The following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n1 = 40 n2 = 50 x1 = 25.7 x2 = 22.8 σ1 = 5.3 σ2 = 6 (a) What is the value of the test statistic? (Round your answer to two decimal places.)

Answer:

a. The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57

b. Yes

c. The power of the test is 0.03836

d. The sample size can be considered adequate

Step-by-step explanation:

a. The given data in the study

Catalyst 1: 57.9, 66.2, 65.4, 65.4, 65.2, 62.6, 67.6, 63.7, 67.2, 71.0

Catalyst 2: 66.4 , 71.7, 70.3, 69.3, 64.8, 69.6, 68.6, 69.4, 65.3, 68.8

Using the Average, Standard Deviation function from Microsoft Excel, we have;

The mean for Catalyst 1, [tex]\overline x_1[/tex] = 65.22

The standard deviation for catalyst 1, σ₁ = 3.444416

The mean for Catalyst 2, [tex]\overline x_2[/tex] = 68.42

The standard deviation for catalyst 2, σ₂ = 2.22401

The 95% confidence interval on the difference in mean is given as follows;

[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}[/tex]

The critical-z for a 95% confidence interval = 1.96

Therefore, we have;

[tex]\left (65.22-68.42 \right ) \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}}[/tex]

Therefore, we have;

The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57

The test statistics is given as follows;

[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]

Therefore we have;

[tex]z=\dfrac{(65.22-68.42)}{\sqrt{\dfrac{3^{2} }{10}+\dfrac{3^{2}}{10}}} = -2.385[/tex]

The p-value = P(Z<-2.39 or Z > 2.39) = 2P(Z<-2.39) = 2 × 0.00842 = 0.01684

b. From the confidence interval which range from approximately -5.83 to -0.57 and does not include 0, therefore, there is a difference in mean active concentration which depends on the choice of catalyst

c. The power of the test

 The sample mean difference is given as follows;

[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}[/tex]

Therefore, we have;

[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}} = \pm 2.6296[/tex]

The z-value is given as follows;

[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]

μ₁ - μ₂ = 5

When [tex]\bar{x}_1-\bar{x}_{2} = 2.6296[/tex]

[tex]z=\dfrac{2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -1.7667918[/tex]

When [tex]\bar{x}_1-\bar{x}_{2} = -2.6296[/tex]

[tex]z=\dfrac{-2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -5.686768[/tex]

The power of the test is given by P = P(Z<-5.69) + P(Z>-1.77) = 0 + 0.03836 = 0.03836

The power of the test = 0.03836

d. The sample size is statistically adequate because the confidence interval of -5.83 < μ₁ - μ₂ < -0.57 has a value of -5 as a possible population difference in mean

The assumption of normality seems adequate because the confidence interval obtained by using the sample standard deviation is given as follows;

(-5.74, -0.66) which also contains -5 which is the difference in the population mean

Answer: 3

Step-by-step explanation:

12.9/4.3 will give you the number it was multiplied by.

Answer:

there is no opposite number but no means opposite

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

if it has a square in the center of the angle it means it is 90 degrees

so a straight line adds up to 180b

90 +30+x=180

x=60

Answer:

The answer is A.

if im wrong im truly sorry

Answer:

The total number of students is 800.

Step-by-step explanation:

Given that in an examination, 40% students passed in Maths only, 30% passed in Science only and 10% students failed in both the subjects, to determine the total number of students if 400 students passed in Science the following calculation must be performed:

100 - 40 - 30 - 10 = 20

20 + 30 = 50

50 = 400

100 = X

100 x 400/50 = X

800 = X

Thus, the total number of students is 800.

Answer:

12.57

Step-by-step explanation:

same as last time you know

Answer:

x = 5.85

Step-by-step explanation:

Given that,

One angle = 26°

Middle angle = 90°

Third angle = 180-(90+26) = 64°

Height, H = 12

We need to find the value of x. Using trigonometry to find it such that,

[tex]\tan64=\dfrac{12}{x}\\\\x=\dfrac{12}{\tan(64)}\\\\x=5.85[/tex]

So, the value of x is equal to 5.85.

