Advantage of using paired samples William S. Gosset was employed by the Guinness brewing company of Dublin. Sample sizes available for experimentation in brewing were necessarily small, and new techniques for handling the resulting data were needed. Gosset consulted Karl Pearson (1857-1936) of University College in London, who told him that the current state of knowledge was unsatisfactory. Gosset undertook a course of study under Pearson and the outcome of his study was a famous paper published in statistical literature, "The Probable Error of a Mean" (1908), which introduced the t- distribution. Since Gosset was contractually bound by Guinness, he published under a pseudonym, "Student"; hence, the t distribution is often referred to as 'Student's t distribution.' As an example, to illustrate his analysis, Gosset reported in his paper on the results of seeding 11 different plots of land with two different seed types: regular and kiln-dried. There is reason to believe that drying seeds before planting will increase plant yield. Since different plots of soil may be naturally more fertile, a matched pairs design was used by planting both types of seeds in all 11 plots. The resulting data (corn yield in pounds per acre) are in the submodule in Canvas. Open the 'seeds' dataset in Minitab. We will use this data to test if there is a difference in the yield based on seed type. Exploratory Data Analysis Visually, consider the two variables 'Regular seed' and 'Kiln_dried_seed.' Create a graph that displays a boxplot for each variable. Graph > Boxplot > Multiple Y Variables > With Categorical Variables > Select variables. 1. What do you observe? What are the shapes of the distributions? Is there an obvious difference in the centers of the distributions? Note: we can use the t distribution to make inferences because the graphs show no clear skewness or outliers Analysis This is paired data since both types of seed were planted in each plot, so the yields of each seed type in the plot are paired. The unit/case is the plot. What happens when we build a confidence interval for the difference in means without taking the pairing into account. 2. Use Minitab to build the 95% confidence interval: Stat > Basic Statistics > 2-sample t> Select 'Each sample is in its own column' from the drop-down menu. Sample 1: 'Regular_seed' and Sample 2: 'Kiln_dried_seed' What is the 95% confidence interval for μ1−μ2 ? 3. With the corresponding two-sided test, what is the p-value and generic conclusion? Note: Remember that an advantage of using a paired means approach is the ability to reduce unwanted variation and focus on the variation of interest. 4. Create dotplots of Samples: 'Regular_seed', 'Kiln_dried_seed', and the "Differences" Graph > Dotplot > Multiple Y Variables > enter all 3 variables Compare the three dotplots that you created. Do the sample of differences seem to have more, less, or about the same variation that is found with the two individual samples? 5. Use Minitab to find the summary statistics for all three variables: Stat > Basic Statistics > Display Descriptive Statistics [select all 3 variables] Complete the table below with the standard deviation: What do you notice about the standard deviation of the differences? 6. Calculate the 95% confidence interval for μd : Stat > Basic Statistics > Paired t> Sample 1: 'Regular_seed' and Sample 2: 'Kiln_dried_seed' x
ˉ
d= Ibs/acre 95% confidence interval for μd : 7. Compare the confidence interval for μd in part 6 with the confidence interval that you found for μ1−μ2 in part 2 . What is the most salient difference between the two intervals? 8. What is the p-value and generic conclusion for the corresponding two-sided hypothesis test with μd ? 9. Compare the p-values from the two tests. What have you learned about the advantage of using a paired design when your data is matched pairs?

Answer:

14

Step-by-step explanation:

The cumulative frequency of the 3rd bin in a frequency distribution table represents the number of data values that are less than the maximum value of the 3rd bin. The correct option is a.

A frequency distribution table, often known as a frequency table, is a table that displays the frequency or amount of occurrences of different values in a dataset. Frequencies may be written as total values or as percentages of the total (relative frequency).

Cumulative frequency is the total frequency of values less than or equal to a given value in a dataset. The cumulative frequency of the 3rd bin in a frequency distribution table represents the total number of data values that are less than or equal to the maximum value of the 3rd bin.

Because it is a cumulative frequency, it contains all the values that came before it as well as its own frequency. The frequency distribution table is used to compute cumulative frequency.

The calculation of cumulative frequency may be done using the data's ascending or descending order.

Thus, the correct option is a.

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The differential equation governing the variation of the charge (c) in the given RC circuit is 2(d^2q/dt^2) + (1/0.5)(dq/dt) = d(E(t))/dt, where q represents the charge, t represents time, and E(t) represents the electromotive force of the circuit. This equation describes the relationship between the charge, current, and voltage in the RC circuit.

