Test the claim that the two samples described below come from populations with the same mean. Assume that the samples are independent simple random samples. Use a significance level of α = 0.01
Sample 1: n1 = 13, ¯x1 = 23, s1 = 6
Sample 2: n2 = 16, ¯x2 = 29, s2 = 5.9
(a) The degree of freedom is _____
(b) The test statistic is _____
(c) Determine the rejection region for the test of H0:μ1−μ2=0 and Ha:μ1−μ2≠0
(d) |t| > _____
To test the claim that the two samples described come from populations with the same mean, we can use a two-sample t-test.
(a) The degree of freedom is 27
(b) The test statistic is -2.67
(c) Determine the rejection region for the test of H0:μ1−μ2=0 and Ha:μ1−μ2≠0 : we do not reject the null hypothesis.
(d) |t| > 2.70
(1) The degree of freedom for the two-sample t-test is calculated as
df = n1 + n2 - 2 = 13 + 16 - 2 = 27.(2) The test statistic for the two-sample t-test is calculated as:
t = (¯x1 - ¯x2) / sqrt[(s1^2 / n1) + (s2^2 / n2)]Plugging in the values, we get:
t = (23 - 29) / sqrt[(6^2 / 13) + (5.9^2 / 16)] = -6 / sqrt[(36/13) + (34.81/16)] = -6 / sqrt[2.77 + 2.18] = -6 / sqrt[4.95] = -6 / 2.23 = -2.67(3) To determine the rejection region for the test, we can use a significance level of α = 0.01. For a two-tailed test with α = 0.01, the critical value for t is approximately 2.70. Since our test statistic (-2.67) is less than the critical value, we do not reject the null hypothesis.
(4) For the rejection region, we need to consider values of t that are either greater than or less than the critical value. Therefore, we need to consider |t| values that are greater than 2.70. |t| > 2.70.
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find the measure of m< YBA
The measure of an angle m ∠YBA=47°.
What is meant by an angle?In Euclidean geometry, an angle is a figure made up of two rays that have a shared vertex, also known as a common terminus, and are referred to as the angle's sides. The angles of two rays are situated in the plane containing the rays. An angle is also created when two planes intersect at an angle. These are referred to as dihedral angles. Another technique to define two curves is to specify the angle generated by rays that are tangent to the intersection of two curves. Angle is another word for how long a rotation or angle is.
Since,
ΔFBA=ΔYBA
The two triangles in the provided illustration are comparable.
So,
From the figure:
m ∠FBA=47°
So, m ∠YBA=47°
Therefore, the measure of angle m ∠YBA=47°
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pls i need it now
thx i might gv brainliest
The total pay that Nelly will get for last week is £220.
What will the total pay of Nelly be ?From the information given, the following can be deduced:
£8 per hour for the first 15 hours
£10 let hour for any extra hour.
The above are applicable for Monday to Friday.
£16 is the rate for Saturdays.
The number of hours that Nelly worked from Monday to Friday will be:
= 3 1/2 + 5 + 2 1/2 + 4 + 2
= 17 hours
On Saturday, he worked 5 hours.
The total earnings will be:
= (£8 × 15) + (£10 × 2) + (£16 × 5)
= £120 + £20 + £80
= £220
The total amount is £220.
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Sara needs to determine the number of 3/4 pound servings into 9 3/4 pounds of turkey.she calculates that there are 13 servings.is stated calculation correct why or why not
There are 9.75 servings, not 13 servings.
What are arithmetic operations?
Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.
We have,
the number of 3/4 pound servings in pounds of turkey
she calculates that there are 13 servings.
so,
9 (3/4) = (36 + 3) /4
= 39/4
= 9.75
Hence, there are 9.75 servings, not 13 servings.
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In rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB=11 and BC=6, what is the area of the shaded region? Write your answer as a decimal, if necessary. Do not include units in your answer.
Answer:
The area of the shaded region is 36.
In rectangle ABCD, point E lies halfway between sides AB and CD and halfway between sides AD and BC. This means that line segment AE is parallel to line segment CD and is half as long, and line segment BE is parallel to line segment AD and is also half as long.
