A liquid dietary product implies in its advertising that use of the product for one month results in an average weight loss of at least three pounds. Eight subjects use the product for one month, and the resulting weight loss data are reported as follows.
Subject Initial Weight (lbs) Final Weight(lbs)
1 165 161
2 201 195
3 195 192
4 198 193
5 155 150
6 143 141
7 150 146
8 187 183
a) Do the data support the claim of the producer of the dietary product with the probability of Type 1 error of .05?
b) Do the data support the claim of the producer of the dietary product with the probability of Type 1 error of .01?
c) In an effort to improve sales, the producer is considering changing its claim from "at least three pounds" to "at least five pounds". Repeat parts a and b to test this new claim.
Answers
Answer:
Following are the responses to the given question:
Step-by-step explanation:
Please find the table in the attached file.
mean and standard deviation difference: [tex]\bar{d}=\frac{\Sigma d}{n} =\frac{-4-6-.......-4-4}{8}=-4.125 \\\\S_d=\sqrt{\frac{\Sigma (d-\bar{d})^2 }{n-1}}=\sqrt{\frac{(-4 + 4.125)^2 +.......+(-4 +4.125)^2 }{8-1}}= 1.246[/tex]
For point a:
hypotheses are:
[tex]H_0 : \mu_d \geq -3\\\\H_a : \mu_d < -3\\\\[/tex]
degree of freedom:
[tex]df=n-1=8-1=7[/tex]
From t table, at[tex]\alpha = 0.05[/tex], reject null hypothesis if [tex]t <-1.895[/tex].
test statistic:
[tex]t=\frac{\bar{d}-\mu_d }{\frac{s_d}{\sqrt{d}}}=\frac{ -4.125- (-3)}{\frac{1.246}{ \sqrt{8}}} =-2.55[/tex]
because the [tex]t=-2.553 <-1.895[/tex], removing the null assumption. Data promotes a food product manufacturer's assertion with a likelihood of Type 1 error of 0.05.
For point b:
From t table, at [tex]\alpha =0.01[/tex], removing the null hypothesis if [tex]t<-2.998[/tex].
because [tex]t=-2.553 >-2.908[/tex], fail to removing the null hypothesis.
The data do not help the foodstuff producer's point with the likelihood of a .01-type mistake.
For point c:
Hypotheses are:
[tex]H_0: \mu_d \geq -5\\\\H_a: \mu_d < -5[/tex]
Degree of freedom:
[tex]df=n-1=8-1=7[/tex]
From t table, at [tex]\alpha =0.05[/tex], removing the null hypothesis if [tex]t <-1.895[/tex].
test statistic: [tex]t=\frac{\bar{d}-\mu_d}{\frac{s_d}{\sqrt{n}}} =\frac{-4.125-(-5)}{\frac{1.246}{\sqrt{8}}}=1.986[/tex]
Since [tex]t-1.986 >-1.895[/tex], The null hypothesis fails to reject. The results do not support the packaged food producer's claim with a Type 1 error probability of 0,05.
From t table, at[tex]\alpha= 0.01[/tex], reject null hypothesis if[tex]t<-2.998[/tex].
Since [tex]t=1.986>-2.998[/tex] , fail to reject null hypothesis.
Data do not support the claim of the producer of the dietary product with the probability of Type 1 error of .01.
Related Questions
you want to make five-letter codes that use the letters A, F, E, R, and M without repeating any letter. What is the probability that a randomly chosen code starts with M and ends with E?
A. 0.01
B. 0.02
C. 0.05
D. 0.10
Answers
Answer:
its C. 0.05 #edmentumgang
Step-by-step explanation:
Answer:
Option C is the correct anwer for plato
Step-by-step explanation:
C. 0.05
How many unique tree graphs (i.e. with different degree patterns) can be made with
4 vertices?
a) 0
b) 1
c) 2
d) 3
Answers
Kind of stuck any tips would also help!!
Answers
Answer:
Step-by-step explanation:
You must place in the question sign box the value of x that is above the question sign box because you are trying to fill out the y row.
