There would be a 68% chance that the average blood pressure would be between 193 to 197.
The subset chosen from the larger set to make assumptions is known as a random sample. A range of values is a confidence interval.
We know that,
E = z ( α / 2 ) × σ / √n → 1
As per the given question,
Blood pressure in a population of very at risk people has an expected value ( x ) = 195Standard deviation ( σ ) = 20Number of random samples ( n ) = 100For 68% confidence,
z ( α / 2 ) = 0.9944
Substitute the values in 1,
E = z ( α / 2 ) × σ / √n
= 0.9944 × 20 / √100
= 0.9944 × 20 / 10
= 0.9944 × 2
E = 1.9888 ≅ 1.99
Let us consider,
⇒ x - E < μ < x + E
⇒ 195 - 1.99 < μ < 195 + 1.99
⇒ 193.01 < μ < 196.99
⇒ 193 < μ < 197 ( ∵ 193.01 ≅ 193 and 196.99 ≅ 197 )
⇒ μ = ( 193 , 197 )
Therefore, A 68% chance that the average blood pressure lies between 193 to 197. Hence Option b is correct.
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The complete question is
Blood pressure in a population of very at risk people has an expected value of 195 and a standard deviation of 20. Suppose you take a random sample of 100 of these people. There would be a 68% chance that the average blood pressure would be between Select one:
a.) 155 to 235
b.) 193 to 197
c.) 175 to 215
d.) 191 to 199
e.) 200 to 230
fidn teh are of the shaded region of the circle of radius a if the chord i h units from the center of the circle
Answer:
1027
Step-by-step explanation:
Describe the location of the point that has the following coordinates: negative abscissa, zero ordinatea. between Quadrant III and Quadrant IVb. between Quadrant II and Quadrant IVc. between Quadrant I and Quadrant IVd. between Quadrant II and Quadrant III
The correct location of the point is (d) between Quadrant II and Quadrant III.
We must choose the response that accurately describes the position of the point whose coordinates have a negative abscissa and a zero ordinate.
Any point with a negative abscissa and a zero ordinate on the XY plane in two dimensions can be represented as
Where a > 0, (x, y) = (-a, 0).
Let's plot (-1, 0), (-2, 0), (-3, 0), etc. on the coordinate plane as an example. The corresponding figure illustrates this.
The figure shows that every point of the type (-a, 0) is located on the X-axis' negative side.
The location of the negative X-axis between Quadrants II and III is known. As a result, the supplied point is situated between Quadrants II and III.
the appropriate answer is (d).
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alpha can produce either 18 oranges or 9 apples an hour, while beta can produce either 16 oranges or 4 apples an hour. which of the following statements is true?
If alpha specialize in growing apples beta specialize in growing oranges the both could gain profit by the trade is true for the statement
Comparative advantage describes a situation in which a person or a country involved in trade processes may not have an absolute advantage, but can still benefit from trade on a comparative basis.
The nations frequently trade goods based on their comparative advantages so that both parties can benefit from trade.
According to the stated information,
Alpha can produce either 18 oranges or 9 apples per hour, while beta can only produce 16 oranges or 4 apples per hour, it is stated.
so ,If alpha specialize in growing apples and beta specialize in growing oranges the both could gain profit by the trade
Hence, option C is true
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Researchers randomly selected 1700 people from Canada who had never suffered a heart attack and rated the happiness of each person. Ten years later, the researchers followed up with each person and found that people who were initially rated as happy were less likely to have a heart problem. Which of the following is the most appropriate conclusion based on this study?
Happier people in the study were less likely to have heart problems.
The correct answer is People in Canada who are happier are less likely to suffer cardiac problems.
We have been given four options from which we have to select the correct one.
a. Happiness causes better heart health for all people.
b. Happiness causes better heart health for Canadians.
c. Happiness causes better heart health for the people in the study.
d. Happier people in Canada are less likely to have heart problems.
e. Happier people in the study were less likely to have heart problems.
The researchers followed up with each person 10 times later and discovered that those who had been deemed pleased at the start were no longer so. People in Canada who are happier are less likely to suffer cardiac problems.
Therefore, the conclusion is people in Canada who are happier are less likely to suffer cardiac problems.
