the linear relationship between the SAT and ACT scores 0.6675 or 66.75% of the variation in the values of the SAT scores is accounted
Given that many high school students take either the SAT or the ACT.
However, some students take both.
Data were collected from 60 students who took both college entrance exams.
SAT score ACT score with a of 180.
Average 912 21
standard deviation 180 5
Correlation between the two variables r = 0.817
WE have for two variables if we have correlation coefficient then the square of correlation coefficient gives the fraction of variation in the values of the SAT scores is accounted for by the linear relationship between the SAT and ACT scores
So we find square of r
i.e. r by the linear relationship between the SAT and ACT scores 0.6675 or 66.75% of the variation in the values of the SAT scores is accounted
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Answer:
j
Step-by-step explanation:
Suppose a certain state university's college of business obtained the following results on the salaries of a recent graduating class:Finance Majors Business Analytics Majorsn1 = 140 n2 = 30x1 = $48,237 x2 = $55,417s1 = $19,000 s2 = $10,000(a) Formulate hypotheses so that, if the null hypothesis is rejected, we can conclude that salaries for Finance majors are significantly lower than the salaries of Business Analytics majors. Use α = 0.05. (Let μ1 = the population mean salary for Finance majors, and let μ2 = the population mean salary for Business Analytics majors.
b) What is the value of the test statistic? (Use μ1 − μ2. Round your answer to three decimal places.)
(c)What is the p-value? (Round your answer to four decimal places.)
(d) What is your conclusion?
Reject H0. We can conclude that salaries for Finance majors are significantly lower than the salaries of Business Analytics majors.
Do not reject H0. We can conclude that salaries for Finance majors are significantly lower than the salaries of Business Analytics majors.
Reject H0. We cannot conclude that salaries for Finance majors are significantly lower than the salaries of Business Analytics majors.
Do not reject H0. We cannot conclude that salaries for Finance majors are significantly lower than the salaries of Business Analytics majors.
Using the confidence interval and null hypothesis we can conclude that the salaries for the finance majors are significantly lower than the salaries of the business analytics majors.
a) The null and alternative hypothesis is given by
H₀: μ1 − μ2 = 0
H₁: μ1 − μ2 < 0
b) Test statistic is given by [tex]\frac{\bar{x}_1-\bar{x}_2-0}{\sqrt{\frac{S_1^2}{n_1}+\frac{S_2^2}{n_2}}}[/tex]
here:
S₁ = 19000
S₂ = 10000
x₁ = 48237
x₂ = 55217
n₁ = 120
n₂ = 30
Putting the above values we get:
[tex]z=\frac{48237-55217}{\sqrt{\frac{19000^2}{120}+\frac{10000^2}{30}}}[/tex]
or, z = -2.7717744...
or, z ≈ -2.772
c) p-value
= P(Z<-2.772)
= 0.002786
= 0.0028
d) now we will use the p-value to essentially use or reject the the hypothesis.
So the confidence interval of 955 is used for the p-value.
p-value(0.0028) < ∝(0.05)
Hence we will reject the H₀ .
Hence we will conclude that the salaries for the finance majors are significantly lower than the salaries of the business analytics majors.
A confidence interval is a range of estimates for an unknown parameter (CI). The most common confidence level is 95%, but when calculating confidence intervals, other levels, such 90% or 99%, are also occasionally employed.
The confidence level is a measure of how many related CIs over the long run include the actual value of the parameter. For instance, the parameter's true value should be included in 95% of all intervals produced at the 95% confidence level.
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This right circular cone has radius 2p and height
5p.
The dimensions are in centimetres.
The volume of the cone is 22500 cm³.
Work out the value of p
How do i work this out?
