Answer:
[tex]S_{1 } (x,y) = (0.333, 0.815)[/tex] (Absolute minimum) and [tex]S_{2} (x,y) = (-1, 2)[/tex] (Absolute maximum)
Step-by-step explanation:
The critical points are determined with the help of the First Derivative Test:
[tex]f'(x) = 3\cdot x ^{2} +2\cdot x -1[/tex]
[tex]3\cdot x^{2} + 2\cdot x - 1 = 0[/tex]
The critical points are:
[tex]x_{1} \approx 0.333[/tex] and [tex]x_{2} \approx -1[/tex]
The Second Derivative Test offers a criterion to decide whether critical point is an absolute maximum and whether is an absolute minimum:
[tex]f''(x) = 6\cdot x +2[/tex]
[tex]f''(x_{1}) = 3.998[/tex] (Absolute minimum)
[tex]f''(x_{2}) = -4[/tex] (Absolute maximum)
The critical points are:
[tex]S_{1 } (x,y) = (0.333, 0.815)[/tex] (Absolute minimum) and [tex]S_{2} (x,y) = (-1, 2)[/tex] (Absolute maximum)
The global maximum is at x = -1 with f(-1) = 2, and the global minimum is at x = -2 with f(-2) = -1.
To find the global and local maxima and minima of the function f(x) = [tex]x^3 + x^2[/tex] − x + 1 over the interval [-2, 1/2], follow these steps:
Find critical points: First, we need to find the derivative of the function f(x):
f'(x) = [tex]3x^2[/tex]+ 2x - 1
Solve f'(x) = 0 to find critical points within the interval:
[tex]3x^2[/tex]+ 2x - 1 = 0
Using the quadratic formula x = (-b ± √(b²-4ac)) / 2a, where a = 3, b = 2, and c = -1:
x = [-2 ± √(4 + 12)] / 6
x = [-2 ± 4] / 6
This gives two solutions:
x = 1/3 and x = -1
Both are within the interval [-2, 1/2], so we consider these as critical points.
Second Derivative Test (SDT): Find the second derivative to apply the SDT:
f''(x) = 6x + 2
Evaluate f''(x) at the critical points:
f''(-1) = 6(-1) + 2 = -4 (which is negative, indicating a local maximum)
f''(1/3) = 6(1/3) + 2 = 4 (which is positive, indicating a local minimum)
Evaluate the function at the endpoints: Compute f(x) at the bounds of the interval:
f(-2) = (-2)³ + (-2)² - (-2) + 1 = -8 + 4 + 2 + 1 = -1
f(1/2) = (1/2)³ + (1/2)² - (1/2) + 1 = 1/8 + 1/4 - 1/2 + 1 = 7/8
Additionally, compute the function at the critical points:
f(-1) = (-1)³ + (-1)² - (-1) + 1 = -1 + 1 + 1 + 1 = 2
f(1/3) = (1/3)³ + (1/3)² - (1/3) + 1 = 1/27 + 1/9 - 1/3 + 1 ≈ 0.963
Interpret the results:
The maximum and minimum values for f(x) over [-2, 1/2] are:
Local maximum at x = -1 with f(-1) = 2
Local minimum at x = 1/3 with f(1/3) ≈ 0.963
Global maximum at x = -1 with f(-1) = 2
Global minimum at x = -2 with f(-2) = -1
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:
Also SSR (X1 ∣ X2) = 36400.6326 and SSR (X2 ∣ X1) = 3297.7917
What fraction of the variability in house size is explained by income and size of family?
A. 84.79%
B. 71.89%
C. 17.56%
D. 70.69%
Answer:
Correct option: (B) 71.89%.
Step-by-step explanation:
R-squared is a statistical quantity that measures, just how near the values are to the fitted regression line. It is also known as the coefficient of determination.
The coefficient of determination R² specifies the percentage of the variance in the dependent variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent variable).
