The diet which is developed by the nutritionist is effective at the 0.05 level of significance. Claim is agreed.
When do we use two-sample t-test?The two-sample t-test is used to determine if two population means are equal.
A nutritionist has developed a diet that she claims will help people lose weight. In this,
Twelve people were randomly selected to try the diet. Their weights were recorded prior to beginning the diet and again after 6 months.Here are the original weights, in pounds, with the weight after 6 months in parentheses.
Before 192 212 171 215 180 207 165 168 190 184 200 196 After 183 196 174 211 160 191 162 175 190 179 189 195The mean of the weights before 6 moths is,
[tex]\overline X_1=\dfrac{192+ 212 +171 +215 +180 +207 +165 +168 +190 +184 +200 +196 }{12}\\\overline X_1=190[/tex]
The mean of the weights after 6 months is,
[tex]\overline X_2=\dfrac{ 183 +196 +174 +211 +160 +191 +162 +175 +190 +179 +189 +195 }{12}\\\overline X_1=183.75[/tex]
Standard deviation of both the data is 16.9 and 14.7.
1. Null and Alternative Hypotheses.
The following null and alternative hypotheses need to be tested:
[tex]\begin{array}{ccl} H_0: \mu_1 & = & \mu_2 \\\\ \\\\ H_a: \mu_1 & > & \mu_2 \end{array}[/tex]
This corresponds to a right-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.
(2) Rejection RegionBased on the information provided, the significance level is α=0.05 and the degrees of freedom are df = 22. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal:
[tex]df_{Total} = df_1 + df_2 = 11 + 11 = 22[/tex]
Hence, it is found that the critical value for this right-tailed test is
[tex]t_c=1.717[/tex], for α=0.05 and df=22
The rejection region for this right-tailed test is,
[tex]R = \{t: t > 1.717\}[/tex]
(3) Test Statistics
Since it is assumed that the population variances are equal, the t-statistic is computed as follows:
[tex]t = \displaystyle \frac{\bar X_1 - \bar X_2}{\sqrt{ \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}(\frac{1}{n_1}+\frac{1}{n_2}) } }[/tex]
[tex]\displaystyle \frac{ 190 - 183.75}{\sqrt{ \frac{(12-1)16.9^2 + (12-1)14.7^2}{ 12+12-2}(\frac{1}{ 12}+\frac{1}{ 12}) } } = 0.967[/tex]
(4) Decision about the null hypothesisSince it is observed that t=0.967≤tc=1.717 it is then concluded that the null hypothesis is not rejected.
Using the P-value approach: The p-value is p=0.1721 and since p=0.1721≥0.05p = 0.1721 it is concluded that the null hypothesis is not rejected.
(5) Conclusion
It is concluded that the null hypothesis H₀ is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1 is greater than μ2, at the α=0.05 significance level.
Confidence Interval
The 95% confidence interval is −7.16<μ<19.66
Thus, the diet which is developed by the nutritionist is effective at the 0.05 level of significance. Claim is agreed.
Learn more about the two-sample t-test here;
https://brainly.com/question/27198724
#SPJ1
50 POINTS!!! PLEASE HELP DUE SOON
A fireman needs to get water to a second-floor fire. His ladder is 30 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground.
(a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest tenth of a degree and show all your work.
(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 65°. Will the ladder be safe the way it is positioned? Explain.
Answer:
sorry I tried But Don't Know The Answer
There are 114 cans of soup in a grocery store. The ratio of large cans of soup to small cans of soup is 12:7. A customer buys 2 large cans of soup. What is the new ratio of large cans of soup to small cans of soup in the grocery store? Choose all the correct answers. A. 3:5 B. 5:3 C. 8:5 D. 10:7 E. 35:21 F. 37:21
The ratio of the large cans to small cans shows the distribution of both cans
The new ratio of large cans of soup to small cans of soup in the grocery store is (b) 5 : 3 and (e) 35: 21
How to determine the ratio?The given parameters are:
Ratio = 12 : 7
Rewrite as:
Large : Small= 12 : 7
The number of cans is given as:
Can = 114
So, the distribution of the cans are:
Large = 12/(12 + 7) * 114
Large = 72
Small = 7/(12 + 7) * 114
Small = 42
When 2 large cans are purchased, the remaining number of cans are:
Small = 42
Large = 70
Express as ratio
Large : Small = 70 : 42
Simplify
Large : Small = 35 : 21
Large : Small = 5 : 3
Hence, the new ratio is (b) 5 : 3 and (e) 35: 21
Read more about ratio at:
https://brainly.com/question/16981404
PLEASE HELP howard has 3 times money as ronald if howard gives ronald $50, Ronald will then have 3 times as much as howard how much money in dollars will the two of them have together. Brainliest for answer
Answer:
$100
Step-by-step explanation:
What we know,
Howard has 3 times more money than RonaldIf Howard gives Ronald $50, Ronald will then have 3 times more money than HowardLet us assume that Ronald has $25, so Howard must have $75,
Now Howard gives $50 to Ronald, Now Ronald has $75,
Therefore our assumption is correct,
Therefore Ronald and Howard together will have $100.