Answer:
p ≈ 10.24 cm
Step-by-step explanation:
r = 2p
h = 5p
Volume of a cone = (1/3)πr²h
22,500 = (1/3)π(2p)²(5p)
Now solve for p:
67500 = π4p²5p
67500 = π20p³
p³ = (67500)/π20 = 1074.3
p = ∛1074.3
p ≈ 10.24 cm
use the student's t -distribution to find the t -value for each of the given scenarios. round t -values to four decimal places. find the value of t such that the area in the left tail of the t -distribution is 0.05, if the sample size is 48. t
the value of t such that the area in the left tail of the t -distribution is 0.05, if the sample size is 48. t is 0.76197086
Consider a t distribution with 7 degrees of freedom. Compute P(-1.29 < t < 1.29)
P(-1.29 < t < 1.29) would be the area under the t distribution curve with 7 degrees of freedom between -1.29 and 1.29, that is in the interval (-1.29, 1.29).
This can be done the old style by looking up in a table or by using the technology with a spreadsheet.
In Excel, the function TDIST(x,n,2) with x>0 gives the area outside the interval (-x, x) of the t distribution with n degrees of freedom.
So TDIST(1.29,7,2) gives the area outside (-1.29, 1.29).
If we subtract this value from 1 we get the desired result
Hence
P(-1.29 < t < 1.29) = 1 - TDIST(1.29,7,2) = 1 - 0.23802914 = 0.76197086
In OpenOffice Calc, the function is the same replacing “,” with “;”
That is
P(-1.29 < t < 1.29) = 1 - TDIST(1.29;7;2) = 0.76197086
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roblem 9-15 (Algorithmic) Doug Casey is in charge of planning and coordinating next spring’s sales management training program for his company. Doug listed the following activity information for this project: Immediate Time (weeks) Activity Description Predecessor(s) Optimistic Most Probable Pesssimistic A Plan topic — 1 1.5 2 B Obtain speakers A 2 2.5 9 C List meeting locations — 1.5 2 2.5 D Select location C 2 2 2 E Finalize speaker travel plans B, D 0.5 1 1.5 F Make final check with speakers E 1.5 2 2.5 G Prepare and mail brochure B, D 4 4.5 8 H Take reservations G 2 4 6 I Handle last-minute details F, H 1.5 3 4.5 Prepare an activity schedule. If required, round your answers to two decimal places. If your answer is zero, enter "0". Activity Expected Time Variance A B C D E F G H I Earliest Latest Earliest Latest Critical Activity Start Start Finish Finish Slack Activity A B C D E F G H I What are the critical activities and what is the expected project completion time? If required, round your answer to one decimal place. Expected project completion time = weeks. If Doug wants a 0.99 probability of completing the project on time, how far ahead of the scheduled meeting date should he begin working on the project? Base your calculation solely on the critical path. Note: Use Appendix B to identify the standard score. If required, round your answer to one decimal place. T = weeks.
If the 0.99 probability of completing the project on time, then the scheduled meeting date should he begin working on the project is 2.39 weeks
How to calculate the probability?
In math, the probability can be determined by first knowing the sample space of outcomes of an experiment and then by dividing the number of outcomes of an event by the total number of possible outcomes or sample space.
Here we have given that Doug Casey is in charge of planning and coordinating next spring’s sales management training program for his company.
And we need to find the If Doug wants a 0.99 probability of completing the project on time, how far ahead of the scheduled meeting date should he begin working on the project.
Here we know that the duration of the critical path determines the completion of the whole project.
Therefore, the mean completion time of the project =μ=15
And the the variance of the critical path = sum of the variances of the activities A, B, G, H, and I =0.03+0.44+0.44+0.11+0.03=1.06
Therefore, the standard deviation of the critical path or that of the whole project =σ=√1.06=1.03
Here we know that, if a 0.99 probability of completion is required, then the corresponding Z-score =2.3263
Then the actual completion time corresponding to a Z-score of
=> 2.3263 = μ+(Z×σ) = 15+(2.3263×1.03) = 15+2.39 = 17.39 weeks
Which states that the extra time needed over and above the mean completion time of the project of 15 weeks to have a 0.99 probability of completion =17.39−15=2.39 weeks
Therefore, in order to have a 0.99 probability of completing the project on time, the project should be started 2.39 weeks ahead of the scheduled meeting date.