The coefficient of determination R² can be computed by the formula,
[tex]R^{2}=\frac{SSR}{SST}[/tex]
Here,
SSR = sum of squares of regression
SST = sum of squares of total
From the output attached below the value of SSR and SST are:
SSR = 37043.3236
SST = 51531.0863
Compute the value of R² as follows:
[tex]R^{2}=\frac{SSR}{SST}[/tex]
[tex]=\frac{37043.3236 }{51531.0863}[/tex]
[tex]=0.7188539\\\approx 0.7189[/tex]
Thus, the fraction of the variability in house size is explained by income and size of family is 71.89%.
The correct option is (B).
To find the fraction of the variability in house size that is explained by family income and size, we sum the two SSR values and express this as a fraction or percentage of the total variability in house size. The actual value could not be determined from the provided information as it appears to be missing.
Explanation:The question focuses on understanding the impact of family income and family size (the independent variables) on the house size (the dependent variable). The builder calculated the Sum of Squares for Regression (SSR) considering each independent variable given other independent variables constant. These calculations provide crucial insights into the contribution made by each independent variable to the variation in the dependent variable.
The total SSR (from both variables) can be calculated by summing the SSRs given: SSR(X1 ∣ X2) = 36400.6326 and SSR(X2 ∣ X1) = 3297.7917, which gives 39698.4243. This total variability is a representation of the entire variability in house size that is accounted for by both family income and family size. Express this as a fraction or percentage of total variability in house size to determine the proportion of variability explained by the two predictors.
Note: The Excel output and the options (A. 84.79%, B. 71.89%, C. 17.56%, D. 70.69%) should contain the exact proportion but in the provided information, these values are missing.
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Graph the line with slope 1 passing through the point (1,1)
Answer:
start at (0,0) and go up 1, right 1, and mark a point and keep doing that
Step-by-step explanation:
a table cost 5 times as much as a chair. for $40000 a trader can buy 20 more chairs than tables. find the cost of a chair and number of tables.
Answer:
Chair is $1600
Table are 5 pieces
Step-by-step explanation:
Let the cost of a chair be x then for a table, it will be 5x since table cost 5 times as much as a chair.
For $40000, chairs alone will be 40000/x while tables will be 40000/5x=8000/x
The difference between these numbers is 20 hence
40000/x-8000/x=20
32000/x=20
X=32000/20=1600
The cost of a chair is $1600
Table will be 5*1600=$8000
The number bought will be proved as follows
Chairs=40000/1600=25 pieces
Tables=40000/8000=5 pieces
Difference in number is 25-5=20
Owen has completed his education and is looking for a job. He received three different offers. He researched each job, and what he learned is shown in the table.
A 4-column table with 3 rows. Column 1 has entries Salary, benefits, average monthly rent at job location. Column 2 is labeled Job A with entries 46,650 dollars, 14,000 bonus and health insurance and 401 k, 850 dollars. Column 3 is labeled Job B with entries 38,750 dollars, 15,000 dollar bonus and health insurance and 401 k, 790 dollars. Column 4 is labeled Job C with entries 52,880 dollars, 8,000 dollar bonus and health insurance and 401 k, 950 dollars.
Based on the information in the table, which job should Owen take?
Job
Job A is the correct answer! :)
Based on the information in the table, Owen should take Job A with total earnings of $50,400 before tax.
What determines job acceptance?The factors that should determine if a job should be accepted or not include:
Base salaryBenefits (e.g. 401(K)Working hoursResidential /transportation costsCareer advancement.Data and Calculations:Job A Job B Job C
Salary $46,650 $38,750 $52,880
Benefits 14,000 15,000 8,000
Average monthly rent 850 790 950
Annual rent $10,200 $9,480 $11,400 ($950 x 12)
Earnings before tax $50,400 $44,270 $49,480
Thus, based on the information in the table, Owen should take Job A with total earnings of $50,400 before tax.
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Which are solutions of the linear equation?
Select all that apply.
3x + y = 10
(1, 6)
(2, 4)
(3, 1)
(4, –1)
(5, –5)
The solutions of the linear equation are; (2, 4), (3, 1) and (5, –5)
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
The given linear equation is;
3x + y = 10
For (1, 6)
3x + y = 10
y = 10 - 3x
y = 10 - 3(1)
y = 10 -3 = 7
So, this is not the solution of the linear equation.