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a store is selling laptops with six different operating systems. a company would like to buy 35 of those laptops for their employees. in how many ways can this company buy them?. show all your work step by step to get credit. final answers must be provided in decimal form
On solving the provided question, based on the information, we can say that there are 35 X 6 = 210 ways
What are combinations?Combining means selecting all or part of a set of objects, regardless of the order in which the objects are selected. Suppose we have a set of three characters.
[tex]^nC_{r} = \frac{n!}{r!(n - r)!}[/tex]
ways can this company buy them are - 35 X 6 = 210 ways
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13. So far, two-thirds of the seniors bought prom
tickets. If they need a minimum of 250 people
to attend in order to keep the venue, how
many students must be in the senior class to
ensure they sold enough tickets? Please write out the equation
Answer:
[tex]\dfrac{2}{3}x \geq 250[/tex]
Step-by-step explanation:
Let x be the number of students in the senior class.
If two-thirds of the seniors bought prom tickets and a minimum number of 250 tickets needs to be sold, the inequality that models this scenario is:
[tex]\boxed{\dfrac{2}{3}x \geq 250}[/tex]
Solving the inequality:
[tex]\implies \dfrac{2}{3}x \geq 250[/tex]
[tex]\implies 2x \geq 250 \cdot 3[/tex]
[tex]\implies 2x \geq 750[/tex]
[tex]\implies x \geq 750 \div 2[/tex]
[tex]\implies x \geq 375[/tex]
Therefore, there must be at least 375 students in the senior class to ensure they sold enough tickets to keep the venue.
4 time the sum of 8 and 1 is divided by six. Make expression and simplity.
Answer:
[tex]\frac{4(8-1)}{6}[/tex]
6
Step-by-step explanation:
[tex]\frac{4(8 + 1) }{6}[/tex]
[tex]\frac{4(9)}{6}[/tex]
[tex]\frac{36}{6}[/tex]
6
Answer:
The expression is:
4(8+1)/6
Simplify:
= 6
Step-by-step explanation:
The expression is:
4(8+1)/6
Simplify:
= 4(9) / 6
= 36/6
= 6
Joe Jan wants to receive $22,000 each year for the next 22 years. Assume a 6% interest rate compounded annually. How much must Joe invest today? (Round your answer to the nearest cent.)
If Joe deposits $264,954.31 today then he will reach his goal
Define Present Value
Finding the appropriate quantity of money to deposit today in order to ensure a specific amount of future payments is one objective of financial analysis. The target payment amount, the quantity and frequency of payments, and the interest rate all influence the present value, which is the value in today's dollars.
Given,
Joe want to receive each month = $22,000
Interest rate = 6%
number of payment = 22 years
We know, the formula of present value is
Present value = pmt * (1 - (1/ (1+r)ⁿ) ) / r
pmt = $22,000
r = 0.06
n = 22 years
Now, plug in the values
Present value = $22,000( 1 - (1/(1+0.06)²² ) / 0.06
=$22,000( 1 - (1/(1+0.06)²² ) / 0.06
≈ $264,954.311
Hence, If Joe deposits $264,954.31 today then he will reach his goal.
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The sum of two numbers is 21. Trice the larger number minus twice the smaller number is 18. find the numbers
Answer:
15, 6
Step-by-step explanation:
x = large number
y = small number
1) x + y = 21
2) x = 21 - y
3) 2x - 2y = 18
substitute equation 2 into equation 3 so you have an expression all in terms of y, then you can solve for y.
2(21-y) - 2y = 18
42 - 2y - 2y = 18
-4y = -24
y = -24/-4 = 6
Now you can solve for x, plug y=6 into equation 1 :
x + 6 = 21
x = 21 - 6 = 15
Find the 10% trimmed mean of the following data. If necessary, round to one more decimal place than the largest number of decimal places given in the data.
MLB Batting Averages 0.278 0.285 0.299 0.304 0.306 0.306 0.306 0.308 0.309 0.310 0.313 0.313 0.315 0.317 0.317 0.318 0.322 0.322 0.324 0.326
10% trimmed mean of the given data is xbar20 = 0.3269
In between the mean and the median, the trimmed means have some of the advantages of both without some of the disadvantages.
The 10% trimmed mean is the mean computed by excluding the 10% largest and 10% smallest values from the sample and taking the arithmetic mean of the remaining 80% of the sample (other trimmed means are possible: 5%, 20%, etc.
