step explanation:
Passes through, (1,3)
Perpendicular to x-2y=-8.
Step 1
write the equation in form of y=mx+c
x-2y=8
-2y=-x+8
Dividing both sides of the equation by -2 we get;
y=-x/2+8
y=-½x+8
Thus the gradient is -½. Call it M1
Recall, The product of the gradients(slopes) of perpendicular lines is -1 i.e
M1 × M2= -1
Solve for M2
-½×M2=-1.
Dividing both sides by -½ we get
M2=-1×-2
M2=2Now, use this slope(M2) with the points (1,3) to find the new equation that is perpendicular to x-2y=-8
Note: Given two points (x1,y1) and (x2,y2) the the slope would be ∆x/∆y i.e (x1-x2)/(y1-y2).
Therefore, identify new point (x,y). Use this new point with point (1,3) and the slope M2 to get the new equation.
Slope=∆x/∆y
M2=(x-1)/(y-3)
but M2 is 2
2=(x-1)/(y-3)
2/1=(x-1)/(y-3) Note: 2= 2/1
Cross multiplying we get:
2(y-3)=1(x-1)
Open the brackets
2y-6=x-1
Solve for y so as to write the equation in form of y=mx+c
2y=x-1 +6
2y=x+5
Divide both sides of the equation by 2
y=x/2+5
y=½x+5Use the dot plot to find the MEAN.
Answers
Answer:
Step-by-step explanation: To find the mean of the dot plot, you will need to add all of the dots together.
For example: Above 2, there are 3 dots , so you would need to multiply 2 by three to get 6 dots above the number 2.
Do that for all of the numbers on the dot graph from 1 - 6, and you will have this equation:
1 + 6 + 18 + 20 + 15 + 12
Next, you will need to add all those numbers together and you will get 72.
Lastly, divide by how many numbers there are, and there are 6 numbers.
So, that will be 72/6 which is 12.
Your answer will be 12.
If f(x) = 3x + 2, what is f(5)?
Answers
Answer:
f(5)= 17
Step-by-step explanation:
f(5)= 3(5)+2 5 is taking the place of x
15+2
f(5)= 17
Hope this helps!
A stop sign in the shape of a regular octagon is
resting on a brick wall, as shown in the
accompanying diagram.
STOP
X
What is the measure of angle x?
Answers
Answer:
45°
Step-by-step explanation:
First, find the measure of each interior angle of the octagon.
Measure of each interior angle of the octagon = [tex] \frac{(n - 2)180}{n} [/tex]
Where, n = 8.
Plug in the value of n into the formula
[tex] = \frac{(8 - 2)180}{8} [/tex]
[tex] = \frac{(6)180}{8} [/tex]
[tex] = \frac{1,080}{8} = 135 [/tex]
x = 180 - 135 (straight line theorem.)
x = 45°
Chaleah deposited $900 in a new account that earns 6% simple interest. After 2 years, how much interest will she have earned?
Answers
Answer:
$108
Step-by-step explanation:
Use the equation i = prt (interest = principle*rate*time):
Principle: $900
Rate: 0.06 (6%)
Time: 2 years
Put it all in an equation:
i = 900*0.06*2
i = $108
The trapezoids are similar shapes. Find the lengths
Answers
Y = 10.8
All I did is divide 30 by 50 which is .6 then I multiple by 18 which is 10.8 for y. Then 15 divided by .6 equals to 25
PLEASE ANSWER QUICKLY!!! PLZZZZZ!!!!!!!
Answers
Step-by-step explanation:
each 20m miles takes 1g gallon.
Answer:
[tex]y=-\frac{1}{20} x + 20[/tex]
Step-by-step explanation:
The slope equation is always [tex]\frac{rise}{run}[/tex]. In this case, the gallons went down by 1- so we can call the rise -1. When it went down by 1, the miles went up by 20- so we can call the run 20. This gives us a fraction (the "m" value) to put in the slope equation [tex]y=mx+b[/tex]. To find the y intercept (the "b" value), you find out what y is when x = 0, which is given in the chart: 20.
Simplify as much as possible (and only have positive exponents)
Answers
One moment...
A farmer has a rectangular plot of land. There is a bother identical plot of land 100 yards east and 100 yards north. Find the combined area of the two plots of land
Answers
Answer:
Step-by-step explanation:
Area of a rectangular plot = Length × width
With the aid of the diagram attached below.
For plot 1:
The area = ( 60 - 20 ) × ( 80 - 20 )
Area = 40 × 60
Area = 2400 sq yard
For plot 2:
Area = (160 - 120 ) × ( 180 - 120 )
Area = 40 × 60
Area = 2400 sq yard
Therefore, the combined area of the two plots of land = 2400 + 2400
= 4800 square yards
How much will you need to invest each month to reach a savings goal of $200,000 at the end of 20 years, if you invest in an annuity that pays 3% interest, compounded monthly?
Round your answer to the nearest dollar.