For (2, 4)
y = 10 - 3x
y = 10 - 3(2)
y = 10 -6 = 4
So, this is the solution of the linear equation.
For (3, 1)
y = 10 - 3x
y = 10 - 3(3)
y = 10 -9 = 1
So, this is the solution of the linear equation.
For (4, –1)
y = 10 - 3x
y = 10 - 3(4)
y = 10 -12 = -2
So, this is not the solution of the linear equation.
For (5, –5)
y = 10 - 3x
y = 10 - 3(5)
y = 10 -15 = -5
So, this is the solution of the linear equation.
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{71.NS.6b and 18.NS.6c} The three points (4,0), (-6,0), and (-6,-4) form three corners of a rectangle. Determine the coordinates of the fourth point.
Answer:
(4,-4)
Step-by-step explanation:
Diagonals of a rectangle share a common midpoint
(4-6)/2 , (0-4)/2 = (-6+x)/2, (0+y)/2
-2 = -6 + x
x = 4
-4 = y
We determined the fourth point of a rectangle by ensuring that the sides of the rectangle are parallel to the axes and the sides are equal in length. The fourth point of the rectangle formed by the points (4,0), (-6,0), and (-6,-4) is (4,-4).
Explanation:The fourth point of the rectangle should have the same x-coordinate as the point (4,0) and the same y-coordinate as the point (-6,-4). Therefore, the fourth point is (4,-4)
To better understand the reasoning, let's consider the points on a plane. We recall that rectangles have sides of equal length and parallel to the axes. Therefore, since the line connecting (4,0) and (-6,0) is parallel to the x-axis, the fourth point's x-coordinate has to be the same as the point on the opposite side of the rectangle, which is 4. Similarly, as the line connecting (-6,0) and (-6,-4) is parallel to the y-axis, the fourth point's y-coordinate has to equal the y-coordinate of the point on the opposite side (-6,-4), which is -4. Hence, the fourth point is (4,-4).
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The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 4.0 minutes. It is known that the standard deviation of the checkout time is one minute. The 98% confidence interval for the average checkout time of all customers is Group of answer choices 3.02 to 4.98 3.00 to 5.00 3.795 to 4.205 3.767 to 4.233
Answer:
[tex]4-2.326\frac{1}{\sqrt{100}}=3.767[/tex]
[tex]4+2.326\frac{1}{\sqrt{100}}=4.233[/tex]
So on this case the 98% confidence interval would be given by (3.767;4.233)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X=4[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=1[/tex] represent the population standard deviation
n=100 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
Since the Confidence is 0.98 or 98%, the value of [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that [tex]z_{\alpha/2}=2.326[/tex]
Now we have everything in order to replace into formula (1):
[tex]4-2.326\frac{1}{\sqrt{100}}=3.767[/tex]
[tex]4+2.326\frac{1}{\sqrt{100}}=4.233[/tex]
So on this case the 98% confidence interval would be given by (3.767;4.233)
The value of a gold coin picturing the head of the Roman Emperor Vespasian is increasing at the rate of 5% per year. If the coin is worth $105 now, what will it be worth in 11 years?
Answer:
255.75
Step-by-step explanation:
Answer:
$179.59
Step-by-step explanation:
Step 1 Write the exponential growth function for this situation.
y = a(1 + r)t Write the formula.
= 105(1 + 0.05)t Substitute 105 for a and 0.05 for r.
= 105(1.05)t Simplify.
Step 2 Find the value in 11 years.
y = 105(1.05)t Write the formula.
= 105(1.05)11 Substitute 11 for t.
≈ 179.59 Use a calculator and round to the nearest hundredth.
A recent report estimated that 25% of all college students in the United States have a sexually transmitted disease (STD). Due to the demographics of the community, the director of the campus health center believes that the proportion of students who have a STD is lower at his college. He tests H0: p = 0.25 versus Ha: p < 0.25.
The campus health center staff select a random sample of 50 students and determine that 18% have been diagnosed with a STD.
a) Is the sample size condition for conducting a hypothesis test for a population proportion satisfied?