Since AE is half as long as CD, and CD is twice as long as AE, we can say that CD is equal to 2 * AE. Similarly, since BE is half as long as AD, and AD is twice as long as BE, we can say that AD is equal to 2 * BE.
Since AD is equal to 2 * BE and CD is equal to 2 * AE, the lengths of AD and CD are equal. This means that the shaded region is a parallelogram with sides of equal length.
The area of a parallelogram is equal to the product of its base and height. In this case, the base of the parallelogram is 6 (the length of side BC) and the height is AE + BE (the combined length of the two sides of the parallelogram).
We know that AE is half as long as CD, and CD is twice as long as AE, so CD is equal to 2 * AE. Since CD is equal to 2 * AE, AE is equal to CD / 2. Since CD is equal to 11 (the length of side AB), AE is equal to 11 / 2 = 5.5.
Similarly, we know that BE is half as long as AD, and AD is twice as long as BE, so AD is equal to 2 * BE. Since AD is equal to 2 * BE, BE is equal to AD / 2. Since AD is equal to 6 (the length of side BC), BE is equal to 6 / 2 = 3.
The combined length of AE and BE is 5.5 + 3
one and three fifths plus three and two thirds equals blank
Answer:
5 [tex]\frac{4}{15}[/tex]
Step-by-step explanation:
1 [tex]\frac{3}{5}[/tex] = 8/5
3 [tex]\frac{2}{3}[/tex] = 11/3
In order to add fractions, the denominators, or the bottom numbers, have to be the same. To make them the same, find the common denominator (the lowest number that both the numbers can be divisible by)
8/5+ 11/3 the common denominator would be 15 so multiply the appropriate numbers to the denominators and the numerators (the top number)
24/15 + 55/15 = 79/15
Now simplify
79/15 = 5 [tex]\frac{4}{15}[/tex]
The distance around a circular park is 88 yards.
What is the area of the park? Use 3.14 for π.
Answer:
616.25 [tex]yd^2[/tex]
Step-by-step explanation:
The equation for the area of a circle is
[tex]A=\pi r^2[/tex]
Since the problem does not give a value for r, it must be derived. Recall that the equation for the circumference of a circle is
[tex]C=2\pi r[/tex]
Using the given value of the circumference,
[tex]C=88yd=2\pi r[/tex]
So,
[tex]88yd=2\pi r\\\frac{88yd}{2\pi}=r\\14.01yd=r[/tex]
Insert the derived value of r into the formula for area:
[tex]A=\pi r^2\\A=\pi(14.01yd)^2\\A=616.25yd^2[/tex]
help Me out and I’ll give you brainliest
Answer: 5/8
Step-by-step explanation: There are 8 members. Out of 8, there are 5 people's weight that are higher than 135. Therefore the answer is 5/8.
Each marble bag sold by Jane's Marble Company contains 4 purple marbles for every 5 red marbles. If a bag has 24 purple
marbles, how many red marbles does it contain?
The no: of red marbles, that the bag contains if it has 24 purple marbles are 30 marbles.
What is a unitary in math?a single state. This has an identity element in math, in an algebra. Whose inverse is equivalent to its adjoint (in mathematics, linear algebra, mathematical study of a matrix or operator).
What is unitary formula?The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.
What is the unitary rule?A unitary government is a type of government in which the whole government is controlled by a single entity, known as the central government. Actually, the center of authority for all administrative divisions and powers.
In the given question,
for every 4 purple marbles there are 5 red marbles
then for 1 purple marble there is 5/4 red marbles
again for 24 purple marbles, there are 30 red marbles
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Nine less than two times a number is five more than this number. What is the number?
Answer:
14
Step-by-step explanation:
let n be the number then 2 times the number is 2n and so
2n - 9 = n + 5 ( subtract n from both sides )
n - 9 = 5 ( add 9 to both sides )
n = 14
then the required number is 14
Answer the question below and for part B write the equation with the answer that you get for part A.
A
B
C
D
From the linear function, the rate of change is 35 and the unit cost is 35
Linear FunctionA linear function is defined as a function that has either one or two variables without exponents.
In this problem, we have to write a linear function that models the table given. This will take the form of y = mx + c
m = slope or rate of change and c = constant or unit cost of the product.