Answers
Answer:
$609
Step-by-step explanation:
4,8and 12 find the LCM of each numbers
Answers
Answer:The LCM of 4, 8 and 12 is 24.
Step-by-step explanation:
Wes had 4.75 in quarters and dimes if he had 25 coins how many of each did he have?
Answers
Answer:it would be 15 quarters and 10 dimes
Step-by-step explanation:
15 quarters is 3.75 and 10 dimes is $1, add them up you get $ 4.75
Answer:
15 quarters and 10 dimes
Step-by-step explanation:
25x + 10(25-x) = 475
x = 225/15
x = 15
So that has to mean he has 10 dimes
Hope this helps!!!
please answer these to with working
Answers
Answer:
Convert into decimals:
a) 70.3 b)3.7
Find:
a) 360.45
b) 112.997
What should be added to 2.8 to get 10?
7.2
Do 10 - 2.8
What should be subtracted from 20 to get 11.8?
8.2
Do 20 - 11.8
Hope this helps!!!
:D
solve cos(2x + 30) = 0.5 for -180≤x≤180
Answers
Answer:
x = 15°
x = 135°
x = -45°
x = -180°
Step-by-step explanation:
Trigonometric Equations
Solve
cos(2x + 30°) = 0.5 for -180° ≤ x ≤ 180°
Applying the inverse cosine function:
2x + 30° = arccos(0.5)
There are several angles whose cosine is 0.5. They are 60°, 300°, -60° and -300°, thus we have these candidate solutions:
2x + 30° = 60°
2x + 30° = 300°
2x + 30° = -60°
2x + 30° = -300°
Subtracting 30° to all the equations:
2x = 60° - 30° = 30°
2x = 300° - 30° = 270°
2x = -60° - 30° = -90°
2x = -60° - 300° = -360°
Dividing by 2 we have the complete set of solutions:
x = 15°
x = 135°
x = -45°
x = -180°
Molly opened a bank account. She deposited $86.50 into her account every month for 20 months. She used $24.50 every month to pay for singing lessons. After 20 months, she used 1 over 4 of the total money left in her account to go to a summer camp for singers. What is the total amount of money Molly spent to go to the summer camp?
Answers
Answer:$310
Step-by-step explanation:
Consider the sets A = fa; b; c; ; ; ; 1; 2; 3g, B = f ; ; ; ; ; g , C = f1; 2; 3; 4; 5; 6g and D = fa; b; cg. (a) List the elements of (A \ B)c (2 marks)
Answers
Answer:
hsad
Step-by-step explanation:
Vincent had both chocolate cake and coconut cake at his birthday party. There were 20
people at the party, and 6 of them picked chocolate cake. What percentage of the people at
the party picked chocolate cake?
Write your answer using a percent sign (%).
Answers
Answer:
30%
Step-by-step explanation:
Step 1:
6/20 Divide
Step 2:
3/10 Simplify
Step 2:
30/100 Multiply
Answer:
30%
Hope This Helps :)
Answer:
[tex] \huge \bf \: solution[/tex]
[tex] \sf \: total \: people \: = 20[/tex]
[tex] \sf \: people \: picked \: chocolate \: cake = 6[/tex]
[tex] \huge \tt \: \: percent \: = \frac{6}{20} [/tex]
[tex] \tt \: now \: \\ \tt \: \frac{3}{10} [/tex]
[tex] \tt \: 3 \times 10 = 30[/tex]
[tex] \large \boxed{30\%}[/tex]
Which is the better buy?
4-quart carton of fruit punch for $2.08
4-cup carton of fruit punch for $0.80
Answers
Answer:
$0.90
Step-by-step explanation:
1 quart = 2 pints
Write a proportion:
$1.80 / 4 pint = x / 2 pint
Cross multiply:
4x = 3.60
Divide:
x = 0.90
The price per quart is $0.90.
Answer:
4-quart carton of fruit punch for $2.08
Step-by-step explanation:
4-quart carton of fruit punch for $2.08
2.08 : 4 = 0.52
check your work: 0.52 x 4 = 2.08
so for the first offer you will be paying $0.52 per quart .
4-cup carton of fruit punch for $0.80
1 cup = 0.25 quarts
4 cups = 1 quart
0.80 : 1 = 0.80
for the second offer you will be paying $0.80 per quart of fruit punch. 4-quart carton of fruit punch for $2.08 is a better buy because you will be paying for each quart than in first offer.
hope this helps!
If a shirt manufacturer wanted to make shirts that fit most individuals, what characteristics would be better?
Answers
Answer:
a stretch shirt
Step-by-step explanation:
An architect makes 14455.32 a year. If they get paid weekly, how much do they get each paycheck? Round to the nearest cent
Answers
Answer: $277.99
Step-by-step explanation:
There are 52 weeks in a year. Assuming the architect would get paid every week, you would divide their salary by 52.
14,455.32/52 = 277.9869
Rounding to two decimal places, the answer would be $277.99.