Answer:
The sample size condition for conducting a hypothesis test for a population proportion is satisfied for this question.
Step-by-step explanation:
a) The sample size condition for conducting a hypothesis test for a population proportion is satisfied is when
np > 5 and n(1 - p) > 5
n = sample size = 50
p = proportion that have STD = 18% = 0.18
np = 0.18 × 5 = 9 > 5
n(1 - p) = 0.82 × 50 = 41 > 5
Hope this Helps!!!
Answer:
Step-by-step explanation:
Given :
Can someone please help me solve this
Answer:
30
Step-by-step explanation:
Everything has to add up to 90.
Add EVERYTHING together.
3x + 33
3x + 33 = 90
90 - 33 = 57
57 / 3 = 19
19 = x
19 x 2 = 38
38 - 8 = 30
Answer:
The answer for ∠CDF is 30°.
Step-by-step explanation:
It ia given that complemetary angle is 90° so we can make an expression in terms of x :
It ia given that complemetary angle is 90° so we can make an expression in terms of x :∠AFB + ∠BFC + ∠CFD = 90°
32° + (x+9)° + (2x-8)° = 90°
In order to find ∠CFD, we have to find the value of x first so we have to move all the like-terms to one side :
32° + x + 9° + 2x - 8° = 90°
2x + x = 90° - 32° - 9° + 8°
3x = 57°
Then divide both sides by 3 :
3x ÷ 3 = 57° ÷ 3
x = 19°
We have already found the value of x. Now, the question ask us to find ∠CDF, (2x-8)°. We just have to substitute x value into the expression :
Let x = 19,
∠CDF = 2x - 8
= 2(19) - 8
= 30°
Consider a hypothesis test to decide whether the mean annual consumption of beer in the nation's capital is less than the national mean. Answer the following questions.
1. "The mean annual consumption of beer in the nation's captial is less than the national mean and the result of the hypothesis test does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean" is a:________
a. Correct decision
b. Type II error
c. Type I error
2. "The mean annual consumption of beer in the nation's captial is less than the national mean and the result of the sampling leads to the conclusion that the mean annul consumption of beer in the nation's capital is less than the national mean" is a:_________
a. Correct decision
b. Type II error
c. Type I error
3. "The mean annual consumption of beer in the nation's captial is less than the national mean but the result of the sampling does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean" is a:________
4. Correct decision
b. Type II error
c. Type I error
d. "The mean annual consumption of beer in the nation's captial is not less than the national mean and the result of the sampling does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean" is a:________
a. Correct decision
b. Type II error
c. Type I error
Answer:
Step-by-step explanation:
Type I error occurs when the null hypothesis is rejected even when it is true.
Type II error occurs when the null hypothesis is not rejected even when it is false.
The null hypothesis is
The mean annual consumption = the national mean
The alternative hypothesis is
The mean annual consumption < the national mean
1) it is a type II error because the null hypothesis was not rejected even when it is false
2) it is a correct decision because the decision corresponds to the outcome
3) it is also a type II error
d) it is a correct decision because the null hypothesis is accepted when it is true
By interpreting the various scenarios related to hypothesis testing, it is determined that scenarios 1 and 3 represent Type II errors, while scenarios 2 and 4 represent correct decisions. This shows an understanding of statistical hypothesis tests.
Explanation:This problem falls within the discipline of statistical hypothesis testing, a method used to make statistical decisions using data. In the context of this problem, the null hypothesis states that the mean annual consumption of beer in the nation's capital is not less than the national mean.