The formula of slope of a line is given as
m = y₂ - y₁ / x₂ - x₁
Taking two points from the table;
m = 215 - 180 / 5 - 4
m = 35
Using the slope of the line, we can find the y - intercept of the function.
y = mx + c
215 = 35(5) + c
215 = 175 + c
c = 215 - 175
c = 40
The linear function of the table is y = 35x + 40
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HELP URGENT
A set of data items is normally distributed with a mean of 200 and a standard deviation of 40. Find the data item in this
distribution that corresponds to the given z-score.
z = -3
The data item that corresponds to z = -3 is ___
(Type an integer or a decimal.)
Answer:
the data item that corresponds to z = -3 is 80.
Step-by-step explanation:
NO LINKS!! Write an expression for the nth term of the geometric sequence. Then find the indicated term.
a1= 3, r = √(2), n = 10
a_n =
a_10=
Answer:
[tex]tn = {3 \times \sqrt{2} }^{n - 1} [/tex]
Step-by-step explanation:
since it is geometric sequence we will use the formula
[tex]tn = {ar}^{n - 1} [/tex]
n = 10
r = √2
a = 3
lets first see the result of the 10th term
[tex]t10 = {ar}^{10 - 1} [/tex]
[tex]t10 = {ar}^{9} [/tex]
[tex]t10 = {3 \times \sqrt{2} }^{9} [/tex]
t10 = 3 × 22.63
t10 = 67.89
approximately 68
t10 = 68
for the nth term
Tn = ar^n–1
[tex]tn = {3 \times (\sqrt{2} })^{n - 1} [/tex]
i hope this helps
Answer:
[tex]a_n=3\left(\sqrt{2}\right)^{n-1}[/tex]
[tex]a_{10}=48 \sqrt{2}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given:
[tex]a = 3[/tex][tex]r = \sqrt{2}[/tex][tex]n=10[/tex]Substitute the given values of a and r into the formula to create an equation for the nth term:
[tex]a_n=3\left(\sqrt{2}\right)^{n-1}[/tex]
To find the 10th term, substitute n = 10 into the equation:
[tex]\implies a_{10}=3\left(\sqrt{2}\right)^{10-1}[/tex]
[tex]\implies a_{10}=3\left(\sqrt{2}\right)^{9}[/tex]
[tex]\implies a_{10}=3 \cdot 2^{\frac{9}{2}}[/tex]
[tex]\implies a_{10}=3 \cdot 2^{4+\frac{1}{2}}[/tex]
[tex]\implies a_{10}=3 \cdot 2^{4} \cdot 2^{\frac{1}{2}}[/tex]
[tex]\implies a_{10}=3 \cdot 16 \cdot \sqrt{2}[/tex]
[tex]\implies a_{10}=48 \sqrt{2}[/tex]
Which equation shows the quadratic formula used correctly to solve 7x² = 9+ x for x?
-1± √(1)²-4(7) (9)
2(7)
O
X=
X=
OX=
Ox=
1± √(-1)²-4(7)(9)
2(7)
-1± √(-1)² +4(7) (9)
2(7)
1± √(-1)² +4(7) (9)
2(7)
Answer: X= -1± √(-1)² - 4(7)(9)
2(7)
Step-by-step explanation: The correct equation for using the quadratic formula to solve 7x² = 9 + x for x is:
X= -1± √(-1)² - 4(7)(9)
2(7)
The quadratic formula is given by the equation X = -b ± √(b² - 4ac) / 2a, where a, b, and c are the coefficients of the quadratic equation. In this case, we have a = 7, b = 1, and c = 9, so plugging these values into the formula gives us the equation above.
The equation used to solve Quadratic Equation is -1 ± [√((-1)² - 4(7)(-9])/2(7)
What is 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. LHS = RHS is a common mathematical formula.
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:
we have the Quadratic Equation as:
7x² = 9+ x
7x² -x -9= 0
Using Discriminant method
x = -b ± √(b² -4ac)/2a
x = 1 ± √(1² - 4(7)(-9)/2(7)
x = 1 ± √(1 + 196)/14
Thus, the formula used 1 ± [√(1² - 4(7)(-9])/2(7)
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Find an equation of the line passing through the pair of points. Write the equation in the form Ax+By = C.