The 10% trimmed means omits 0.278 and 0.326 and yields
xbar10 = 0.278+ 0.285+0.299 + 0.304 + 0.306+ 0.306+ 0.306+ 0.308 +0.309 +0.310+ 0.313+ 0.313+ 0.315+ 0.317+ 0.317 +0.318+ 0.322+ 0.322+ 0.324+ 0.326 / 20
= 5.885 / 20
= 0.29
xbar = 1.29 and xbar = 1
Trimmed means are examples of robust statistics (resistant to gross error).
The 20% trimmed mean excludes the 2 smallest and 2 largest values in the sample above, and
xbar20 = 0.278+ 0.285+0.299 + 0.304 + 0.306+ 0.306+ 0.306+ 0.308 +0.309 +0.310+ 0.313+ 0.313+ 0.315+ 0.317+ 0.317 +0.318+ 0.322+ 0.322+ 0.324+ 0.326 / 18
xbar20 = 0.3269
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denote the volume of the cylinder as vcyl. if the cylinder has a total length l, write an equation for the volume of the cylinder in terms of r, l and any other constants
The volume of cylinder is denoted as πr²h
The density of a cylinder is determined by its volume, which indicates how much material it can hold or how much can be submerged inside it. The volume of a cylinder can be calculated using the formula r2h, where r denotes the radius of the circular base and h denotes the height of the cylinder. Any substance that can be evenly put into the cylinder, including liquid, may be used as the material. Shape volumes can be seen here.
This article contains a basic explanation of cylinder volume as well as examples with solutions for your convenience. The study of shapes and their characteristics is a key component of geometry in mathematics. Any three-dimensional shape must have both volume and surface area.
Hence, the volume of cylinder is denoted as πr²h
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Combine the methods of row reduction and cofactor expansion to compute the determinants in Exercises 11-14.
By combining the methods of row reduction and cofactor expansion the determinant of the given matrix is 1 .
In the question ,
it is given that ,
the matrix is [tex]\left[\begin{array}{ccc}0&4&1\\5&-3&0\\2&3&1\end{array}\right][/tex]
we need to compute the determinant using the row reduction that means using the row values [0 4 1 ] to find the determinant .
using the row [0 4 1] , the signs on the values on the first row will be +0, -4 and +1
the by applying the cofactor expansion , determinant will be equal to
= 0 -4[5×1 - 0] + 1[5×3 + 3×2]
= -4(5) + (15 + 6)
= -20 + 21
= 1
Therefore , the determinant is 1 .
The given question is incomplete , the complete question is
Combine the methods of row reduction and cofactor expansion to compute the determinant of the matrix [tex]\left[\begin{array}{ccc}0&4&1\\5&-3&0\\2&3&1\end{array}\right][/tex] .
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A rectangular paperboard measuring 20 in long and 12 in wide has a semicircle cut out of it, as shown below. Find the area of the paperboard that remains. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer
The area of the remaining paperboard is 246.91 in²
How to we calculate cut out area?A shape can be cut-out of another shape. For example a circle cut off a rectangle. The area of the remaining part of the shape can be calculated as area of original shape - area of cut-out shape
The area of a rectangle = l×w
= 20×21 = 420in²
a semi circle is the shape cut-out, therefore the area of the semi circle= ½πr²
= ½×3.14× 10.5²= 173.09in²
Therefore the area of the remaining part of the paperboard is 420-173.09= 246.91 in²
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All of the Pythagorean Identities are related. Describe how to manipulate the equations to get from sin^2t +cos^2t = 1 to the other forms.
[tex]1 + cot^{2}2t = csc^{2}2t[/tex] can be manipulated from [tex]sin^{2}2t +cos^{2}2t =1[/tex]
What is Pythagorean Identity?
An identity, in mathematics, is an equation that is true for all possible values.(It is always true regardless of the values that are substituted into the equation.)
A trigonometric identity is an equation that involves trigonometric functions and is true for every single value substituted for the variable (assuming both sides are "defined" for that value) You will find that trigonometric identities are especially useful for simplifying trigonometric expressions.
The most common trigonometric identities are those involving the Pythagorean Theorem.