To compute the differential equation governing the variation of the charge (c) in the given RC circuit, we can start by using Kirchhoff's voltage law (KVL) and the relationship between charge, capacitance, and voltage.

Kirchhoff's voltage law states that the sum of the voltages in a closed loop in a circuit is equal to zero. In this case, the voltage across the resistor (VR) and the voltage across the capacitor (VC) must sum up to the electromotive force (E) of the circuit.

The voltage across the resistor can be calculated using Ohm's Law: VR = IR, where I is the current flowing through the circuit.

The voltage across the capacitor can be calculated using the formula: VC = (1 / C) ∫Idt, where ∫Idt represents the integral of the current over time.

Combining these equations, we have:

E(t) = VR + VC

E(t) = IR + (1 / C) ∫Idt

Differentiating both sides of the equation with respect to time, we get:

d(E(t)) / dt = d(IR) / dt + d((1 / C) ∫Idt) / dt

Since the resistance R and the capacitance C are constant values, their derivatives with respect to time are zero.

d(E(t)) / dt = R(dI / dt) + (1 / C)(I)

Substituting I with dq / dt, where q represents the charge c, we get:

d(E(t)) / dt = R(d^2q / dt^2) + (1 / C)(dq / dt)

Simplifying the equation, we obtain the differential equation governing the variation of c:

R(d^2q / dt²) + (1 / C)(dq / dt) = d(E(t)) / dt

In summary, the differential equation governing the variation of the charge (c) in the given RC circuit is:

2(d^2q / dt²) + (1 / 0.5)(dq / dt) = d(E(t)) / dt

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Step-by-step explanation:

area of a quadrilateral is b x h

if the base is 7 the height is x and the area is 63 then:

7x=63

divide both sides by 7

7/7x=63/7

x=9

Hope that helps :)

Answer:

Air

Step-by-step explanation:

You can't really measure air

Answer:

Air

Step-by-step explanation:

You cannot measure air because it is invisible.

Answer:

y = 4x+1

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Subtract the number with the term both sides ( which is 9)

[tex] {x}^{2} + {y}^{2} - 6x + 4y = - 9[/tex]

Complete the square for the x terms and y terms.

( To complete the square divide the coefficient term by 2 and square it, then add that product to both sides.)

[tex] {x}^{2} - 6x + 9 + {y}^{2} +4y + 4 = - 9 + 9 + 4[/tex]

[tex] (x - 3) {}^{2} + (y + 2) {}^{2} = 4[/tex]

Take the square root of the right side to find the radius

[tex] \sqrt{4} = 2[/tex]

The correct option is (C) 23.7%.

If the coefficient of determination is 0.237, the percentage of the data about the regression line that is explained is 23.7%.

The coefficient of determination is used to explain how much variability in a dependent variable is due to the independent variable in a regression analysis.

It is usually represented as R², which is a fraction between 0 and 1, or expressed as a percentage between 0% and 100%.

It measures the proportion of variability in the dependent variable that can be attributed to the independent variable(s).

In this problem, the coefficient of determination is given as 0.237, which means that 23.7% of the variability in the dependent variable is explained by the independent variable(s) in the regression line. Therefore, the correct option is (C) 23.7%.

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Answer:

64y^2

Step-by-step explanation:

Given that a manufacture has been selling 1350 television sets a week at $480 each. A market survey indicates that for each $15 rebate offered to a buyer, the number of sets sold will increase by 150 per week.

a) The demand function is p(x) = 480 - 15x/150, Where x is the number of television sets sold per week.

b) The company should offer a rebate of $25 to maximize its revenue.

c) The company should offer a rebate of $23 to maximize its profit.

a) Demand function:

p(x) = 480 - 15x/150, Where x is the number of television sets sold per week.

b) To maximize revenue, we need to find the point where the marginal revenue equals zero.

Marginal revenue is the derivative of the revenue function.

Revenue function is given by R(x) = x p(x), where x is the number of television sets sold and p(x) is the price per set.

