A researcher wants to determine whether or not a five-week crash diet is effective over a long period of time. A random sample of 15 dieters is selected Each person's weight is recorded before starting the diet and one year after it is concluded. Based on the data shown at right (weight in pounds), Can we conclude that the diet has a long-term effect, that is, that dieters manage to not regain the weight they lose? Include appropriate statistical evidence to justify your answer.
BEFORE
158 185 176 172 164 234 258 200 228 246 198 221 236 255 231
AFTER
163 182 188 150 161 220 235 191 228 237 209 220 222 268 234
Answers
Using the t-distribution, as we have the standard deviation for the sample, it is found that it cannot be concluded that the diet has a long-term effect.
What are the hypotheses tested?At the null hypotheses, it is tested if there is no difference in the weights, that is:
[tex]H_0: \mu_A - \mu_B = 0[/tex]
At the alternative hypotheses, it is tested if the weights decrease, that is:
[tex]H_1: \mu_A - \mu_B < 0[/tex]
What is the mean and the standard deviation of the distribution of the difference?Using a calculator, for each sample, we have that:
[tex]\mu_B = 210.8, s_B = 33.85, sE_B = \frac{33.85}{\sqrt{15}} = 8.74[/tex]
[tex]\mu_A = 207.2, s_A = 33.47, sE_A = \frac{33.47}{\sqrt{15}} = 8.64[/tex]
Hence, for the distribution of differences, we have that:
[tex]\overline{x} = \mu_A - \mu_B = 207.2 - 210.8 = -3.6[/tex]
[tex]s = \sqrt{sE_B^2 + sE_A^2} = \sqrt{8.74^2 + 8.64^2} = 12.3[/tex]
What is the test statistic?It is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Then:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{-3.6 - 0}{12.3}[/tex]
[tex]t = -0.29[/tex]
What is the decision?Considering a left-tailed test, as we are testing if the mean is less than a value, with a standard significance level of 0.05 and 15 + 15 - 2 = 28 df, the critical value is of [tex]t^{\ast} = -1.7[/tex].
Since the test statistic is greater than the critical value for the left tailed test, it cannot be concluded that the diet has a long-term effect, as the null hypothesis is not rejected.
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Related Questions
If cos(x)= 3/4 and tan(x), what is cos(2x)?
-3sqroot7/8
-1/8
1/8
3sqroot7/8
Answers
Answer:
The answer is 1/8 or C.
Step-by-step explanation:
I know this is correct because I got it right on edge 2021.
**please mark brainliest!**
.The value of cos(2x) is 1/8
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.
Given:
cos x = 3/4
Using identity,
cos 2x = 2 cos^2 (x)-1
=2(3/4*3/4)-1
=2*9/16-1
=9/8-1
=1/8.
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he statement “Angles that measure more than 50 degrees are obtuse angles” has a counterexample.
Answers
Ralph painted 1/6 of a wall in 2/3 hour. At this rate, how many hours will it take Ralph to paint the whole wall?
Answers
Answer:
4 hours
Step-by-step explanation:
Let the size of whole wall be x.
Given that
Ralph painted 1/6 of a wall in 2/3 hours
thus, writing it in mathematical form we have,
time taken to pain 1/6 of x = 2/3 hours
=>time taken to pain x/6 wall = 2/3 hours
since, we have taken size as x so to find time to pain x size of wall ,
we divide both side by 6
=>time taken to pain x/6 * 6 wall = 2/3 *6 hours
=> time taken to pain x wall = 4 hours
Thus, It will take 4 hours to paint whole wall
Tory and her friend Terrence ride their bikes to school each day. On one particular day, Tory started out 5 minutes before Terrence. Tory rides at a rate of 880 feet per minute and Terrence rides at a rate of 1.056 feet per minut
How long had Tory been riding when Terrence caught up with her?
Answers
Answer:
4:30 minutes im thinking
Step-by-step explanation:
The value is 30 minutes. Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression.
What is meant by expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the expression 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
The expression that give us the distance that Tory has ride after t minutes is:
D = 880t
Because Tory rides at 880 feet per minute.