When studying the unit circle (radius of 1), it was observed that a point on the unit circle (a vertex of the right triangle) can be represented by the coordinates (cos 2t, sin 2t ).
Since the legs of the right triangle in the unit circle have the values of sin 2t and cos 2t, the Pythagorean Theorem can be used to obtain [tex]sin^{2}2t +cos^{2}2t =1[/tex]
Given Equation : [tex]sin^{2}2t +cos^{2}2t =1[/tex]
To proof : [tex]1 + cot^{2}2t = csc^{2}2t[/tex]
[tex]1 + cot^{2} \alpha = csc^{2} \alpha [let \alpha =2t] \\\\1 + cot^{2} \alpha = 1 + \frac{cos^{2}\alpha }{sin^{2} \alpha } \\\\1 + cot^{2} \alpha = \frac{sin^{2}\alpha }{sin^{2} \alpha } + \frac{cos^{2}\alpha }{sin^{2} \alpha }\\\\1 + cot^{2} \alpha = \frac{sin^{2}\alpha + cos^{2} \alpha }{sin^{2} \alpha }\\ \\1 + cot^{2} \alpha = \frac{1 }{sin^{2} \alpha } [ since ,sin^{2}\alpha + cos^{2}\alpha = 1]\\\\1 + cot^{2}\alpha = sec^{2} \alpha\\\\or\\1 + cot^{2}2t = sec^{2} 2t[/tex]
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Simplify: (-6 + 10) + [ 14+ ( -7 ) ]+ (-10)
Answer:
1
Step-by-step explanation:
Bc I have calculator
How to multiple fractions with different denominators?
Please explain step by step to get picked brainliest!!
To multiply fractions with multiple denominators, you have to change the fraction to get the same denominator.
For example, if you have 1/3 * 1/2, you will have to find the least common multiple of 3 and 2, which is 6. Then, multiply the numerator by the same number that you multiplied the denominator to get 6.
1/3 * 1/2
LCM = 6
[tex]\frac{1*2}{3*2} *\frac{1*3}{2*3} =\frac{2}{6} *\frac{3}{6}[/tex]
Then, multiply across the numerator
[tex]\frac{2}{3}*\frac{3}{6} =\frac{6}{6}=1[/tex]
general: what is represented on the x and y axis in this graph? what does the black observed line represent in each graph?
The given question is incomplete as the graph is missing.
But, considering a line graph, the following parameters can be represented on the x-axis and y-axis:
X-Axis Y-Axis
Year Population
Time Number of employees hired
Identical items purchased Total cost in dollars
What does the blank observed line represent in each graph?
The blank observed line represents the time. A line graph is basically used to connect the quantitative values over the different time intervals. The change in values over time is easier to estimate, by the help of the line graph. For example: in a graph showing the year on the x-axis and the population on the y-axis, the blank line represents the change in population over the years, the increase or decrease or the rate of change.
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A couple just had a baby. How much should they invest now at 5.5% compounded weekly in order
to have $40,000 for the child’s education 17 years from now? Compute the answer to the nearest
dollar. (Assume there are 52 weeks in a year.)
Answer:
To find the amount that the couple needs to invest now, we can use the following formula:
investment = education cost * (1 + interest rate / number of compounding periods per year) ^ (number of years * number of compounding periods per year)
Plugging in the given values, we get:
investment = $40,000 * (1 + 0.055 / 52) ^ (17 * 52)
Solving this equation, we find that the couple needs to invest $11,226.31 now to have $40,000 for the child's education in 17 years. Rounded to the nearest dollar, this is $11,226.
Step-by-step explanation:
I need help with this please help me
According to the figure, the side congruent to line GK is line HL
What is congruency of triangle?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
Some of the rules include
Side - Side - Side = SSS
Side - Angle - Side = SAS
Angle - Side - Angle = ASA
Angle - Angle - Side = AAS
Hypotenuse and one leg = HL
The problem requires the prove by Angle - Side - Angle = ASA to ensure that the the triangles are congruent
The Angle and sides used for the proof include
< F = < J
FL = JK
< L = < K
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Answer:
A. HL
Step-by-step explanation:
You want to identify the side corresponding to GK in the figure showing congruent triangles.