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What percent of 75 is 36?
Answer:
48%
Step-by-step explanation:
Finding percents
P * 75 = 36
Divide each side by 75
P = 36/75
P =.48
Change to percent form
P = 48%
Answer:
48%%%%%
Step-by-step explanation:
7 of 107 of 10 Questions
Question 1
Write the inverse variation equation for xand yif yvaries inversely with x,and y=34when x=8.
The inverse variation equation is
Question 2
Find ywhen x=12and find xwhen y=30.
If an answer is not an integer, enter it as a fraction.
When x=12, y=
Question 3
When y=30, x=
1. The equation of the inverse variation is, y = 272/x.
2. When x = 12, y = 68/3
When y = 30, x = 136/15.
What is an Inverse Variation?An inverse variation is defined by the equation, y = k/x, where k is the constant of proportionality between the relationship of y and x.
1. Given that y varies inversely with x, substitute y = 34 and x = 8 into y = k/x, and find the value of the constant of proportionality, k:
34 = k/8
34 × 8 = k
k = 272
To write the equation, substitute k = 272 into y = k/x:
y = 272/x
2. When x = 12, we have:
y = 272/12
Simplify
y = 68/3
When y = 30, we have:
30 = 272/x
30x = 272
30x/30 = 272/30
x = 136/15
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If two loads are applied to a cantilever beam as shown in the drawing below, the bending moment at 0 due to the load is a1X1+a2X2.
Suppose that X1 and X2 are independent random variables with means of 2 and 4 kips respectively, and standard deviations pf .5 and 1 kip, respectively. If a1 = 5 ft and a2 = 10 ft, what is the expected bending moment and what is the standard deviation of the bending moment?
b) If X1 and X2 are normally distributed, what is the probability that the bending moment will exceed 75 kip-ft?
c) Suppose the positions of the two loads are random variables. Denoting them by A1 and A2, assume that these variables have means 05 5 and 10 ft, respectively, that each has a standard deviation of .5, and that all Ai's and Xi's are independent of one another. What is the expected moment now?
d) For the situation of part (c), what is the variance of the bending moment?
e) IF the situation is as described in part (a) except that Corr(X1, X2) = .5 (so that the two loads are not independent), what is the variance of the bending moment?
Answer: Step-by-step explanation:
rewrite 1/12 x^3 y + 5/12 xy^2 using a common factor
1/6 xy(2x2 + 5y)
1/6 x2y(2x + 5y)
1/12 xy(x2 + 5y)
1/12 x3y(y + 5)
The expression using the common factor is 1/12xy(x² + 5y)
How to rewrite the expression using the common factor?From the question, we have the following parameters that can be used in our computation:
1/12 x^3 y + 5/12 xy^2
Rewrite properly
So, we have
1/12x³y + 5/12xy²
Factor out 1/12 from the expression
So, we have the following representation
1/12(x³y + 5xy²)
Factor out x from the expression
So, we have the following representation
1/12x(x²y + 5y²)
Factor out y from the expression
So, we have the following representation
1/12xy(x² + 5y)
Hence, the expression is (c) 1/12xy(x² + 5y)
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Answer:The expression using the common factor is 1/12xy(x² + 5y)
Step-by-step explanation:
Which one of the following variables is a continuous variable?
a. The number of people on a bus.
b. The number of computers in a computer room in a school.
c. The height of Year 12 students in a high school.
d. The score out of 90 for a test.
Answer:
c.
Step-by-step explanation:
as this can take on any value (with as many digits after the decimal point as necessary) between certain interval limits.
all the others are usually either pure integers (and every real number in between them is not valid) or at most have finite fractions (like 1/2 or 1/4 points for scores, and between these no value is valid).