(3,4) and (2,1)
Answer:
-3x+y=-5
Step-by-step explanation:
First, find the slope of the equation:
m=(y2-y1)/(x2-x1) ==> m=slope of equation
(x1, y1), (x2, y2) ==> (x1=3, y1=4), (x2=2, y2=1)
m=(1-4)/(2-3) ==> plugin x1=3, y1=4, x2=2, and y2=1
m=-3/(-1)
m=3
y=mx+b ==> slope-intercept equation
1=3(2)+b ==> plugin 3 for m and (2, 1) where x=2 and y=1
1=6+b ==> solve for b
1-6=6-6+b
b=-5
y=3x+(-5) ==> plugin -3 for m and -5 for b
y=3x-5 ==> simplify
Now, Isolate -5 since it is the only constant
y-3x=3x-3x-5 ==> isolate -5 by subtracting 3x on both sides
-3x+y=-5 ==> simplify and put in Ax+By=C form
y = 3x - 5
sorry can't help with step to step explanation......
cos 0 = 0.8192 A = 45
H = ?
The value of H (Hypotenuse) will be 54.93
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The values are,
⇒ cos θ = 0.8192
⇒ A (Base) = 45
Now,
Since, The values are,
⇒ cos θ = 0.8192
⇒ A = 45
We know that;
⇒ cos θ = Base (A) / Hypotenuse (H)
Substitute all the values, we get;
⇒ 0.8192 = 45 / H
⇒ H = 45 / 0.8192
⇒ H = 54.93
Thus, The value of H (Hypotenuse) = 54.93
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Question 2 of 10
Which statement regarding salaried employees is true?
A. Salaried employees get paid more for additional hours worked.
B. Salaried employees have taxes with held from each paycheck.
c. Salaried employees do not receive an agreed-upon annual pay.
D. Salaried employees never receive medical benefits.
HELP FAST!!!!
INVESTMENTS Your aunt receives an inheritance of $20,000. She wants to
put some of the money into a savings account that earns 2% interest annually and
invest the rest in certificates of deposit (CDs) and bonds. A broker tells her that
CDs pay 5% interest annually and bonds pay 6% interest annually. She wants to
earn $1000 interest per year, and she wants to put twice as much money in CDs
as in bonds. How much should she put in each type of investment?
11.
Answer: She needs to invest 6,000 in bonds,6,000inbonds,12,000 in CDs and 2000 in the Savings account to earn a2000intheSavingsaccounttoearna1000 interest.
We follow these steps in order to arrive at the answer:
Let the amount invested in bonds be x
Since the amount to be invested in CDs is twice the investment in bonds, investment in CDs will 2x.
The amount to be invested in the savings bank will be 20000 - (x+2x)20000−(x+2x) or 20,000 - 3x20,000−3x
The interest earned on bonds will be 0.06x0.06x
The interest earned on CDs will be 2x*0.05 = 0.1x2x∗0.05=0.1x
The interest earned on the savings banks accounts will be (20,000-3x)*0.02 = 400-0.06x(20,000−3x)∗0.02=400−0.06x
The total expected interest of $1000 is the sum total of the interest earned from each of the three modes of investment.
Hence total interest is:
1000 = 0.06x + 0.1x+ 400 -0.06x1000=0.06x+0.1x+400−0.06x
Simplifying we get,
1000 -400 = 0.1x1000−400=0.1x
600 = 0.1x600=0.1x
\mathbf{x = 6,000}x=6,000
Since x represents investments in bonds, the investment in CDs will be \mathbf{2x = 2*6,000 = 12,000}2x=2∗6,000=12,000
Finally the investments in savings bank will be \mathbf{20000 - (12,000 + 6,000) = 20,000 - 18,000 = 2,000}20000−(12,000+6,000)=20,000−18,000=2,000
Graph the image of the given triangle after the transformation that has the rule (x, y) → (x - 1, y + 5).
Select the Polygon tool. Click the points of the triangle vertices to create the triangle by connecting the sides.