ASA CongruenceThe larger triangles on the left and right each have an angle marked with one arc, an angle marked with two arcs, and the segment between those angles marked with one hash mark. This identical marking of two angles and the side between them means you can declare the triangles congruent by the ASA (angle-side-angle) congruence postulate.
When we name the triangles in order of the number of marks on the angles (0–2 arcs), we find the congruence statement to be ...
∆HLF ≅ ∆GKJ
Corresponding sidesThe segment of interest is GK, which is identified by the first two letters of its triangle designator in the congruence statement. The corresponding side is identified by the first two letters in the other triangle designator: HL.
∆HLF ≅ ∆GKJ
Side HL is congruent to GK.
__
Additional comment
Like a lot of math, this requires you to match patterns.
A panda bear at the zoo weighs 162 pounds. A polar bear weighs 6 times as much as the panda bear weighs.
Question 10(Multiple Choice Worth 5 points)
(Proportional Relationships LC)
Does the graph represent a proportional relationship?
graph with a line from 0 comma 0 and going through 25 comma 8
No, it is not proportional because the line does not go through (0, 0).
No, it is not proportional because the graph is curved.
Yes, it is proportional because it is a line that goes through (0, 0).
Yes, it is proportional because the x-axis and y-axis are numbered correctly.
Since the graph has a line from 0 comma 0 and going through 25 comma 8, C. Yes, it is proportional because it is a line that goes through (0, 0).
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.
Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.
By critically observing graph of this proportional relationship (see attachment), we can logically deduce that it starts from the origin (0, 0) and as such, it is proportional.
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0.800 divided by 10
Please help meeee
Answer:
.0800
Step-by-step explanation:
Dividing by ten will just move the decimal point one position further to the left
Please help me find the answer to this question
-------------------------------------------------------------------------------------------------------------
Answer: The top right table
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{y = 30 - 3x}[/tex]
Find: [tex]\textsf{Match the table of values with the equation}[/tex]
Solution: First we must understand what form our equation is in and what each of the numbers represent. This form is known as the slope intercept form which is formatted as y = mx + b. Our equation is slightly re-ordered but we can change that by converting it to y = -3x + 30 where m is equal to -3 and b is equal to 30. Let us know talk about what m and b are. M is the slope of the equation or also known as the rise/run or the change in y over the change in x. B is the y-intercept which is basically the value of y when x is equal to 0. In this case, our b is equal to 30.
Looking at the tables we can see what the value of y when x is equal to 0 for each table. The only table that matches up stating that y is equal to 30 when x is 0 is the top right table.
You do not have to go any further but if you want to confirm that the slope is as expected we can do the following: [tex]\frac{y_2\ -\ y_1}{x_2\ -\ x_1}[/tex].
Plug in the values and simplify
[tex]\frac{48\ -\ 30}{-6\ -\ 0}[/tex][tex]\frac{18}{-6}[/tex][tex]-3[/tex]Therefore, we can confirm that the slope matches up with the given equation as well. So, the final answer would be that the top right table would correspond to the equation y = 30 - 3x.
A local theatre sells out for their show. They sell all 500 tickets for a total purse of $7,890.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults. If the band sold three times as many adult tickets as children's tickets, how many of each type were sold?
Answer:the answer is 8070
Step-by-step explanation:
because it is
25 PTS Professor Ivy’s students have a Mean grade of 69.5 and a Standard Deviation of 6.5.
If Johnny has an 82 in the class, what would the z-score for Johnny’s grade be? (round to the tenths place)
What percentile does Johnny’s score put him in? (round to the nearest whole number)
The z-score for Johnny’s grade is 1.92.
Johny's score falls into the 97.28 percentile
What is a normal distribution?
The standard deviation determines the width of the curve in a normal distribution, which depicts a symmetrical representation of data around its mean value. It is represented graphically as the "bell curve."
Here, we have
mean = 69.5, std. deviation = 6.5 , x = 82
A. By normal distribution formula,
z = ( x - mean) / std. deviation
z = (82 - 69.5) / 6.5
= 1.92
Hence, the z-score for Johnny’s grade is 1.92.
B. P(z<1.92) = 0.9728
Hence, Johny's score fall into 97.28 percentile.
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what is 12/7Q minus 1/21Q=Q-2/3
The given equation is solved to obtain Q = -1/21.