'The mean annual consumption of beer in the nation's capital is less than the national mean and the result of the hypothesis test does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean' is a Type II error. This is because the reality is that the consumption in the nation's capital is indeed less, but the test results failed to conclude this.'The mean annual consumption of beer in the nation's capital is less than the national mean and the result of the sampling leads to the conclusion that the mean annul consumption of beer in the nation's capital is less than the national mean' is a correct decision. This is because the reality and the test conclusion are in agreement.'The mean annual consumption of beer in the nation's capital is less than the national mean but the result of the sampling does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean' is a Type II error. Even though in reality the consumption in the nation's capital is less, the test results failed to detect it.'The mean annual consumption of beer in the nation's capital is not less than the national mean and the result of the sampling does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean' is a correct decision. This is because both reality and test results agree that the nation's capital's consumption is not below the national mean.Learn more about statistical hypothesis testing here:https://brainly.com/question/34698067
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What is the area of a circular cardboard piece needed for the base of a model of a volcano that’s is 20 centimeters tall and has a volume of 960 cubic centimeters
Answer: 144 square centimeters
Answer:
the answer is 144 centimeters
Suppose we conduct a hypothesis test to determine if an exercise program helps people lose weight. We measure the weight of a random sample of participants before and after they complete the exercise program. The mean number of pounds lost for the sample turns out to be 7.9 lbs. The hypotheses for the test are: H0: The program is not effective for weight loss. Ha: The program is effective for weight loss. The P-value for the test turns out to be 0.012. Which of the following is the appropriate conclusion, assuming that all conditions for inference are met and the level of significance is 0.05? (i) We reject H0---this sample does not provide significant evidence that the program is effective. (ii) We reject H0---this sample provides significant evidence that the program is effective. (iii) We fail to reject H0---this sample provides significant evidence that the program is not effective. (iv) We fail to reject H0---this sample does not provide significant evidence that the program is effective.
Answer: (ii) We reject H0---this sample provides significant evidence that the program is effective.
Step-by-step explanation:
The null hypothesis is
The program is not effective for weight loss.
The alternative hypothesis is
The program is effective for weight loss.
If the P-value for the test turns out to be 0.012, and the level of significance is 0.05, then
Alpha, 0.05 > p value, 0.012
Therefore, there is enough evidence to reject the null hypothesis. We then accept the alternative hypothesis.
The correct option is
(ii) We reject H0---this sample provides significant evidence that the program is effective.
Dan rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total that is a factor of 15
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
The factors of 15 are numbers that can divide even through 15 without any remainders.
These numbers are 1, 3, 5 and 15;
When we roll two fair dice once, there are about 36 possible out comes and this is the sample space of rolling this fair dice.
1 2 3 4 5 6
1 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
2 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
3 (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
4 (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
5 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
6 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
The total that will give a factor of 15;
(1, 2) (2, 3) (1, 4) (2, 1) (3, 2) (4, 1)
Out of the 36 possible outcomes, we have 6 whose sum will give a factor of 15;
Probability of this = [tex]\frac{6}{36}[/tex] = [tex]\frac{1}{6}[/tex]
write 0.1 as a fraction in simpliest form
Answer:
1/1000
Step-by-step explanation:
Cual es la diferencia entre circulo y circunferencia
A random telephone survey of 1,091 adults (aged 18 and older) was conducted by an online tax preparation and e-filing service. The survey results showed that 634 of those surveyed planned to file their taxes electronically. (Round your answers to the nearest whole number.) (a) Develop a descriptive statistic that can be used to estimate the percentage of all taxpayers who file electronically. % (b) The survey reported that the most frequently used method for preparing the tax return is to hire an accountant or professional tax preparer. If 60% of the people surveyed had their tax return prepared this way, how many people used an accountant or professional tax preparer
Answer:
a. The percentage of all taxpayers who file electronically is 58%
b. 654 people used an accountant or professional tax preparer preparing the tax return
Step-by-step explanation:
According to the given data, in order to estimate the percentage of all taxpayers who file electronically, we would have to make the following calculation:
percentage of all taxpayers who file electronically=634×100%=0.58
1,091
Hence, the percentage of all taxpayers who file electronically is 58%
In order to calculate how many people used an accountant or professional tax preparer for preparing the tax return, we would have to make the following calculation:
people used an accountant or professional tax preparer= 60%×1,091=654
100%
654 people used an accountant or professional tax preparer preparing the tax return.
A solid right pyramid has a square base with an edge length of x cm and a height of y cm.
A solid right pyramid has a square base with an edge length of x centimeters and a height of y centimeters.