graph of F(x), shown below, has the same shape as the graph of G(x) = x4, but it is shifted 4 units to the right. What is its equation?F(x) = _____
Answer:
G(x) = (x-4)⁴
Step-by-step explanation:
The equation of the graph of f(x) which is formed by shifting 4 units to the right of g(x) is f(x) = (x - 4)⁴
What is Translation of Functions?Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.
There are horizontal translation and vertical translation of functions.
Given a function G(x).
G(x) = x⁴
A function F(x) is formed by shifting the graph of G(x) to the right by 4 units.
A function h(x) when shifted to the right by k units becomes h(x - c).
So the graph of G(x) when shifted to the right by 4 units becomes G(x - 4).
G(x - 4) = (x - 4)⁴
So, F(x) = (x - 4)⁴
Hence the function is F(x) = (x - 4)⁴.
Learn more about Translation of Functions here :
https://brainly.com/question/29198392
#SPJ7
What is the solution to this inequality? -m > 5
[A] m < -5
[B] m > -5
[C] m > 5
Answer:
the answer is A
Step-by-step explanation:
trust me yw <33
Find center and radius of this circle:
[tex](x-9)^2+(y+4)^2=25[/tex]
Answer:
Center: (9,-4)
Radius: 5
Step-by-step explanation:
Equation for a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
h=9
k=-4
r=5
center is (h,k)
to find the radius, get square root of 25
Answer:
Center is (9,-4)
Radius: 5
Step-by-step explanation:
h=9
k=-4
r=5
55. Find the inverse function of [tex]g(x)=\log _{4}\left(x^{3}+2\right)[/tex] .
[tex]y= g(x) = \log_4 (x^3 +2)\\\\\text{Replace x with y and solve for y:}\\\\~~~~x=\log_4 (y^3 +2)\\\\\implies y^3 +2 = 4^x\\\\\implies y^3 =4^x-2\\ \\\implies y = \sqrt[3]{4^x -2}\\\\\implies f^{-1} (x) = \sqrt[3]{4^x -2}[/tex]
Find the slope of the line containing the pair of points.
(5,1) and (-5, -9)
I really need this
Answer:
1
Step-by-step explanation:
[tex]my \: dear \: \\ to \: find \: the \: slope \: of \: a \: line \: use \: the \: formular \\ slope = \frac{y2 - y1}{x2 - x1} \\ from \: the \: question \: x1 = 5 \: \: y1 = 1\: \: x2 = - 5 \: \: y2 =- 9 \\ slope = \frac{ - 9 - 1}{ - 5 - 5} = \frac{ - 10}{ - 10} = 1 \\ therefore \: slope = 1 \\ hope \: this \: helps \\ stay \: focused \: with \: your \: studies[/tex]
Please help this mad hard
Answer:
First Net
Step-by-step explanation:
The first net will be the answer because you can see that the figure has a square base. The first net has a square base as well. Now, the side of the figure has equal triangles, and so does the first net. The first net fits the figure best.
Hope this helps :)
Fred is baking cookies for a school
bake sale. It takes
2/3 of a cup of
sugar to
make one batch of
cookies. How many cups
of sugar
does he need to double the
recipe?
Answer: Fred needs 4/3 a cup of sugar, which can be simplified into 1 1/3.