Example: y=[tex]-\frac{0}{3} +2[/tex]= -0+2=2
Answer:
Step-by-step explanation:
tip:
plug the x values from the table ( the top row values ) into the equation
in this case its 0
BOX 1:
[tex]-\frac{0}{3} +2\\[/tex]
0 divided by anything = 0
so, 0 + 2 = 2
box 1 = 2
BOX 2:
[tex]-\frac{3}{3} +2[/tex]
3 div by 3 = 1 ( in this case negative 1 )
so, -1 + 2 = 1
box 2 = 1
BOX 3:
[tex]-\frac{6}{3} +2[/tex]
6 div by 3 = 2 ( in this case negative 2)
-2 + 2 = 0
box 3 = 0
50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answers
========================================================
Work Shown:
Apply the pythagorean theorem
a^2 + b^2 = c^2
12^2 + b^2 = 15^2
144 + b^2 = 225
b^2 = 225-144
b^2 = 81
b = sqrt(81)
b = 9
Answer:
9
I am not able to upload my answer unless its 20 characters long
Maya is solving the equation 2(1+7x)=72. She lists an explanation for each step as shown. Which is the missing explanation for Maya's first step after writing the given equation?
Answers
Answer:
apply the distrbutive property
Step-by-step explanation:
...........................
Practice Test
Flashcards
Stu
Question 4 Mathematics Practice Test for the TEAS
Solve the equation and choose the best answer:
9
6
6
4
7
C
6
Answers
Answer:
Where is the equation??
What is the formula to find the perimeter of a pentagon
Answers
Answer:
For a regular polygon, the perimeter is equal to the product of one side length and the number of sides of the polygon. For example, the perimeter of a regular pentagon whose side length 8 cm, is given by; Perimeter of a regular pentagon = 8 x 5 = 40 cm.
Step-by-step explanation:
I hope I've helped :).
Answer:
perimeter = number of sides x the length of any side.
Step-by-step explanation:
brainliest pls
Odin is recording the depreciation of his car. The table displays the number of years and the car's depreciated value for each year.
What will be the value of his car in year 10?
PLEASE GIVE ME THE ANSWER!!
Answers
Answer:
$1,158.08
Step-by-step explanation:
The value of the car in year 10 is $1158.08
How to determine the car value in year 10?From the table, we have the following points
(x, y) = (1,5000) and (2,4250)
Start by calculating the rate of depreciation using:
r = y2/y1
So, we have:
r = 4250/5000
Evaluate
r = 0.85
The value of the car in nth year is calculated using:
y = y1 * r^(n - 1)
For the 10th year, we have:
y = 5000 * 0.85^(10 - 1)
Evaluate the product
y = 1158.08
Hence, the value of the car in year 10 is $1158.08
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Determine the radius of convergence of the following power series.
Σ(-1)^k x^k/3^k
Answers
Answer:
(−1)kxk
Step-by-step explanation:
Therefore, the infinite series ∞∑k=11k does not converge.
(−1)kxk = 1 − x + x2 − x3 + ···. = ∞. ∑ k=0. (−x)k = 1. 1 − (−x). = 1. 1 + x ... 3. )k. = x. 1 − (x2/3). = 3x. 3 − x2 for |x2/3| < 1. 1.2 Radius of Convergence.
A sequence is shown below
6, 8, 10, 12, 14
Which function represents this sequence?
A. f(n) = 4 + 2(n - 1)
B. f(n) = 4 + 2(n + 1)
C. f(n) = 6 + 2(n - 1)
D. f(n) = 6 + 2(n + 1)
Answers
Answer:
[tex]c \: is \: correct \\ you \: can \: put \: 1 \: 2 \: 3 \: 4numbers \: in \: equations \: and \: find \: best \: answer[/tex]
A crate is shaped like a rectangular prism. The
crate is 3 ft wide, 5 ft long, and 7 ft tall. What is the
volume of the prism in cubic feet?
Answers
Answer:
I think 105.
Step-by-step explanation:
3 × 5 = 15
15 × 7 = 105.
Answer: The answer is 105 cubic feet.
Step-by-step explanation: V= l x w x h, so V= 3 x 5 x 7 is the equation.
Exponential Function
Which of the following is true about the function y = 4 · 3×?
a. the function decreases
b. the function has a y-intercept of (0, 3)
c. if the value of x increases by 1, the value of y will triple.
d. the function contains the point (1, 4)
Please select the best answer from the choices provided
Answers
Answer:
C. If the value of x increases by 1, the value of y will triple.
Step-by-step explanation:
I calculated it logically
The weight of a bag of Brand A cookies is labeled as 4 ounces on the bag. However, the actual weights of the bags vary by a small amount. According to the package
specifications, the weights are approximately normally distributed with a mean of 4.10
ounces and a standard deviation of 0.10 ounce. During a quality control check on the bag weights, a bag was found that weighted 3.95 ounces. how many standard deviations below the mean was the bag weight?