Answer:

5.9

Step-by-step explanation:

im doing this rn

Answer:

y = 18

x = 15.588

Answer:

The value of X should be 0

The value of Y should be 30

However your teacher gave next to no context, so these might be wrong

Step-by-step explanation: protractor

Answer:

-6.3

Step-by-step explanation:

Its the only thing I can think of. |-6.3| |6.3|

Answer:

d = 5

Step-by-step explanation:

For:

(X1, Y1) = (2, 3)

(X2, Y2) = (2, 8)

Distance Equation Solution:

d=(2−2)2+(8−3)2−−−−−−−−−−−−−−−√

d=(0)2+(5)2−−−−−−−−−√

d=0+25−−−−−√

d=2–√5

d=5

Answer:

5,8  8,3

Step-by-step explanation:

hoped this helped <33

Answer: 2a/3 + b/3

Since it has two different variables, there is no final answer. To find the answer, you must first expand the equation and then apply the fraction rule.

Answer:

  MC7.  B

  MC8.  A

Step-by-step explanation:

Given events are mutually exclusive and the probability of either is 0.64, you want possible probabilities for each. Given independent events have a joint probability of 0.16, you want possible probabilities for each.

Mutually exclusive events cannot occur simultaneously (by definition). This means the probability of occurrence of either is the sum of the probabilities of occurrence of each:

  P(A∪B) = P(A) + P(B) . . . . . . . only if P(A∩B) = 0

The answer to this question will be two probabilities that have a sum of 0.64. This requirement is met by ...

  b.)  P(A) = 0.42, P(B) = 0.22

Events are independent when their conditional probability is the same as the unconditioned probability:

  P(A|B) = P(A∩B)/P(B) . . . . . definition of conditional probability

When this is the same as P(A), you have ...

  P(A) = P(A∩B)/P(B)

  P(A)·P(B) = P(A∩B)

The answer to this question will be two probabilities that have a product of 0.16. This requirement is met by ...

  a.) P(A) = 0.4, P(B) = 0.4

__

Additional comment

So, the two formulas used here are the one for "or" (union) and the one for conditional probability:

  P(A∪B) = P(A) +P(B) -P(A∩B) . . . . . . "mutually exclusive" means P(A∩B)=0

  P(A|B) = P(A∩B)/P(B) . . . . . . . "independent" means P(A|B) = P(A)

The plus sign (+) is often used in probability and in logic to mean "or". That is, P(A∪B) can also be written P(A+B). That is NOT the same as P(A)+P(B), where this "+" means addition.

The multiplication symbol (·, or no symbol) is often used in probability and in logic to mean "and", or "intersection." That is, P(A∩B) can also be written P(A·B) or P(AB). That is NOT the same as P(A)·P(B), where the symbol means multiplication in this context.

<95141404393>

The possible probabilities are given as follows:

7 b) P(A) = 0.42, P(B) = 0.22.

8 a) P(A) = 0.4, P(B) = 0.4.

The two parameters that are needed to calculate a probability are listed as follows:

Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.

For mutually exclusive events, we have that:

P(A U B) = P(A) + P(B).

Hence:

0.42 + 0.22 = 0.64.

For independent events, we have that:

P(A and B) = P(A) x P(B)

Hence:

0.8 x 0.8 = 0.64.

Learn more about the concept of probability at https://brainly.com/question/24756209

#SPJ1

Answer:

35 cm^3

Step-by-step explanation:

the area is 35 hoped that helped

Answer:

Step-by-step explanation:

radius of the cylindrical construction pipe = 2.5 ft

height of cylinder = 25 ft

volume of cylinder = [tex]\pi r^{2} h[/tex]

                             = 3.14 x 2.5 x 2.5 x 25

                             = 490.625

                             = 490 [tex]ft^{3}[/tex]

Hope this helps

please mark as brainliest!!!

Answer:

490 ft³

Step-by-step explanation:

The radius of the cylindrical construction pipe is 2.5ft, if the pipe is 25ft long, what is the volume? 490 ft³

Answer:

1=94 max  2=96 max

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

Triangle DEF was rotated and dilated so that's why is looks different than triangle ABC, but it maintained the same shape that is presented in ABC and that is why A is the answer.