Step-by-step explanation:
If you do 2/3 times 2/1 (because double means twice the amount) you will get 4/3, which again, can be simplified into 1 1/3.
also may i have help with this one
which is bigger 25 fl oz or 1 pint
if you help it would be appreciated
#learning with brainly
Answer:
25 fl oz
Step-by-step explanation:
1 pint is equivalent to 16 fl oz, so we're left with 25 fl oz and 16 fl oz. As you can see, 25 is greater than 16, making 25 fl oz the correct answer.
whai is numarates what is
Answer:
Not a proper question. But I think it's a 5
[tex] \huge \pink{ \underline{ \overline{ \: 5 \: i \: think}}}[/tex]
URGENT PLEASE HELP 50 POINTS AND WILL NAME BRAINLIEST An ice cream store has the pricing shown below. You want to determine the best value. The height of the cone is 4.5 in and the diameter is 2 in. The diameter of each scoop is 3 in. Assume the cone is stuffed full with ice cream. single is $3.50, double is $4.50, and triple is $5.50 Create a table showing the total cost of each size, the total volume of ice cream for each size, and the unit cost (per unit volume) of each size. Include units with your table entries. you dont have to create the table, but i really need the values!
u take x then multiply it by b, the add 9 to x then we will get the answer xb9x, hope u understand;>
Two of the angles in a triangle measure 17° and 153° What is the measure of the third angle?
Answer:
10
Step-by-step explanation:
153+17=170
180-170=10
Please help me thank you!
Find the area (image attached) this is literally my 3 time asking
I'll help you!
Answer:
EXACT: 2.7√1.71 + 4.05 units²
APPROX: 3.5307 + 4.05 = 7.58 units²
Step-by-step explanation:
See the attached help image
Total A = 2 triangles + 1 trapezoid
Triangles
Find missing side:
2.7² + b² = 3²
b² = 3² - 2.7²
b = √1.71
Find area of triangles:
A = bh/2
A = b(2.7)/2
A = √1.71(2.7)/2
A = 1.35√1.71 units²
Trapezoid
A = (a + b)(h)/2
A = ((3-√1.71) + √1.71)(2.7)/2
A = (3)(2.7)/2
A = 4.05 units²
Total
2(1.35√1.71) + 1(4.05)
EXACT: 2.7√1.71 + 4.05 units²
APPROX: 3.5307 + 4.05 = 7.58 units²
Question 3 of 10
which choice is equivalent to the quotient
According to the property
below?
O A -5
B. 25
C5
OD. - 5
ES
Answer: D: Square Root Of 5
Step-by-step explanation: 30/6 is 5, now fill in the sqrt symbol. Hope this helped. (This problem was one of the simpler, friendlier numbers.)
What is the equation of a line that has a slope of One-half and passes through point (2, –3)?
Answer: y = one-half x minus 4
Step-by-step explanation:
y = 1/2 x + b
-3 = 1/2 (2) + b
-3 = 1 + b
-3 - 1 = b
-4 = b
Jim is 8 ft 9 in tall. Jane is 23.5 in tall. How many times taller than Jane is Jim?
Alguien podra ayudarme en pregunta numero 8
Answer:
jb
Step-by-step explanation:
9
Help please!! MY LIFE DEPENDS ON THIS
Answer:
D
Step-by-step explanation:
A total of 18 teams made 26 or more feild goals.
What is 10,000 written as a power with a base of 10?
Enter your answer in the boxes.
Answer:
10 to the power of 4
Step-by-step explanation:
3. Subtract
x)--5x2 + x-2
g(x) = -3x2 + 3x + 9 9
Step-by-step explanation:
For example: Subtract 4x - 10y + 15z from 5x + 8y - 20z.
Step 1: Arrange the polynomials in standard form. In this example, it is already arranged.
Step 2: Place them horizontally.
(4x - 10y + 15z) - (5x + 8y - 20z)
Step 3: Change the sign of the second polynomial through the parentheses.
4x - 10y + 15z - 5x - 8y + 20z
Step 4: Arrange the like terms together.
4x - 5x - 10y - 8y + 15z + 20z
Step 5: Solve the equation
-x - 18y + 35z
Therefore, when we subtract 4x - 10y + 15z from 5x + 8y - 20z = -x - 18y + 35z.
What is the area of a circular cardboard piece needed for the base of a model of a volcano that is 20 centimeters tall and has a volume of 960 cubic centimeters?
Answer:
144
Step-by-step explanation:
im right:D have a good day or night
The sum of the first 10 terms of an arithmetic series is 100 and the sum of next 10 300 .Find the series.