Answers
Answer:
2
Step-by-step explanation:
Mark me the brainliest please
The weight of the bag is 1.5 standard deviations down the mean weight.
What is normal distribution?
'Normal distribution is a continuous probability distribution wherein values lie in a symmetrical fashion mostly situated around the mean.'
According to the given problem,
Mean weight (μ) = 4.10 ounces
Standard deviation (σ) = 0.10
Target weight (x) = 3.95
We know,
Z = ( x - μ ) / σ
= (3.95 - 4.10) / 0.10
= -1.5
Hence, we can conclude, the target weight is 1.5 standard deviations down.
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What is the period of the function F(x) = -4sec (1/2 x)
A. 4 pi
B. pi
C. pi/2
D. 2 pi
Answers
Answer:
A) 4π
Step-by-step explanation:
The period of a secant function, f(x)=a*sec(bx+c)+d, is defined as 2π/|b| where b is the distance of the period. Since we know b=1/2 given by the function, then the period is 2π/|1/2|=2π/(1/2)=2π(2/1)=4π.
Whats 3%9 and 3-9?
pls
Answers
Answer:
3 - 9 = -6
3% of 9 = 0.27
Step-by-step explanation:
Find the value of x
Answers
Answer:
x = 30
Step-by-step explanation:
24(24 + x) = 36² => tangent-secant theorem
Open the bracket
24*24 + 24*x = 36²
576 + 24x = 1,296
24x = 1,296 - 576
24x = 720
Divide both sides by 24
24x/24 = 720/24
x = 30
Restrictions must be indicated for rational functions involving a denominator because__________
is not defined
Answers
Answer:
rational expressions
hope I helped! :)
The value of
Arc sin(1/2) + Arc tan(1) is
Answers
Answer:
75°Step-by-step explanation:
We know that:
sin 30° = 1/2, therefore arcsin (1/2) = 30°tan 45° = 1, therefore arctan (1) = 45°So the value of the expression is:
arcsin (1/2) + arctan (1) = 30° + 45° = 75°Answer:
75°
Step-by-step explanation:
Recall the common trigonometric angles:
[tex]\sin 30^{\circ}=\dfrac{1}{2}[/tex]
[tex]\tan 45^{\circ}=1[/tex]
Arcsin is the inverse of sin.
Arctan is the inverse of tan.
[tex]\implies \arcsin \left(\dfrac{1}{2}\right)=30^{\circ}[/tex]
[tex]\implies \arctan (1) = 45^{\circ}[/tex]
Therefore:
[tex]\implies \arcsin \left(\dfrac{1}{2}\right)+\arctan (1) = 30^{\circ}+ 45^{\circ}=75^{\circ}[/tex]
In a charity marathon to raise money for Typhoon Ulysses, Alex finished 43rd out of 200 entrants. Find his percentile rank.
Answers
explanation: 43 divided by 200 = 0.215
Move the decimal to the right two times to make it a percent. Therefore answer will be 21.5%
The percentile rank in a charity marathon to raise money for Typhoon Ulysses is 21.5 percentile.
What is the Percentile?A percentile (or a centile) is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations fall. For example, the 20th percentile is the value (or score) below which 20% of the observations may be found.
Rank of Alex is 43rd
Total Entrants is 200
Percentile = Rank of Alex X 100 / Total Entrants
= 43 X 100 / 200
= 21.5 percentile
Thus, the percentile rank in a charity marathon to raise money 21.5 percentile.
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Which statements about quadrilateral WXYZ are
true? Select three options,
The slope of ZW is 2/5
The slope of YX is -5/2
The length of ZY is sqrt29.
The length of WX is 5.
Quadrilateral WXYZ is a square.
Answers
Answer:
the slope of zw is 2/5
the length of zy is sqrt29
Quadrilateral WXYZ is square
The slope of ZW is 2/5, length of ZY is square root of 29, and the quadrilateral WXYZ is a square.
What is a quadrilateral?It is a 4 side figure, four angle and four vertices.
How to find the slope?Points of quadrilateral is Z(-3,1), W(2,3), X(4,-2) AND Y(-1,-4)
Slope of ZW is (3-1)/(2+3)=2/5
Slope of YX=(-2+4)/(-1-4)=-2/5
Length of ZY=root of [tex](-4-1)^{2} +(-1+3)^{2}[/tex]=root of 29
Length of WX =root of [tex](-2-3)^{2} +(4-2)^{2}[/tex]= root of 29
Quadrilateral it is a square.