The equation y = 2x + 3 is graphedbelow. If this graph is shifted up 3 units, what will be the equation of the new graph
Answer:
y = 2x + 6
Step-by-step explanation:
The equation is in point slope form or y = mc + b
where m is the slope and b is the y intercept
Since the graph is simply shifted up 3 units, the y intercept will change by increasing by 3, but the slope will not
How many different ID cards can be made if there are seven digits on a card and no digit can be used more than once? What if digits can be repeated?
The number of ID cards when no digit can be used more than once is 604,800 and when the digits can be repeated it will be 10,000,000 ID cards.
What is Permutations?Permutations are several ways to arrange things in a specific sequence. It can alternatively be stated as the linear reordering of items within an ordered set.
As per the given information in the question,
Let's first make a list of all the potential outcomes. As follows:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
a.
No numeral may be used multiple times in the first instance.
Therefore,
10 × 9 × 8 × 7 × 6 × 5 × 4
= 604,800 ID cards
b.
In the second scenario, assuming it is possible to repeat the digits, then,
10 × 10 × 10 × 10 × 10 × 10 × 10 = 10,000,000 ID cards.
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c) Assume that the sample points in each interval are right endpoints. Find the following sample points:x 1 = 0∘x 2 =08x 3=0 8
Each interval's sample points are at the right ends. sample points :x 1 = 0∘x 2 =08x 3=0 8 is 0°, 8°, 16°
Since the sample points in each interval are right endpoints, we need to find the points that are 8° apart.
The first sample point x1 is 0°. To find the next two sample points, we need to add 8° to the first sample point.
Therefore, the second sample point x2 = 8°, and the third sample point x3 = 16°.
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A cart has 5 boxes on it. Each box weighs 70 pounds. The boxes will be removed from
the cart, one at a time. Which function models the relationship between x, the number of
boxes that have been removed from the cart, and y, the total weight, in pounds, of the
boxes remaining on the cart?
y=-70x+5
B) y = -5x + 350
y = 50x + 70
= 52 +350
D) y =
Y =
based on the text, what is the meaning of collinear? responses a unconnected to any sort of lineunconnected to any sort of line b equally distant in every directionequally distant in every direction c lying on or passing through the same linelying on or passing through the same line d connected sections along a curved lineconnected sections along a curved line
On solving the provided question, we can that the answer - The distance between two points is the length of a line segment that connects them.
What is straight lines?A line is a shape that has no width, depth, or curve in its geometry. It is an item that can be used for a long time. A line can exist in a two-dimensional, three-dimensional, or more dimensional space, but is still a one-dimensional object. A line segment with two endpoints is commonly called a "line".
Main notations:
A plane is a flat, indefinitely long, 2D surface with no thickness. Option 1 is accurate. A point is a precise place. It just has position; it has no length, breadth, or depth. Option 2 is untrue. Collinear points are any two or more points that are situated differently yet are on the same line. Option 3 is untrue. A line has no thickness, is straight (has no bends), and goes in both directions without ending (infinitely). Option 4 is accurate. The length of a line segment that links two places represents their distance. Option 5 is accurate.
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3
Gerry and Claire have been out walking using a map with a scale of 2 cm: 1 km.
The distance they have walked on the map is 14 cm.
How far have they actually walked?
Answer:
7 km
Step-by-step explanation:
14/2 cm which equals 7km
A surveyor needs to measure the distance, AB, across the lake. Beginning at E, he locates the midpoint, C, of AE and
the midpoint, D, of BE. He then measures CD. What is AB?
AB= m
4
49 m
Answer What is the midpoint of /AB? =b. point G
Step-by-step explanation:
AB is the abbreviation of “artium baccalaureus,” which is the Latin name for the Bachelor of Arts (BA) degree. It's a liberal arts degree, so it emphasizes the humanities, languages, and social sciences fields
the formula for the area of a triangle is A=1/2bh. find the area of a triangle with a base (b) of 8 feet and a height (h) of 11 feet. the area of the triangle is_ spuare feet.