Which expression represents the volume of the pyramid?
One-thirdxy cm3
One-thirdx2y cm3
One-halfxy2 cm3
One-halfx2y cm3
Answer:
B
Step-by-step explanation:
One-thirdx2y cm3 i got it right on edg
The volume of the pyramid with a square base of side x and height (y) is (1/3)x²y cm³
How to calculate volume?Volume is the amount of space occupied by a three dimensional shape or object.
The area of the square base = x cm * x cm = x² cm²
The volume of the pyramid = (1/3) * area of square base * height = (1/3) * x² * y = (1/3)x²y cm³
The volume of the pyramid with a square base of side x and height (y) is (1/3)x²y cm³
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You see that country B can make 60 units of X and no Y at point j, or it can make no X and 30 Y at point f. So, if country B decides to produce point j instead of point f (if can do any point f through j) where it gives up units of Y it gets back X, how many units of X does it gain for each unit of Y given up
Answer:
Country B gaines 2 units of good X , per unit of Good Y sacrifised.
Step-by-step explanation:
Country B's production possibilities in form of goods (X,Y) are :
Point J [Only good X] = (60,0) Pont F [Only good Y] = (0,30)The country can produce 60 units of good X or 30 units of good Y, by complete specialisation in either good & not producing the other good.
The country has more (twice) advantage in producing good X. As, it can produce 2 times more good X, than good Y, from the same available resources.
If it decides to produce at point J, production specialising in Good X: It will produce only good X, no units of Y. This implies that - it gains 2 units of good X per unit of good Y sacrifised, as per their production potential ratio (60:30)
2x + 3y = 12 is an equation in slope intercept form.
True
False
Factor 16p^4 - 24p^3.
Answer:
8p^3(2p - 3) is the factor
Step-by-step explanation:
An agricultural researcher plants 25 plots with a new variety of yellow corn. Assume that the yield per acre for the new variety of yellow corn follows a Normal distribution with unknown mean LaTeX: \mu and standard deviation LaTeX: \sigma = 10 bushels per acre.Q: Which of the following would produce a confidence interval with a smaller margin of error than the 90% confidence interval?A) Plant only 5 plots rather than 25, because 5 are easier to manage and control.B) Plant 10 plots rather than 25, because a smaller sample size will result in a smaller margin of error.C) Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error.D) Plant 100 plots rather than 25, because a larger sample size will result in a smaller margin of error.
Answer:
Correct Answer: CA larger sample size results in a smaller margin error, i.e. with a plant of 100 plots instead of 25, the margin error will be smaller.
Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
An agricultural researcher plants 25 plots with a new variety of yellow corn.
Assume that the yield per acre for the new variety of yellow corn follows a Normal distribution with unknown mean and standard deviation of 10.
We need to find a confidence interval with a smaller margin of error than the 90% confidence interval
n=25, x=150,s=10,a=0.95
Unknown mean u means we use t table.
[tex]150 ± t_{0.975} \frac{10}{\sqrt{25}}[/tex]
150±[tex]t_{0.975}[/tex]×2
Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error
Hence, option C is correct. Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error
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Can someone please answer this question I am confused
Answer:
Step-by-step explanation:
Fast-food restaurants spend much time studying the amount of time cars spend in their drive-thrus. Certainly, the faster the cars get service, the more opportunity for making money. According to a recent study by QSR magazine, Wendy’s has the best time, with a mean time spent in the drive thru of 138.5 seconds. Assuming drive-thru time is normally distributed with a standard deviation of 29 seconds, what proportion of cars spends between 120 and 180 seconds in Wendy's drive-thru? Write answer as decimal rounded to the thousandth.
Answer:
0.663
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 138.5, \sigma = 29[/tex]
What proportion of cars spends between 120 and 180 seconds in Wendy's drive-thru?
This is the pvalue of Z when X = 180 subtracted by the pvalue of Z when X = 120. So
X = 180
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{180 - 138.5}{29}[/tex]
[tex]Z = 1.43[/tex]
[tex]Z = 1.43[/tex] has a pvalue of 0.924
X = 120
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{120 - 138.5}{29}[/tex]
[tex]Z = -0.64[/tex]
[tex]Z = -0.64[/tex] has a pvalue of 0.261
0.924 - 0.261 = 0.663
Final answer:
0.662 when rounded to three decimal places.