At the same way, the distance that Terrence has ride after t minutes is equal to:
D = 1056(t - 5)
Because Terrence rides at 1056 feet per minute and he starts out 5 minutes after Tory
Now, we need to find t when both expressions are equal, so we can formulate the following equation:
[tex]880t=1056(t-5)[/tex]
So, solving for t, we get:
[tex]880t=1056t - 1056.5[/tex]
[tex]880t=1056t - 5280[/tex]
[tex]880t=1056t =-5280[/tex]
[tex]-176t=-5280[/tex]
[tex]t=-5280/-176[/tex]
[tex]t= 30[/tex]
Therefore the answer is 30 minutes
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A trail mix has 16 cups of raisins, 3 cups of dates, 24 cups of peanuts, and 2 cups of cashews. Which
Ingredients are in the same ratlo as cashews to raisins
Answers
cashews: raisins = 2:16= 1:8
dates : peanuts = 3:24= 1:8 so the answer is dates and peanuts!
TV−→− bisects ∠STU, m∠STV=(14x+8)∘, and m∠UTV=(x+2)∘. Find m∠STU
Answers
Answer:
m∠STU is 20°
Step-by-step explanation:
If a ray bisects an angle, then it divides it into two equal angles in measures and the measure of each one is half the measure of this angle
∵ Ray TV bisects ∠STU
→ That means it divides it into two angles STV and UTV
∴ m∠STV = m∠UTV = [tex]\frac{1}{2}[/tex] m∠STU
∵ m∠STV = ([tex]\frac{1}{4}[/tex]x + 8)°
∴ m∠UTV = (x + 2)°
→ Equate them
∴ x + 2 = [tex]\frac{1}{4}[/tex]x + 8
→ Subtract 2 from both sides
∴ x + 2 - 2 = [tex]\frac{1}{4}[/tex]x + 8 - 2
∴ x = [tex]\frac{1}{4}[/tex]x + 6
→ Subtract [tex]\frac{1}{4}[/tex]x from both sides
∴ x - [tex]\frac{1}{4}[/tex]x = [tex]\frac{1}{4}[/tex]x - [tex]\frac{1}{4}[/tex]x + 6
∴ [tex]\frac{3}{4}[/tex]x = 6
→ Divide both sides by [tex]\frac{3}{4}[/tex] to find x
∴ x = 8
→ Substitute the value of x in the measure of any given angle
∵ m∠UTV = 8 + 2 = 10°
∵ m∠UTV = [tex]\frac{1}{2}[/tex] m∠STU
∴ 10° = [tex]\frac{1}{2}[/tex] m∠STU
→ Multiply both sides by 2
∴ 20° = m∠STU
∴ The measure of angle STU is 20°
The tank in Sabina’s car hold 12.7 gallons of gasoline. Currently, the gas tank is 3/4 full. How much gasoline is in the car’s tank? Round your answer to the nearest tenth.
Answers
Answer:
9.5 gallons
Step-by-step explanation:
12.7 x .75
multiplying by .75 is the easiest way to get 3/4 of something
The highest elevation in the United States is Mt. McKinley in Alaska, which measures 6,194 m above sea level. The lowest elevation in the United States is Death Valley in California, which measures 86 m below sea level. What is the height difference, in meters, between the highest and lowest elevations in the United States?
Answers
Answer:
the difference is 6280 m
Step-by-step explanation:
Find the value of 8724 - 3568
Answers
Answer:
10312 i think
Step-by-step explanation:
Translate point (2, -1) seven units up. Write the new coordinate as an
ordered pair. help pls!
Answers
Answer:
(2,6)
Step-by-step explanation:
Up on a graph is adding to the y-value. (x,y)
x-value = 2
y-value = -1
-1 + 7 = 6
(2,6)
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
It was 12°C when Preston got home from school.
The weather report shows a storm front moving
in that will drop the temperature by 17°C. What
is the expected temperature
Answers
Answer:
-5 degrees C
Step-by-step explanation:
drop indicates minus
12-17=-5
-5 degrees C
Write the equation y+4+-1 (x-3) in standard form.
Answers
Answer:
−x+y+7
Step-by-step explanation:
Find the circumference of the circle to the nearest
tenth. Use 3.14 for T.
28 m
Answers
Answer:
I wish I've known, but try using Symbo-Lab or Math-Way. They help a lot.
Step-by-step explanation:
Solve for B.
Ax+By=C
What is B equal to?