9514 1404 393

Answer:

  f(x) = {-x for x < 2; 2x-3 for x ≥ 2}

Step-by-step explanation:

The blue line extending to the left has a slope of -1 and a y-intercept of 0. Its equation is y = -x. That part of the definition of f(x) is applicable for values of x less than 2. (The open dot at (2, -2) tells you that point is not included.)

The red line extending to the right has a slope = rise/run = 2/1 = 2. The y-intercept can be found by extending the line to the y-axis, or from the computation ...

  b = y -mx

  b = 1 -2(2) = -3 . . . . . for the point (x, y) = (2, 1)

Then the slope-intercept equation for the red line is ...

  y = 2x -3

That part of the definition of f(x) is applicable for values of x ≥ 2. The solid dot tells you the point (2, 1) is included.

Putting these parts together, we get ...

  [tex]f(x)=\left\{\begin{array}{cc}-x&\text{if $x<2$}\\2x-3&\text{if $x\ge2$}\end{array}\right.[/tex]

Answer:

$2,067.59

Step-by-step explanation:

To calculate the balance of the savings account, we can use the continuous compounding interest formula:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Interest Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

Given values:

Substitute the given values into the formula and solve for A:

[tex]\begin{aligned}A&=1727 \cdot e^{0.03 \cdot 6}\\&=1727 \cdot e^{0.18}\\&=1727 \cdot 1.19721736...\\&=2067.59438...\\&=2067.59\end{aligned}[/tex]

Therefore, the balance of the savings account 6 years from now is $2,067.59.

Using the triangle inequality theorem, we can figure this out.

2-  Yes

3- No

4- No

5- Yes

6-  Yes

Answer:

9514 1404 393

Answer:

  7×10⁻¹ +6×10⁻² +5×10⁻³

Step-by-step explanation:

Place value in any place-value number system increases by a factor of the base for each place to the left of the "decimal" point. It is reduced by a factor of the base for each place to the right of the "decimal" point.

For base-10 numbers, the powers of 10 are -1, -2, -3, ... as you go to the right of the decimal point. Hence the number 0.765 decomposes as ...

  7×10⁻¹ +6×10⁻² +5×10⁻³

Answer:

Step-by-step explanation:

simpify each term

x- 2/x +3+ 10/x -9

combine fractions

x+3 -9 + 8/x

find common denominator then simplify terms                          [tex]\frac{x*x}{x}+\frac{3x}{x}+\frac{-9x}{x}+\frac{8}{x}[/tex]

[tex]\frac{x^{2}-6x+8 }{x}[/tex]

factor

[tex]\frac{(x-4) (x-2)}{x}[/tex]

Answer:

(x−4)(x−2)x

Step-by-step explanation:

Answer:

Bueno esto es lo que yo calculo

3×‐12

3(×‐4)

3 14x12

A calcule

A 12×3 =14

es lo que me calcula

Answer:

Step-by-step explanation:

14/6 = 21 / 3x - 12            

first, cross multiply

14 (3x - 12) = 6*21

Remove the brackets

42x - 168 = 126

Add 168 to both sides

42x = 168 + 126

Combine

42x = 294

Divide by 42

x = 294/42

x = 7                                                                                                                                                                                  

Kamryn would save $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

To determine the amount of interest Kamryn will save by raising her credit score from 665 to 680, we need to compare the interest rates associated with each credit score range.

According to the given information, a credit score of 665 falls within the range of 580-669, where the corresponding simple interest rate is 10.358%.

Let's calculate the interest Kamryn would pay on a loan of $13,250.00 at an interest rate of 10.358%.

Interest = Principal * Rate

= $13,250.00 * 0.10358

≈ $1,370.56

Therefore, if Kamryn were to borrow $13,250.00 with a credit score of 665, she would pay approximately $1,370.56 in interest.

Now, let's consider the scenario where Kamryn raises her credit score to 680. A credit score of 680 falls within the range of 670-739, where the corresponding simple interest rate is 9.132%.

Calculating the interest with a credit score of 680:

Interest = Principal * Rate

= $13,250.00 * 0.09132

≈ $1,210.57

Thus, if Kamryn were able to raise her credit score from 665 to 680, she would save approximately $1,370.56 - $1,210.57 = $159.99 in interest.

Therefore, Kamryn would save approximately $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

For more question on interest visit:

https://brainly.com/question/25720319

#SPJ8