Explanation:
To determine the proportion of cars that spend between 120 and 180 seconds in Wendy's drive-thru, we can use the properties of the normal distribution. Given that the mean time is 138.5 seconds and the standard deviation is 29 seconds, we can calculate the corresponding z-scores for both 120 seconds and 180 seconds.
Firstly, calculate the z-score for 120 seconds:
z = (X - µ) / σ = (120 - 138.5) / 29 ≈ -0.6379.
Next, calculate the z-score for 180 seconds:
z = (X - µ) / σ = (180 - 138.5) / 29 ≈ 1.4310.
By looking up these z-scores in a standard normal distribution table, we find that:
P(Z < 1.4310) ≈ 0.9236
P(Z < -0.6379) ≈ 0.2616.
To find the proportion of times between 120 and 180 seconds, we subtract the smaller probability from the larger:
P(120 < X < 180) = P(Z < 1.4310) - P(Z < -0.6379) ≈ 0.9236 - 0.2616 = 0.6620.
The average annual inflation rate in the United States over the past 98 years is 3.37% and has a standard deviation of approximately 5% (Inflationdata). In 1980, the inflation rate was above 13%. If the annual inflation rate is normally distributed, what is the probability that inflation will be above 13% next year
Answer:
2.68% probability that inflation will be above 13% next year
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 3.37, \sigma = 5[/tex]
If the annual inflation rate is normally distributed, what is the probability that inflation will be above 13% next year
This is the pvalue of Z when X = 13. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{13 - 3.37}{5}[/tex]
[tex]Z = 1.93[/tex]
[tex]Z = 1.93[/tex] has a pvalue of 0.9732
1 - 0.9732 = 0.0268
2.68% probability that inflation will be above 13% next year
Answer:
[tex]P(X>13)=P(\frac{X-\mu}{\sigma}>\frac{13-\mu}{\sigma})=P(Z>\frac{13-3.37}{5})=P(Z>1.926)[/tex]
And we can find this probability using the complement rule and the normal standard distirbution table or excel:
[tex]P(Z>1.926)=1-P(Z<1.926)=1-0.9729=0.0271[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the annual inflation of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(3.37,5)[/tex]
Where [tex]\mu=3.37[/tex] and [tex]\sigma=5[/tex]
We are interested on this probability
[tex]P(X>13)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(X>13)=P(\frac{X-\mu}{\sigma}>\frac{13-\mu}{\sigma})=P(Z>\frac{13-3.37}{5})=P(Z>1.926)[/tex]
And we can find this probability using the complement rule and the normal standard distirbution table or excel:
[tex]P(Z>1.926)=1-P(Z<1.926)=1-0.9729=0.0271[/tex]
Two numbers have a sum of 23 and a difference of 9. Find the two numbers
Answer:
The numbers are 16 and 7
Step-by-step explanation:
Let the numbers be x and y
x+y = 23
x-y = 9
Add the two equations together
x+y = 23
x-y = 9
-------------------
2x = 32
Divide each side by 2
2x/2 = 32/2
x = 16
Now subtract the two equations
x+y = 23
-x +y = -9
-------------------
2y = 14
Divide by 2
2y/2 = 14/2
y = 7
Final answer:
The two numbers with a sum of 23 and a difference of 9 are 16 and 7. Solved by setting up equations for the sum and difference, then solving for the two unknowns.
Explanation:
To find the two numbers with a sum of 23 and a difference of 9, we can set up two equations based on the given information:
x + y = 23 (Equation for sum)x - y = 9 (Equation for difference)Adding the two equations together, we get:
2x = 32
Dividing both sides by 2:
x = 16
Now, substituting x back into one of the original equations, for example, x + y = 23:
16 + y = 23
y = 23 - 16
y = 7
Therefore, the two numbers are 16 and 7.
Which of the following are like radicals? Check all of the boxes that apply.