Copy and complete the equation of line G below
y=___x+____
Answer:
y = 3x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (1, 7) ← 2 points on the line
m = [tex]\frac{7-4}{1-0}[/tex] = [tex]\frac{3}{1}[/tex] = 3
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = 3x + 4 ← equation of line
Date Exchange Rate
October 8, 1982 267.38 Yen = 1 US dollar
June 30, 1995 84.90 Yen = 1 US dollar
a. Determine the cost, in US dollars, for a souvenir that cost 3,500 Yen
on October 8, 1982. Show your work in the provided space.
Using proportions, the value of 3500 Yen on October 8, 1982 is 13.1 USD
ProportionsProportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
On October 8, 1982;
267.38 Yen = 1US
The cost of 3500 Yen = ?
267.38 Yen = 1 USD
35000 Yen = x USD
Cross multiply both sides and solve for x
x * 267.38 = 3500 * 1
267.38x = 3500
Divide both sides by coefficient of x
267.38x / 267.38 = 3500 / 267.38
x = 13.1
The value of 3500 Yen is 13.1 USD
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Help fast please !!!
Answer:
D.
Step-by-step explanation:
Thousandhts
Answer:
d. 7 thousandths
WHY?
0.007 places is a decimal representation of a number. In the decimal system, the value of a digit is determined by its position relative to the decimal point. In this case, the number 0.007 has three digits to the right of the decimal point, so it is said to have three decimal places. The value of each digit in this number is determined by its position: the first digit (0) is in the hundredths place, the second digit (0) is in the thousandths place, and the third digit (7) is in the ten-thousandths place.
What is 7,899 to the nearest thousand
Answer: 8,000
Step-by-step explanation: So, to find how to round this to the nearest 1000, we need to look at the 3 digits being the 7. So, 899 is greater than 500, so we round up, so 7 + 1 is 8, and we change those 3 digits behind the zero to 0's, so we get 8,000. I hoped this helped.
Answer:
8000
7899 rounded to nearest thousand is 8000, because 7 is in thousand's place value, and the number after that is 8, which is more than 5, so 1 is added to 7, and it becomes 8. The rest of the numbers turn to 0.
so you get 8000.
hope it helps :)
Is the weight of a bike a function of how old it is?
The weight of an object is the amount of the gravitation pull of the Earth on the object. No, the weight of a bike is not a function of its age.
What i weight?The mass of an object is the quantity of matter it contains, while the weight is the amount of gravitational pull of the Earth on the object. Thus the greater the mass of an object is, the greater its weight. This implies that the weight of an object can be influenced by its value of mass.
The mass of an object can be determined or measured by the use of any of the weighing balances, while the weight of an object can be measured by the use of any of the spring balances. Therefore, the answer to the given question is NO. The weight of a bike is NOT a function of its age. The weight of the bike will depend on the number, and weight of its component parts.
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Sarah received 23 chromosomes from her mother and 23 chromosomes from her father. The combination of genes on these chromosomes code for proteins that express her traits. Choose the words or phrases to complete the sentence. A diagram of a Punnett square. The top of the Punnett square is labeled Father with x and y above the boxes. The side of the square is labeled Mother with x and x on the left side of the boxes. The top row, first box has xx female, the top row, second box has xy male. The second row, first box has xx female, the second row, second box has xy male. There are two long, tubular object along the side of the diagram labeled x chromosome. There is a small circular object on the bottom of the diagram labeled y chromosome. The chromosomes in the image are called Choose... , and the chances of being born male or female are Choose... .
The chromosomes in the image are called sex chromosomes, and the chances of being born male or female are 1:1.
What is a chromosome?In Science, a chromosome can be defined as a thread-like linear strand of deoxyribonucleic acid (DNA) that is typically found in the nucleus of each cell in a living organism.
What are the characteristics of a chromosome?In Genetics, some of the characteristics of a chromosome include the following:
Chromosomes are made up of a long deoxyribonucleic acid (DNA) molecule that is tightly wound.Every chromosome consist of many genes with each gene being a single segment of deoxyribonucleic acid (DNA).Furthermore, the human somatic cell primarily comprises 46 chromosomes which are normally sub-divided into 23 pairs of chromosomes with 22 of these pairs being autosomes and a pair of sex chromosomes (X and Y).