Answer: 44ft^2
Step-by-step explanation:
plug it into the equation, h=11, b=8
so A=1/2(11)(8) = 44ft^2
Player First
Round Final
Round
Golfer 11 72 72
Golfer 12 72 70
Golfer 13 70 73
Golfer 14 70 77
Golfer 15 68 70
Golfer 16 68 66
Golfer 17 71 70
Golfer 18 70 68
Golfer 19 69 68
Golfer 20 67 71
Suppose you would like to determine if the mean score for the first round of a golf tournament event is significantly different than the mean score for the fourth and final round. Does the pressure of playing in the final round cause scores to go up? Or does the increased player concentration cause scores to come down?
(a) Use α = 0.10 to test for a statistically significantly difference between the population means for first- and fourth-round scores. State the null and alternative hypotheses. (Use μd = mean score first round − mean score fourth round.
Calculate the value of the test statistic. (Round your answer to three decimal places.)
Calculate the p-value. (Round your answer to four decimal places.)
p-value =
(b) What is the point estimate of the difference between the two population means? (Use mean score first round − mean score fourth round.)
The point estimate of the difference between the two population means is -1.05.
Here, we are given the data representing the scores of the golf players in the 1st and final rounds.
a. The significance level is: α = 0.10
we can construct the following hypothesis test-
Null hypothesis H₀ ⇒ μd = 0
This implies that there is no difference between the population mean of the first round and final round.
Alternative hypothesis: Ha ⇒ μd ≠ 0
This implies that there is a difference between the population mean of the 1st round and final round.
Now, the test statistic will be-
[tex]t = (d-mean_{d})\sqrt{n}/ s_{d\\}[/tex]
we can use excel to calculate the test statistic.
This will give us: 0.10 < P < 0.20
b. the main margin of error is 90% confidence level. This means that there is no significant difference, hence - 1.05.
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Your question was incomplete. Check for the missing figure below.
Calculate the difference and enter below. -4 + (-4)
Answer: -8
Step-by-step explanation: When adding 2 negative numbers, you go farther back left on the number line. (Negative side) So, 4 + 4 = 8, and a negative + a negative = negative, so this results in -4 + (-4) = -8. I hoped this helped!
16.13- cerebral tumors and cell phone use. in a case-controlled study on cerebral tumors and cell phone use, tumors occurred more frequently on the same side of the head where cellular telephones had been used in 26 of 41 cases. test the hypothesis that there is an equal distribution of contralaterial and ipsilateral tumors in the population. use a two-sided alternative.
The two sided hypothesis of the given situation is H0 : p = 0.50 and Ha : p ≠ 0.50
in statistics, hypothesis is defined as a statement that explains the predictions and reasoning of your research.
Here we have given that cerebral tumors and cell phone use. in a case-controlled study on cerebral tumors and cell phone use, tumors occurred more frequently on the same side of the head where cellular telephones had been used in 26 of 41 cases.
And we need to find the test to the hypothesis that there is an equal distribution of contralateral and ipsilateral tumors in the population. use a two-sided alternative.
Here we have to find Hypothesis, for that we have to so the steps are shown below:
Let us considered the hypotheses for the study as shown below:
H0 : p =0.50
Versus,
Ha : p ≠ 0.50
Therefore, this is two tailed hypothesis test.
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A bag of marbles contained 40 blue marbles and 46 white marbles (and no other marbles). For a game, marbles of each color were chosen from the bag. Of the 40 blue marbles,3/5 were chosen.
Use this information to answer the questions below.
If not enough information is given to answer a question, click on "Not enough information."
(a) How many of the bag's marbles were not chosen?
(b) How many marbles were in the bag before the game?
(c) How many of the bag's blue marbles were chosen?