Let a be the first term in the sequence, and d the common difference between consecutive terms. If aₙ denotes the n-th term in the sequence, then
a₁ = a
a₂ = a₁ + d = a + d
a₃ = a₂ + d = a + 2d
a₄ = a₃ + d = a + 3d
and so on, up to the n-th term
aₙ = a + (n - 1) d
The sum of the first 10 terms is 100, and so
[tex]\displaystyle \sum_{n=1}^{10} a_n = 100 \\ \sum_{n=1}^{10} (a + (n-1)d) = 100 \\ (a-d) \sum_{n=1}^{10} 1 + d \sum_{n=1}^{10} n = 100 \\ 10a+45d = 100[/tex]
where we use the well-known sum formulas,
[tex]\displaystyle \sum_{n=1}^N 1 = 1 + 1 + 1 + \cdots + 1 = N[/tex]
[tex]\displaystyle \sum_{n=1}^N n = 1 + 2 + 3 + \cdots + N = \frac{N(N+1)}2[/tex]
The sum of the next 10 terms is 300, so
[tex]\displaystyle \sum_{n=11}^{20} a_n = 300 \\ (a-d) \sum_{n=11}^{20} 1 + d \sum_{n=11}^{20} n = 300 \\ (a-d) \left(\sum_{n=1}^{20} 1 - \sum_{n=1}^{10} 1\right) 1 + d \left(\sum_{n=1}^{20} n - \sum_{n=1}^{10} n\right) = 300 \\ 10a+145d = 300[/tex]
Solve for a and d. Eliminating a gives
(10a + 145d) - (10a + 45d) = 300 - 100
100d = 200
d = 2
and solving for a gives
10a + 145×2 = 300
10a = 10
a = 1
So, the given sequence is simply the sequence of positive odd integers,
{1, 3, 5, 7, 9, …}
given recursively by the relation
[tex]\begin{cases}a_1 = 1 \\ a_n = a_{n-1} + 2 & \text{for }n>1\end{cases}[/tex]
and explicitly by
[tex]a_n = 1 + 2(n-1) = 2n - 1[/tex]
for n ≥ 1.
A table showing Tickets Sold, Cost, and Total. The first row shows Child, with the entries, c, 3, and 3 c. The second row shows Adult, with entries, x, 5, 5 x. The last row shows Total, with all three entries blank.
Tickets to a baseball game cost $3 for a child’s ticket and $5 for an adult ticket. At the last game, $521 was collected when 139 people attended the game. Which value could replace x in the table so that a single-variable equation can be written and solved to determine the number of child’s tickets, c, sold?
Answer:
x = 52, c = 87
Step-by-step explanation:
Set up and then solve this system of equations:
3c + 5x = 521--->3c + 5x = 521
c + x = 139 --->3c + 3x = 417
-------------------
2x = 104
x = 52, c = 87
Answer: the answer is 139-c
Help solving this problem
Answer:
A=0.50
B=0.477
C=0.423<p<0.531
Step-by-step explanation:
sample size N :333
number of success X: 159
sample part of success x/n = 159/333
x=0.477 B
0.50 A Half a chance to flip a tail or head
part C:
[tex]0.477 plusminus 1.96 * \sqrt{ \frac{0.477 (1 - 0.477)}{333} } [/tex]
simplify
[tex]0.477 plusminus 1.96 * 0.0536[/tex]
expand
[tex]0.477 + 1.96 * 0.0536[/tex]
[tex]0.531[/tex]
expand minus
[tex]0.477 - 1.96 * 0.0536[/tex]
[tex]0.423[/tex]
finally answer part c
[tex]0.423 < p < 0.531[/tex]
Two cables are securing a kayak to a roof rack. The forces are represented by vectors Vector u = LeftAngleBracket negative 5, 6, 3 RightAngleBracket. and Vector t = LeftAngleBracket negative 8, negative 2, 1 RightAngleBracket.. If both cables are replaced by a single cable, what vector would represent the cable?
LeftAngleBracket 3, 8, 2 RightAngleBracket.
LeftAngleBracket negative 13, 4, 4 RightAngleBracket.
LeftAngleBracket negative 3, negative 8, negative 2 RightAngleBracket.
LeftAngleBracket 13, negative 4, negative 4 RightAngleBracket.
Answer:
< –13, 4, 4 >
Step-by-step explanation:
Vector u = < –5, 6, 3 >
Vector t = < –8, –2, 1 >
-5 6 3
+ -8 -2 1
-13 4 4
Vector u + t = < –13, 4, 4 >
Answer:
B. <14,-3>
Step-by-step explanation:
What was likely the purpose of the Great Enclosure?
A. To keep slaves and workers from escaping
B. To protect Zimbabweans from outside invasion
C. To separate the wealthy from the poor in society
D. To enclose cattle and horses