R(x) = x p(x)

R(n) = (1350 + 150n)(480 - 15n/150)

R(n) = 648000 - 2250n - 45n²

R’(n) = -2250 - 90n

For marginal revenue, we need

R’(n) = 0

2250 - 90n = 0

n = -2250/90

n = -25

So, the company should offer a rebate of $25 to maximize its revenue.

c) Cost function: C(x) = 108000 + 160x

Total revenue (TR) = x p(x)

= (1350 + 150n)(480 - 15n/150)

= 648000 - 2250n - 45n²

Total cost (TC) = C(x)

= 108000 + 160n

Profit (P) = TR - TCP

P = 648000 - 2250n - 45n² - (108000 + 160n)

P = 540000 - 2090n - 45n²

For maximum profit, we need

P’(n) = 0 -2090 - 90n

P'(n) = 0

2090 - 90n = 0

n = -2090/90

n = -23.2

Since n has to be a whole number, the number of TVs sold will be

1350 + 150n = 1350 + 150(-23)

= 1020.

Therefore, the company should offer a rebate of $23 to maximize its profit.

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The Economic Stimulus Act of 2008 focused on providing tax relief, while the American Recovery and Reinvestment Act of 2009 focused on a combination of tax cuts, government spending, and investments for economic growth.

the Economic Stimulus Act of 2008 was enacted in response to the economic downturn that occurred during the Great Recession. Its main objective was to provide immediate relief to the economy by implementing tax incentives and rebates for individuals and businesses. The act aimed to encourage consumer spending and investment by putting more money into people's pockets and reducing the tax burden on businesses.

On the other hand, the American Recovery and Reinvestment Act of 2009 was a broader and more comprehensive economic stimulus package. It included a mix of tax cuts, grants, loans, and direct government spending on infrastructure projects, renewable energy, healthcare, education, and other areas. The goal was to not only provide short-term economic relief but also to make long-term investments that would promote sustainable economic growth and job creation.

Overall, while both acts were aimed at stimulating the economy, the focus of the Economic Stimulus Act of 2008 was primarily on tax relief, while the American Recovery and Reinvestment Act of 2009 encompassed a wider range of measures to boost the economy and address various sectors affected by the recession.

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1. The participants would be a member of all four groups. In a within-subjects ANOVA, participants are exposed to all levels of the factor, so they experience each group.

2. The within-groups sums of squares is only found in a one-way within-subjects ANOVA. This represents the variability within each group or condition.

3. In this case, you would typically conduct a post-hoc analysis to determine which specific groups or conditions differ significantly from each other. Common post-hoc tests for within-subjects ANOVA include the Bonferroni or Tukey tests. These tests help identify pairwise differences between the groups.

4. True. Eta-squared, partial eta-squared, and R-squared are all measures of effect size that indicate the proportion of variance explained within a study. They provide information about the strength and magnitude of the effect being studied.

5. When conducting a two-way between-subjects ANOVA, you would typically run two F-tests: one for each main effect and one for the interaction effect. The main effects assess the effects of each independent variable separately, while the interaction effect examines whether the combined influence of the variables is significant.

6. The between-groups sums of squares is only found in a two-way between-subjects ANOVA. It represents the variability between the different groups or levels of the independent variables.

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(a) The estimated coefficient of X₂ captures the average impact of X₂ on the response variable Y, given the specified regression model. (b) a higher R² value indicates a better fit of the model to the data and a higher degree of explained variability.

(a.) The estimated coefficient of X₂ in the multiple linear regression equation (Y = 8 + 45X₁ + 16X₂) represents the expected change in the dependent variable (Y) for a one-unit increase in the independent variable X₂, while holding all other independent variables constant.

In this case, the estimated coefficient of X₂ is 16, so for every one-unit increase in X₂, the expected change in Y is an increase of 16 units, assuming X₁ and other variables remain constant.

(b.) The coefficient of determination (R²) is a measure of the proportion of the total variation in the dependent variable (Y) that can be explained by the independent variables (X₁ and X₂) in the regression model. In this case, if the R² value is 0.98, it means that approximately 98% of the total variation in Y can be explained by the linear relationship between X₁, X₂, and the constant term.

A high R² value of 0.98 indicates a very strong fit of the regression model to the data. It suggests that 98% of the variability in the dependent variable Y is accounted for by the independent variables X₁ and X₂, while the remaining 2% may be attributed to other factors or random variation.

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Using Romberg integration, f(1) = 4.01.

Based on the given information, we can deduce the order of approximation for [tex]R_{33}[/tex] in Romberg integration as h10, h8, h4, h6. Additionally, we are given the values [tex]R_{21} = 7[/tex] and [tex]R_{22} = 7.21[/tex].

Romberg integration typically follows the pattern R(k, m), where k represents the number of iterations and m denotes the number of function evaluations per iteration.