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
The given equation is as below,
12/7Q - 1/21Q = Q - 2/3
It can be simplified as follows,
12/7Q - 1/21Q = Q - 2/3
=> 12/7Q - 1/21Q - Q = -2/3
=> (36 - 1 - 21)Q = -2/3
=> 14Q = -2/3
=> Q = -1/21
Hence, the solution of the given equation is -1/21.
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Shirley bought 20.8 pounds of bird seed at a bargain store. She wants to fill her feeder 100 times with an equal amount. How much seed should she put in the feeder each time?
Part A
Which expression represents the problem?
20.8 ÷ 100
20.8 + 100
20.8 × 100
100 ÷ 20.8
Part B
When solving Part A, how is the decimal point moved?
3 places to the right
3 places to the left
2 places to the right
2 places to the left
Part C
How much seed should she put in the feeder each time?
pound(s)
Answer: Part A 20.8 divided Part B 2 places to the left Part C 0.208
Step-by-step explanation:
Part A the question ask each time and when it ask each time it means dividing Part B when dividing you move to the left and their are two 0s and moving the decimal two places to the left would get you 0.208 so, therefor the answer is 0.208
CAN SOMEONE HELP WITH THIS QUESTION?✨
The coordinates of point B are (4, 0)
How to determine the coordinates of point B?From the question, we have the following parameters that can be used in our computation:
A = (6, 10)
Midpoint = (5, 5)
The midpoint of a line from its endpoints is calculated using the following equation
Midpoint = (x₂ + x₁)/2 + (y₂ + y₁)/2
Substitute the known values in the above equation, so, we have the following representation
(5, 5) = (6 + x₁)/2 + (10 + y₁)/2
Multiply by 2
(10, 10) = (6 + x₁) + (10 + y₁)
By comparison, we have
x + 6 = 10
y + 10 = 10
Evaluate
x = 4
y - 0
Hence, the point is (4, 0)
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as the cubes increased in size, describe what happened to the surface area to volume ratio. explain mathematically why this happened in terms of the formula for each.
As the cube size increases, the surface -area - to - volume ratio decreases .
Given :
as the cubes increased in size, describe what happened to the surface area to volume ratio, mathematically why this happened in terms of the formula for each.
Volume :
Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
Volume of cube = a^3
Surface area :
Surface area is the amount of space covering the outside of a three - dimensional shape.
Surface area of cube = 6a^2
suppose side length = 1
1^3 : 6 * 1^2
= 6 * 1 : 1
= 6 : 1
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Assume that you want to test the claim that the paired sample data come from population for which the mean difference is Kd = 0. Compute the value of the test statistic. Round intermediate calculations to four decimal places as needed and final answers to three decimal places as needed. Subject Before 168 180 157 132 202 124 190 210 171 After 162 178 145 125 171 126 180 195 163 0 A 0.351 .052 3.156 9.468
The test statistic value for the given sample data with population mean difference is equal to optic C. 3.156.
As given in the question,
Given population mean difference μd = 0
sample size 'n' = 9
Sample data is:
x y [tex]d_{i}[/tex] ( x - y) [tex]( d_{i} - \bar{d} )^{2}[/tex]
168 162 6 15.21
180 178 2 62.41
157 145 12 4.41
132 125 7 8.41
202 171 31 445.21
124 126 -2 141.61
190 180 10 0.01
210 195 15 26.01
171 163 8 3.61
∑[tex]d_{i}[/tex] = 89 ∑ [tex]( d_{i} - \bar{d} )^{2}[/tex] = 706.89
[tex]\bar{d}[/tex] = ( 1/ n ) ∑[tex]d_{i}[/tex]
= (1/9) (89)
= 9.889
= 9.9
Standard deviation of the mean difference '[tex]S_{d}[/tex]'
= √[1 / (n - 1)]( ∑ [tex]( d_{i} - \bar{d} )^{2}[/tex] )
= √706.89/ 8
=√88.361
= 9.4
test statistic
t = ( [tex]\bar{d}[/tex] - μd)/ ( [tex]s_{d} /\sqrt{n}[/tex] )
= ( 9.9 - 0) / ( 9.4 / √9)
= 9.9/ 3.133
= 3.156
Therefore, the test statistic value for the given sample data is equal to option C. 3.156
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