Number of marbles were not chosen = 62 marbles
Number of marbles were in the bag before the game = 86 marbles
Number pf blue marbles were chosen = 24
Number of blue marbles = 40
Number of white marbles = 46 marbles
Total number of marbles = 40 + 46
= 86 marbles
Of the 40 blue marbles, 3/5 fraction were chosen
Number of blue marbles chosen = 40 × (3/5)
= 24 marbles
Part a
Number of bag's marbles were not chosen = 86 - 24
= 62 marbles
Part b
Number of marbles were in the bag before the game = 86 marbles
Part c
Number of blue marbles were chosen = 40 × (3/5)
= 24 marbles
Therefore, the 62 marbles were not chosen. There were 86 marbles before the game and number of blue marbles were chosen is 24 marbles
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Part 1: Choose the equation represented by the model given below.
The linear equation that representing the given model is 6x-3 = 15.
In the given question, we have to choose the equation represented by the model given below.
As we know that;
A linear equation represent the relationship between the two unknown variable. The equation of linear equation is of one degree.
The simplest linear equation shows the correlation between (x,y), which may then be used to make a table or a graph on the coordinate plane or to assess at a specific x or y value.
To write the equation that represented by the given model, we count the variable that are of the same type. Then we write them after counting.
As we can see that in the model have 6 triangles of x, 3 circles of -1 and 15 circles of 1. So the linear equation that representing the given model is 6x-3 = 15.
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11. Members of the student council are conducting a fundraiser by selling school calendars. After selling 80 calendars, they had a loss of $ 360. After selling 200 calendars, they had a profit of $600. Write an equation that describes the relation between y, the profit or loss, and x, the number of calendars sold. How much profit did they make from selling each calendar? How much would they have lost if they had sold no calendars?
a) The equation that describes the relation between x and y is y = 8x - 1000
b) They made 8% profit from selling the calendars
c) They will loss 1000 when they sold no calendars.
Given,
Members of student council had a loss of $360 after selling 80 calenders
They made a profit of $600 after selling 200 calenders.
y be the profit or loss
x be the calendars sold
We have to find the following;
a) The equation of the line in Slope-Intercept form is:
y = mx + b
Where "m" is the slope and "b" is the y-intercept.
We are aware that "y" here stands for the profit or loss and "x" for the quantity of calendars sold.
Then,
According to the exercise, the line passes through these two points:
(80, -360) and (200, 600)
Then,
We can find the slope of the line with the formula;
m = (y₂ - y₁) / (x₂ - x₁)
m = (-360 - 600) / (80 - 200)
m = -960/-120
m = 8
Now,
We can substitute the slope and one of those points into y = mx + b and solve for "b":
600 = 8 × 200 + b
-b = 1600 - 600
b = -1000
Then,
Substituting values, we get that the equation that describes the relation between the profit and loss and the number of calendars sold, is:
y = 8x - 1000
b) The slope of the line is the profit they made from selling each calendar
Profit = 8
c) The y-intercept is the amount they would have lost if they had sold no calendars:
b = -1000
They'd have lost $1000 if they had sold no calendars.
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What would be great resources
Answer:
depends for what?
Step-by-step explanation:
for shoes, stationary, clothes etc be a bit specific
Pre calc
Solve e^2x +3e^x- 28=0
Answer:
x=ln(4)
Step-by-step explanation:
e^2x +3e^x- 28=0
u^2 + 3u - 28 = 0 ==> substitute u for e^x
u^2 - 4u + 7u - 28 = 0
u(u-4) + 7(u-4) = 0
(u-4)(u+7)=0 ==> simplify
u-4=0 u+7=0
u=4 u=-7
e^x=4 e^x=-7 ==> substitute e^x for u
ln(e^x)=ln(4) ln(e^x)=-7 ==> take natural log on each side
x=ln(4) x=ln(-7), which is not possible since natural log>0
x=ln(4)
Answer:
[tex]{e}^{x} = y \\ {y}^{2} + 3y - 28 = 0 \\ (y - 4)(y + 7) = 0 \\ y = 4 \\ y = - 7 \\ {e}^{x} = 4 \\ x = ln(4) \\ x = ln( - 7)[/tex]
Two equalities that are equivalent
Answer:
there is 2/8 and 3/12 .they are both equivalent to each ,and equal 1/4.2 is 1/4 of because 2×4=8 is 1/4 of 12 because 3×4=12.