Answers
Answer:
B=C/y−Ax/y
Step-by-step explanation:
20r + 11r + –19r − –4 = –20
Answers
Answer:
r=-2
Step-by-step explanation:
First, you need to combine like terms so now you have 12r-(-4)=-20. Then you have to subtract -4 to -20 which equals -24 so now you have 12r=-24. Finally, you divide 12 from both sides and you get r=-2
Answer:
r = -2
Step-by-step explanation:
20r + 11r - 19r + 4 = -20
12r + 4 = -20
subtract 4 from both sides of the equation
12r + 4 - 4 = -20 - 4
12r = -24
divide both sides by 12
12r/12 = -24/12
r = -2
The endpoints of RS are R: (9,-4) and S: (2, -8).
Which are the coordinates of the midpoint of RS?
A (11-2
B: (1. –6).
c (3,-2)
D (-6)
Answers
Answer:
B, (11/2,-6)
Step-by-step explanation:
to get the midpoint of two endpoints, simply take the average of each corresponding coordinate
midpoint: ((Rx+Sx)/2,(Ry+Sy/2)).
((9+2/2),(-4+-8/2)) = (11/2,-12/2) = (11/2,-6)
the midpoint formula in general is : ((x+x1)/2),(y+y1)/2))
where x1 is the initial or first x coordinate, y1 is the initial or first y coordinate, x is the second, last, or final x coordinate. and y is the second, last, or final y coordinate.
Order these from greatest to least:
0.009 m, 12 cm, 8 nm, 5 x 10^-1 m
Answers
-1/8 - 0.356 find the sum of this equation
Answers
-0.481 :)
Step-by-step explanation:
NEED HELP ASAP WILL GIVE BRAINLY IF CORRECT PLEASE HELP 20 POINTS out
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Answer:
It would be -27
Step-by-step explanation:
Math
I’m really confused please help!
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Answer:
yes
Step-by-step explanation:
i did this last week
Answer:
Yes, it is.
Step-by-step explanation:
Choose Yes or No to tell if the number 80 will make each equation true.
320 ÷ □ = 40
Choose...
4,800 ÷ □ = 60
Choose...
7,200 ÷ □ = 900
Choose...
16,000 ÷ □ = 200
Choose...
Answers
Answer:
No : 8
Yes : 80
No : 8
Yes : 80
Answer:
Only the second and the fourth option that is true
Step-by-step explanation:
Which of the following choices is NOT GEOMETRIC SEQUENCE.
a.
2, -4, 8, . . .
b.
8, 2, 0.5, . . .
c.
1/2, 1/6, 1/18, . . .
d.
-7, -2, 3, . . .
Answers
B is not a geometric sequence
What is the inverse of the function y = 2x - 3?
Answers
Answer:
f^-1(x)=[tex]\frac{x}{2}[/tex]+[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
I need help(explanation) on how to find h and m. I will give 12 points!
Answers
Answer:
h= 44 degrees
m= 45 degrees
I think this is the answer
answer for brainliest
pic below
correct answers only
Answers
b-3/4
c- 2/4
d- 0/4
A 2-month membership to the gym costs $125. Alex would like to be a member for 1 year (12 months). What is the total amount he will pay for the year?
Answers
Answer:
$750
Step-by-step explanation:
We divide 12 months which is the time Alex would like to be a member by 2 which gives us 6. We know 2 months=$125 so if 2×6=12, $125×6 = A 1 year membership.
Maria's dinner bill is $21.89 after tax. If she wants to leave a15% tip, what will the total cost of the dinner be?a. $24.22b. $3.28c. $18.61d. $25.17
Pls answer quick!
Answers
Answer:
d
Step-by-step explanation:
James has 861 feet of rope. There are 14 teams of hikers.
If James gives an equal amount of rope to each team, how much rope will each team receive?
Answers
Answer:
61.5 Feet of Rope
Step-by-step explanation:
Divide the rope length, 861 feet, by 14 people.
30,688 to the nearest ten thousand is
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548 to the nearest hundred is
Answers
Which of the following is not a benefit of increased physical activity?
Select one:
O a. Sleep Better
O b. Less Energy
O c. Improved Mood
O d. Improved Health
Answers
Answer:Less energy
Step-by-step explanation:Because if you don't have alot of energy in you you'll be tired and cant move that much if that makes since.
Answer is b. Less Energy is not a benefit of increased physical activity.
What is physical activity?Physical activity refers to all movement including during leisure time, for transport to get to and from places, or as part of a person's work.
here, we know that,
not a benefit of increased physical activity is Less Energy.
Because if you don't have a lot of energy in you you'll be tired and cant move that much if that makes since.
Hence, Answer is b. Less Energy is not a benefit of increased physical activity.
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