From [tex]R_{21} = 7[/tex], we can determine that the approximation achieved after two iterations is 7.

From [tex]R_{22} = 7.21[/tex], we can conclude that the approximation achieved after two iterations is 7.21.

Since [tex]R_{21}[/tex] and [tex]R_{22}[/tex] represent the same number of iterations (k = 2), we can directly compare the results of these two approximations.

Therefore, the final answer is: f(1) = 4.01.

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Answer:

-5p+3

Step-by-step explanation:

-p-2-4p+5

-p-4p-2+5

-5p+3

Answer:

Step-by-step explanation:

4(2x+10)=0

8x+40=0

-40       -40

8x=-40

x=-5

Answer:

-5

Step-by-step explanation:

First you have to distribute 4 to 2x and 10, giving us 8x + 40 = 0. Then subtract 40 from both sides, giving us 8x = -40. Now divide -40 by 8, which gives us -5.

Perpendicular means that two lines intersect at a right angle.

D and E have perpendicular sides

(blue rectangle at the bottom left and green trapezoid all the way at the bottom right)

Step-by-step explanation:

the answer is x=-4 ,y=-5

1. to find angle x:

angles on a straight line add to 180º : 180-92º = 88º

to find angle y:

exterior angle equals opposite interior angles: 88+22=110º

2. to find angle x:

angles on a straight line add to 180º : 180-118 = 62º

to find angle y:

exterior angle equals opposite interior angles: 62+52 = 114º

sorry if i got any of the angles wrong, the picture was a bit blurry and I couldn't tell that well, let me know if i got it wrong and i'll fix it

Answer:

12z-32

Step-by-step explanation:

-4z-12-20+16z

The set of real numbers with a repeating decimal expansion is countable because it can be mapped to a countable set of unique pairs of rational numbers.

To show that the set of all real numbers with a repeating decimal expansion is countable, we can prove that it is at most countable.

Let's consider a repeating decimal number 0.d1d2d3...dn(dn+1...dn+m-1dn+m...). This can be represented as 0.d1d2d3...dn + (dn+1...dn+m-1dn+m...)/([tex]10^m - 1[/tex]).

We can see that for any repeating decimal number, the part before the repeating block (0.d1d2d3...dn) is a finite decimal representation, which is a rational number.

The part within the repeating block ((dn+1...dn+m-1dn+m...)/([tex]10^m - 1[/tex])) is also a rational number because it can be expressed as a fraction.

Since both the finite decimal part and the repeating block part are rational numbers, we can map each repeating decimal number to a unique pair of rational numbers (finite decimal part, repeating block part).

Now, we know that the set of rational numbers is countable. Therefore, if we can show that the set of unique pairs of rational numbers is countable, then the set of repeating decimal numbers is at most countable.

To show that the set of unique pairs of rational numbers is countable, we can use the fact that the Cartesian product of countable sets is countable.

Since the set of rational numbers is countable, the set of unique pairs of rational numbers (finite decimal part, repeating block part) is also countable.

Thus, we can conclude that the set of all real numbers with a repeating decimal expansion is at most countable.

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Answer:

65

Step-by-step explanation:

all triangles angles equal 180°

180-72-43=65

Answer: Kianna is incorrect, if Elena’s house was a reflection of her house across the y-axis, the coordinates would be (-4,2).

Step-by-step explanation:

Answer:

286 Degrees

Step-by-step explanation:

A circle is 360 degrees, and from the question, we know that it is asking for ACB, so it would be 360 - 74, which is 286 degrees

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Thus, the adult male foot length of 31.6 cm is significantly high since it falls outside the range of values considered normal for adult male foot length.

Range rule of thumb:The range rule of thumb is a formula used to calculate the range of the data that's spread around the mean. The range is the difference between the maximum and minimum data values. The range rule of thumb estimates the expected range for a normally distributed dataset by taking the difference between the maximum and minimum values, then multiplying that difference by 4. This estimate is usually only useful for datasets with more than 15 data points. Thus, using the range rule of thumb, the range of a normally distributed data set is approximately four times the standard deviation. Thus, the range of the adult male foot length is as follows:Range = 4 × Standard deviation= 4 × 1.41 cm= 5.64 cmWe can then identify the limits separating values that are significantly low or high as follows:Significantly low values are cm or lower: 28.48 - 2 x 1.41 = 25.66 cmSignificantly high values are cm or higher: 28.48 + 2 x 1.41 = 31.3 cmThus, the adult male foot length of 31.6 cm is significantly high since it falls outside the range of values considered normal for adult male foot length.