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What is 2/3 written as a decimal
Answers
Answer:
2.3
Step-by-step explanation:
Answer:
66.66 repeating, or 66.7
Step-by-step explanation:
3rds only go to 99 if your looking for fractions, and to get from 3-99, you would multiply the fraction times 33.3 repeating. to keep the fraction even, you would also multiply the numerator (top number) by 33.3 repeating, getting 66.66 repeating
Does perpendicular lines have something same to intersecting lines
Answers
Answer:
They are similar in a way. Perpendicular lines can intersect, but they must make a 90 degree angle to be prerpendicular lines. A cross is an example of this.
Step-by-step explanation:
Find each angle measure to the nearest degree
1) Find m.
5
S
R
5.7
T
please help, show work if possible :)
Answers
Answer:
RS=26.49 m;
ST =14.08 m;
m<R =28°
Step-by-step explanation:
How man minutes will it take to make and pack an order for 36 parts show your work
Answers
Complete question :
The time taken to make and pack an order represented by the equation ; 2x + 10. How man minutes will it take to make and pack an order for 36 parts:
Answer:
82 minutes
Step-by-step explanation:
Time taken to make and pack an order : 2x + 10
To pack 36 orders ; put x = 36 in the equation :
= 2(36) + 10
= 72 + 10
= 82
82 minutes is required to make and pack an order for 36 parts.
Answer:
2x + 10
= 2(36) + 10
= 72 + 10
= 82
It will take 82 minutes to make and pack an order for 36 parts.
Step-by-step explanation:
Got it right :)
Please mark brainliest
<4?
What is the solution of 3+
X-2
X-3
O x <3
O XS3
Ox>3
0 x23
Answers
Answer:
x < 3
Step-by-step explanation:
3 + x-2/x-3 ≤ 4, x ≠ 3
3 + x-2/x-3 -4 ≤ 0
-1 + x-2/x-3 ≤ 0
-(x-3) + x-2/x-3 ≤ 0
1/x-3 ≤ 0
x-3 < 0
x < 3, x ≠ 3
x < 3
x<3 is the solution of the equation 3 + (x-2) / (x-3) ≤ 4.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given equation can be rewritten as 3 + (x-2) / (x-3) ≤ 4.
To solve for x, we need to multiply both sides by (x-3)
3(x-3) + (x-2) ≤ 4(x-3).
3 + x-2/x-3 -4 ≤ 0
Solve the above equation.
-1 + x-2/x-3 ≤ 0
-(x-3) + x-2/x-3 ≤ 0
1/x-3 ≤ 0
x-3 < 0
x < 3
Hence, x<3 is the solution of the equation 3 + (x-2) / (x-3) ≤ 4.
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An investment of $2,500 compounded continuously at an annual interest rate of 2.5%.
The investment is kept in the account for 25 years.
Answers
Answer:
4,670.61 Dollars
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 2.5/100
r = 0.025 rate per year,
Then solve the equation for A
A = Pert
A = 2,500.00(2.71828)(0.025)(25)
A = $4,670.61
In a storeroom,there are 30 blue balls,48 green balls,some red balls and some white balls. there are 3 times as many green balls as red balls and 5 times as many blue balls as white balls.
(a) How many balls are there altogether?
(b) How many balls are left in the room if 7/10 (fraction) of the balls are taken away?
pls help me answer both
Answers
Answer:
7/30
Step-by-step explanation:
We first have 7 blue and 3 red out of 10, so P(1st ball is red) = 3/10
Now, we have pulled a red ball out of the bag, leaving us with 7 blue and 2 red out of 9 total balls.Then P(2nd ball is blue) = 7/9. Put this together, P(1st red AND 2nd blue) = 3/10⋅7/9 =7/30
Help please. Much appreciated
Answers
Answer:
1=90, 2=53,3=37, 4=53 As sum of angles in triangle 180°
convert 614 into base five number system.
Answers
Answer:
4424
Step-by-step explanation:
the number 614 is in the base ten system that we use every day. the base five system represents each digit in the number represents the number of copies of that power of 5.
check out:
rapidtables.com/convert/number/base-converter.html
Plz help me well mark brainliest if correct!!....
Answers
Answer:
The first one is correct.