In this context, we can reasonably infer and logically deduce that the x and y chromosomes are generally referred to as sex chromosomes.
Since Sarah received 23 chromosomes each from her mother and father, the chances of being born male or female is given by;
Ratio = 23: 23.
Dividing both sides by 23, we have;
Ratio = 1:1.
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Write an inequality that represents the sentence:
14 fewer than a number is at least -8.
and
the product of a number and 5 is no more than 8.
an online magazine allows you to view up to 25 articles free to view 30articles, you pay $49.15. to view 33 articles, you pay $57.40. what is the cost of each article for which you pay a fee?
Answer:
$2.75
Step-by-step explanation:
The difference in cost for 33 articles and 30 articles is
$57.40 - $49.15 = $8.25
From 30 to 33 articles, the difference is 3 articles.
3 articles cost $8.25.
Cost per article = $8.25/3 = $2.75
Three groups of research participants have played a game with various amounts of violence and were assessed on a stress-related scale (where 0 = no stress, 100 = very stressed) afterwards. The first group of participants (Group 1) have played a non-violent game. The second group of participants (Group 2) have played a moderately violent game. The third group of participants (Group 3) have played a very violent game. The researchers would like to know if the results on a stress scale differ for these groups. What is the null hypothesis? (2 points) Your answer: What is the research hypothesis?
Since, F value is =19.056 is greater than F critical value =3.3541
Therefore, We have enough evidence that null hypothesis is not rejected
What is hypothesis ?A hypothesis is a theory that is put up to account for a phenomenon. Unless it can be tested through the scientific method, a hypothesis cannot be referred to as a scientific hypothesis. Scientific theories frequently begin with historical observations that cannot currently be fully explained by existing knowledge.
Here,
Null hypothesis,
[tex]H_{0}[/tex]: u1 = u2 =u3
u1,u2,u3 are means of stress scale for group 1 , group 2 and group 3
Alternate hypothesis,
[tex]H_{A}[/tex] : u1≠u2
The F value is =19.056
Using F critical value α=0.05
df numerator =2 , df denominator = 27
F critical value =3.3541
Conclusion : F value is =19.056 is greater than F critical value =3.3541
Therefore, We have enough evidence that null hypothesis is not rejected
We, conclude that all three groups are equals in terms of mean.
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A shipping firm suspects that the mean life of a certain brand of tire used by its trucks is less than 35,000 miles. To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 34,200 miles with a standard deviation of 1200 miles. At α = 0.05, test the shipping firm's claim. Round the test statistic to the nearest thousandth.
Step 1) Write the null and alternative hypotheses.
Step 2) State a level of significance α. Determine the critical value and critical region.
Step 3) Compute the test statistic. Use classical approach or P-value approach.
Step4) Compare the critical value with test statistic or P-value with α.
Step5) State the conclusion.
Since H0 is not rejected so, the mean life of a contain brand of tire used by it's trucks is not less than 35,000 miles.
What is standard deviation?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
A shipping firm suspects that the mean life of a certain brand of tire used by its trucks is less than 35,000 miles.
To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 34,200 miles with a standard deviation of 1200 miles.
At α = 0.05, test the shipping firm's claim.
Under H0: μ 200 Vs H1: > 200 (Right tailed test)
n = 16, x bar = 205 , s = 14
Null Hypothesis; H0: μ = 35000 Vs H1: < 35000
(Mean life of brand of tire less than 35000 miles).
Under H0 test statistic is
t = (x bar - μ) / (s / √n) ≈ [tex]t_n_-_1[/tex]
Now, n = 18, x bar = 34,200, s = 12000
t = (34000 - 35000) / (1200 / √18) = -2.8284
t - critical value of α = 0.05 for left tailed at (18 - 1) df = -2.11
Therefore t calculated (= -2.8284) < -2.11
So, we do not reject H0.
Hence, since H0 is not rejected so, the mean life of a contain brand of tire used by it's trucks is not less than 35,000 miles.
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is 0 a solution for w+3=w
Answer:No
Step-by-step explanation:
0+3 = 3, not zero