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Answer:

A is incorrect!  B. should be the correct answer

Step-by-step explanation

After some research, i found that the correct answer is most likely B.  a regression line and trend line are equivalent terms

A trendline and a regression can be the same.

A regression line is based upon the best fitting curve Y= a + bX Most often it’s a least-squares fit (where the squared distances from the points to the line (along the Y-axis) is minimized).

It can be quadratic or logistic or otherwise, but most often it is linear.

A trendline is often constructed by smoothing of the results, making it less peaked. (often by using a moving average); but can also come from ARIMA projections or curve fitting techniques (such as regression).

Let me know if i helped you!

The statement that is true about a trend line is B. A regression line and trend line are equivalent terms.

It should be noted that the trend line doesn't represent only the largest data points. It can also represent the smallest data points.

The regression line and the trend line are not opposite terms but rather, the regression line and trend line are equivalent terms.

In conclusion, the correct option is B.

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Heather receives $35 every six months from the corporate bond.

The correct answer to the given question is option D.

To calculate how much Heather receives every six months from the corporate bond, we need to determine the semi-annual interest payment.

The annual interest rate is given as seven percent. Since interest is paid semi-annually, we divide the annual interest rate by 2 to get the semi-annual interest rate:

Semi-annual interest rate = 7% / 2 = 3.5%

Next, we calculate the semi-annual interest payment by multiplying the face value of the bond ($1,000) by the semi-annual interest rate:

Semi-annual interest payment = $1,000 * 3.5% = $1,000 * 0.035 = $35

Therefore, Heather receives $35 every six months from the corporate bond.

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For the CDF of a continuous real function, the answers are as follows:

(i) P(X = Y) = 0 because P(X ≤ Y) > 0 and P(X < Y) > 0 and both are strictly positive

(ii) P(exist i < j with Xi = Xj) = 0 which is a contradiction.

(i) Suppose the CDF F is a continuous real function and note that this does not imply F is differentiable. Assume for simplicity that F(0) = 0 and F(1) = 1 (this does not change the major statements below but makes the proof a bit cleaner). If X, Y are independent F-distributed RVs, then for any n in N, we have; P(X ≤ Y) = P(X ≤ Y, Y ≤ X) = P(X ≤ Y|Y ≤ X) P(Y ≤ X) = P(Y ≤ X|X ≤ Y) P(X ≤ Y) = P(X ≤ Y|X ≤ Y) P(X ≤ Y) = P(X = Y). Hence, P(X = Y) = P(X ≤ Y)P(Y ≤ X) = P(X ≤ Y)P(X ≤ Y) = P²(X ≤ Y).Since F is continuous, P(X ≤ Y) = P(X < Y) = P(X ≤ Y) - P(X = Y). Therefore, P(X = Y) = 0 because P(X ≤ Y) > 0 and P(X < Y) > 0 and both are strictly positive.

(ii) Conclude that P(X = Y) = 0 (remember that you cannot assume F has a density). As for the sample case, we show that P(exist i < j with Xi = Xj) = 0. Suppose, for the purpose of contradiction, that we have X1, . . . , Xn in F such that P(exist i < j with Xi = Xj) > 0. Then, there must be some distinct i < j such that Xi = Xj. Without loss of generality, we may assume i = 1 and j = 2. Then, the probability that this event occurs is; P(X1 = X2, X3 ≠ X1, . . . , Xn ≠ X1) = P(X2 ≤ X1, X3 ≠ X1, . . . , Xn ≠ X1) + P(X1 < X2, X3 ≠ X1, . . . , Xn ≠ X1)Since Xi are independent F-distributed RVs and P(X = Y) = 0, it follows that the probability of the first term in the sum above is zero. Therefore, P(exist i < j with Xi = Xj) = 0 which is a contradiction.

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Mark's approach to solving the problem is incorrect.

We have,

To find the sum of percentages, you cannot simply add the numbers together as you would with regular numbers.

Percentages represent proportions or ratios, so they must be converted to their corresponding decimal or fraction forms before adding them.

To solve 12% + 3%, you need to convert each percentage to its decimal form and then add the decimals together.

Here's the correct approach:

12% = 12/100 = 0.12

3% = 3/100 = 0.03

Now, add the decimals:

0.12 + 0.03 = 0.15

Therefore,

The value of 12% + 3% is 0.15 or 15%.

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