Answer:
301.15
Step-by-step explanation:
First multiply 12 by 4. 12 months 4 weeks in each. You get 48 then you divide 14455.32 and you get 301.15.
A cone has height h and a base with radius r. You want to change the cone so its
volume is halved. What is the new height if you only change the height? What is the
new radius if you only change the radius? Explain.
Answers
9514 1404 393
Answer:
a) h/2
b) r/√2 = (r√2)/2
Step-by-step explanation:
a) The volume of a cone is proportional to height. If the volume is halved, then the height will be halved.
The new height will be h/2.
__
b) The volume is proportional to the square of the radius. If the volume is halved, the square of the radius is halved. The new radius will be ...
(r')² = r²/2
r' = r/√2 = (r√2)/2 . . . radius of half-volume cone
4+4
[tex]4 + 4[/tex]
Answers
Answer:
4+4 = 8.
Step-by-step explanation:
Or 44, depends on whether you're trolling. XD
Hope this helped...
[tex] \huge \: Your \: answer \: is \: 8[/tex]
if there is no number in front of a letter, it is really number 1
Answers
Answer: Yes, if there is no number in front of a variable(or letter, as you said), it is actually 1.
a = 1a
x^2 = 1x^2
2m + n = 0 means 2m + 1n = 0
Step-by-step explanation:
Pretty easy if you know what you’re doing lol please helpppp Bc idk what I am doingggy
Answers
Hope this helps and I can get the brainliest
Which inequality has the graph shown below?
Answers above ^
Answers
Answer:
The inequality the graph has shown is y < 2x - 3 ⇒ C
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
m is the slope of the lineb is the y-interceptFrom the given figure
∵ The line drawn is a dashed line
→ That means the sign of inequality without the equal sign
∴ The sign of the inequality is without the equal sign
∵ The shaded area is under the line
→ That means the sign of the inequality is smaller than
∴ The sign of the inequality is <
∵ The line intersects the y-axis at point (0, -3)
→ That means the y-intercept is -3
∴ The y-intercept = -3 ⇒ (value of b in the equation of the line)
∵ There is only one answer has sigh < and y-intercept -3
∴ The inequality the graph has shown is y < 2x - 3
Which one doesn't belong?Explain why
Answers
Answer:
6 or 33percent
Step-by-step explanation:
because he don't have a numerator
because he is not belong to the group the three is fraction and the first one is a percent
[tex]\huge\boxed{.6}[/tex]
Solution Steps:- Which doesn't belong -______________________________
- A rational number is a terminating or repeating decimal.
- An irrational number is when you can't write that number as a fraction.
Rational or Irrational: [tex]33[/tex]% = Rational number. ([tex]33[/tex]% = [tex]0.33[/tex], This is a terminating decimal.)[tex]\frac{1}{3}[/tex] = Rational number. ([tex]\frac{1}{3}[/tex] = [tex]0.3[/tex], This is a repeating decimal.)[tex]\frac{5}{3}[/tex] = Rational number. ([tex]\frac{5}{3}[/tex] = [tex]1.6[/tex], This is a repeating decimal.) [tex]\frac{}{.6}[/tex] = Irrational number. (You can't turn this into a true fraction, therefore it's irrational.)______________________________
Hope this helps!If you have anymore questions, or need help with anything else, feel free to ask!
e fence factorise completely
this expression
144
Answers
144 = 12² = (3 x 4)²
Hope this helps
A new LED light bulb uses 10 watts of power. Since energy = power × time , then the energy used for this light bulb can be found my multiplying the power times the time the bulb is lit. If the bulb is lit for one hour, the energy used will be 10 watt*hours or 10 Wh. If three 10 watt bulbs in one room are kept on for 5 hours, how many watt*hours of energy are used?
Answers
9514 1404 393
Answer:
150 Wh
Step-by-step explanation:
We know the energy per bulb is 10 Wh per hour, so the total energy used by 3 bulbs in 5 hours is ...
(10 Wh/(bulb·hour))×(3 bulbs)×(5 hours) = 10·3·5 Wh = 150 Wh
1. Write the following as decimals
75
1
(a) 16% (b)
(c) 0.1% (d)
100
16
Answers
Answer:
the question isnt clear
Step-by-step explanation:
Answer:
a) 0.16
b) 100.00
c) 0.001
d) 16.00
16. In the figure below, vertices D and F of ADEF lie on
CG, the measure of ZCDE is 148°, and the measure of
ZEFG is 140°. What is the measure of ZDEF?
E
?
140°
148°
D
C
F 720
G. 989
H. 100°
J. 108°
K. 116°
Answers
Answer:
J. 108°
Step-by-step explanation:
m<EDF = 180 - 148 = 32° (angles on a straight)
m<EFD = 180 - 140 = 40°(Angles in a straight line)
m<DEF = 180 - (m<EDF + m<EFD) (sum of triangle)
m<DEF = 180 - (32 + 40)
m<DEF = 180 - 72
m<DEF = 108°