Answer:
3x√x²y, –12x√x²y, x√yx², 2√x²y. or on Edge is A,B,D,F
Step-by-step explanation:
Got 100% on edge...
Multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E. A random sample of the correct choice on 400 multiple-choice questions on a variety of AP exams1 shows that B was the most common correct choice, with 90 of the 400 questions having B as the answer. Does this provide evidence that B is more likely to be the correct choice than would be expected if all five options were equally likely? Show all details of the test. The data are available in APMultipleChoice.
Answer:
Option B is not the most common correct choice.
Step-by-step explanation:
The multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E.
The probability that any of these five option is the correct answer is:
[tex]p=\frac{1}{5}=0.20[/tex]
A random sample of 400 multiple-choice questions on Advanced Placement exam are selected.
The results showed that 90 of the 400 questions having B as the answer.
To test the hypothesis that option B is more likely the correct answer for most question, the hypothesis can be defined as:
H₀: All the options are equally probable, i.e. p = 0.20.
Hₐ: Option B is more likely the correct option, i.e. p > 0.20.
Compute the sample proportion as follows:
[tex]\hat p=\frac{90}{400}=0.225[/tex]
The test statistic is:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.225-0.20}{\sqrt{\frac{0.20(1-0.20)}{400}}}= 1.25[/tex]
The test statistic is 1.25.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
Compute the p-value as follows:
[tex]p-value=P(Z>1.25)\\=1-P(Z<1.25)\\=1-0.89435\\=0.10565\\\approx 0.1057[/tex]
*Use a z-table.
The p-value is 0.1057.
The p-value of the test is quite large. Thus, the null hypothesis was failed to rejected.
Hence, it can be concluded that option B is not the most common correct choice.
Testing the hypothesis, it is found that since the p-value of the test is of 0.1056 > 0.05, it does not provide evidence that B is more likely to be the correct choice than would be expected if all five options were equally likely.
At the null hypothesis, it is tested if all of them are equally as likely, that is, the proportion of B is [tex]p = \frac{1}{5} = 0.2[/tex]. Thus:
[tex]H_0: p = 0.2[/tex]
At the alternative hypothesis, it is tested if B is more likely, that is, if the proportion of B is more than 0.2. Thus:
[tex]H_1: p > 0.2[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.In this problem, the parameters are: [tex]p = 0.2, n = 400, \overline{p} = \frac{90}{400} = 0.225[/tex].
The value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.225 - 0.2}{\sqrt{\frac{0.2(0.8)}{400}}}[/tex]
[tex]z = 1.25[/tex]
The p-value of the test is the probability of finding a sample proportion above 0.225, which is 1 subtracted by the p-value of z = 1.25.
Looking at the z-table, z = 1.25 has a p-value of 0.8944.
1 - 0.8944 = 0.1056.
Since the p-value of the test is of 0.1056 > 0.05, it does not provide evidence that B is more likely to be the correct choice than would be expected if all five options were equally likely.
A similar problem is given at https://brainly.com/question/24571593
How many times larger is 4 x 10^8 than 2 x 10^-5
Answer:The answer is 8x10^7
Step-by-step explanationi took the thing
Use StatKey or other technology to generate a bootstrap distribution of sample proportions and find the standard error for that distribution. Compare the result to the standard error given by the Central Limit Theorem, using the sample proportion as an estimate of the population proportion p.
Proportion of peanuts in mixed nuts, with n=94 and P =0.52
Round your answer for the bootstrap SE to two decimal places, and your answer for the formula SE to three decimal places.
Answer:
0.0515
Step-by-step explanation:
By the central limit theorem
when n increase distribution when data follows normal
Standard Error, SE of P is
[tex]SE = \sqrt{\frac{p(1-p)}{n} }[/tex]
Bootstrap Standard Error = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
where n = 94 and p = 0.52
hence,
SE of Bootstrap = [tex]\sqrt{\frac{0.52(1-0.52)}{94} }[/tex]
[tex]=\sqrt{\frac{0.2496}{94} }\\\\=0.0515[/tex]
SE and the SE of Bootstrap are the same