Tan(300°)=z/7
What is z?
Answer:
x = -7 sqrt(3)
Step-by-step explanation:
Tan(300°)=z/7
Multiply each side by 7
7 Tan(300°)=z
Replacing tan 300 with tan 120 since they are equal
7 Tan(120°)=z
7 ( - sqrt(3)) = z
x = -7 sqrt(3)
Use a generating function for modeling the number of different selections of r hot dogs when there are four types of hot dogs.
Using generating function number of different selections of r hot dogs when there are four types of hot dogs are g(x) = ( 1/(1-x) )⁴.
What is Generating function?For a sequence a₀,a₁,...,aₙ,... the corresponding generating function f(x) is the sequence
f(x)=a₀+a₁x+...+aₙxₙ+...= ∑aᵢxᵢ , 0 ≤ i ≤ ∞
Since here we have 4 types of hot dogs, from which we need to select "r" hot dogs, we would use a generating function as follows:
There can be any number of selections from any pile of hot dogs ( repitions is allowed). therefore, from each pile, you could pick up 1 or 2 or 3 or ... hot dogs. The same would go for all types of hot dogs. Therefore ,the generating function for the same would be,
g(x) = (1 + x + x² + x³ + x⁴ + ...)(1 + x + x² + x³ + x⁴ + ...)(1 + x + x² + x³+ x⁴ + ...)(1 + x + x² + x³+ x⁴+ ...)
Therefore, g(x) = (1 + x + x² + x³ + x⁴ + ...)⁴
This is an infinite geometric series, which can be solved to give the sum: g(x) = ( 1/(1-x) )⁴. Therefore, our required the coefficient of xʳ in (1/ (1-x) )⁴.
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2/3x+5/6=1/2(x-1/3) simplify the algebraic expression
After solving the given expression, the value obtained for x will be equal to -6,
What is an expression?If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.
The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. A mathematical operation like reduction, addition, multiplication, or division is used to include terms in an expression.
As per the given equation in the question,
2/3x + 5/6 = 1/2 (x - 1/3)
2/3x + 5/6 = 1/2x - 1/6
Substitute like terms together,
2/3x - 1/2x = -1/6 - 5/6
(4x - 3x)/6 = (-1 - 5)/6
x/6 = -6/6
x/6 = -1
x = -6
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A researcher claims that the yearly consumption of soft drinks per person is 52 gallons. In a sample of 50 randomly selected people, the mean of the yearly consumption was 56.3 gallons. The standard deviation of the population is 3.5 gallons. Is the researcher's claim valid? alpha = .05 Find the P-Value, state what your final decision will be based on alpha = .05 and why?
The researcher claim is invalid and the p-value based on alpha = 0.05 is approx. = 0.
In the question ,
it is given that ,
a researches claims that per person yearly consumption (μ) is 52 gallons .
sample size (n) = 50 .
the mean of the consumption (x) = 56.3 .
the standard deviation (σ) is = 3.5 gallons .
the α = 0.05 .
let the null hypothesis ,
H₀ : μ = 52 and
H₁ : μ ≠ 52 .
the test statistics is : z = (x - μ)/(σ/√n)
the critical value ( rejection region ) : {z : |z| ≥ z₀.₀₂₅ = 1.96 }
So , z = (56.3 - 52)/(3.5/√50)
Simplifying further ,
we get ,
z = 8.69
We reject the null hypothesis H₀ , since the absolute value of the test statistics 8.69 is greater than the critical value 1.96 .
Since this is a two tailed test, p-value must be multiplied by two
2 × P(z > 8.69) ≈ 0
Since the p-value is less than α(0.05), So ,we reject the claim of the researcher that the mean yearly consumption of soft drinks per person is 52 gallons
Hence , the claim is not valid .
Therefore , The claim is invalid and p-value is ≈ 0 .
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