The critical value t* gets larger as the confidence level increases. True or false?

Answers

Answer 1

Answer:

We can find the critical value [tex]t_{\alpha/2}[/tex]

And for this case if the confidence increase the critical value increase so then this statement is True

Step-by-step explanation:

For a confidence level given c, we can find the significance level like this:

[tex] \alpha=1 -c[/tex]

And with the degrees of freedom given by:

[tex] df=n-1[/tex]

We can find the critical value [tex]t_{\alpha/2}[/tex]

And for this case if the confidence increase the critical value increase so then this statement is True


Related Questions

Which of the following is the missing side length that completes the
Pythagorean triple below?
5, 12,

Answers

Answer:

13

Step-by-step explanation:

We can find the missing side length by using the pythagorean theorem

a² + b² = c²

5² + 12² = c²

25 + 144 = c²

169 = c²

13 = c

So, 13 is the missing side length.

An article gave the accompanying data on ultimate load (kN) for two different types of beams. Assuming the underlying distributions are Normal, calculate and interpret a 99% Cl for the difference between the true average load for the fiberglass beams and that for the carbon beams.
Type Sample size Sample Mean Sample SD
Fiberglass grid 26 33.4 2.2
Commercial carbon 26 42.8 4.3
grid
1. Calculate and interpret a 99% Cl for true average stance duration among elderly individuals.
2. Carry out a test of hypotheses at significance level 0.05 to decide whether true average stance duration is larger among elderly individuals than younger individuals.

Answers

Answer:

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

Step-by-step explanation:

We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams.

The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2.

The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3.

The difference between sample means is Md=-9.4.

[tex]M_d=M_1-M_2=33.4-42.8=-9.4[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{2.2^2}{26}+\dfrac{4.3^2}{26}}\\\\\\s_{M_d}=\sqrt{0.186+0.711}=\sqrt{0.897}=0.9473[/tex]

The critical t-value for a 99% confidence interval is t=2.678.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_{M_d}=2.678 \cdot 0.9473=2.537[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M_d-t \cdot s_{M_d} = -9.4-2.537=-11.937\\\\UL=M_d+t \cdot s_{M_d} = -9.4+2.537=-6.863[/tex]

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

In this way, we can calculate the individual duration of each one and the duration time, knowing that the sample means:

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is -11.937 and -6.863.

We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams. The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2. The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3. The difference between sample means is Md=-9.4.

[tex]Sm_d= \sqrt{\frac{\sigma^2_1}{n_1} +\frac{\sigma^2_2}{n_2}} = \sqrt{(0.186)+(0.711) }= 0.9473[/tex]

The critical t-value for a 99% confidednce interval is t=2.678. The margin of error (MOE) can be calculated as:

[tex]MOE=t*8M_d = (2.678)(0.9473)= 2.537[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL= M_d-t*SM_d = -9.4-2.537= -11.937\\UL= M_d+t*SM_d= -9.4+2.537= -6.863[/tex]

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

See more about statistics at brainly.com/question/2289255

find the value of x. m<2= x + 119

Answers

Answer:  x = -10

Step-by-step explanation:

see image

A) congruent sides implies congruent angles A = 64°

B) Use the Triangle Sum Theorem: 64° + 64° + B = 180° --> B = 52°

C) B and C are complimentary angles: 52° + C = 90°  --> C = 38°

D) Use the Triangle Sum Theorem knowing that congruent sides implies congruent angles: 38° + 2D = 180°  --> D = 71°

∠2) D and ∠2 are supplementary angles: 71° + ∠2 = 180°  --> ∠2 = 109°

Solve for x:

109° = x + 119

 -10  = x

Answer:

x = -10

Step-by-step explanation:

Find the measure of angle m∠2

The triangles are isosceles triangles, the base angles are equal.

The other base angle is also 64°.

Using Triangle Sum Theorem.

64 + 64 + y = 180

y = 52

The top angle is 52°.

The whole angle is 90°.

90 - 52 = 38

The second triangle has base angles equal.

Using Triangle Sum Theorem.

38 + z + z = 180

z = 71

The two base angles are 71°.

Angles on a straight line add up to 180°.

71 + m∠2 = 180

m∠2 = 109

The measure of m∠2 is 109°

Find the value of x

m∠2 = x + 119

109 = x + 119

x = 109 - 119

x = -10

4. A rectangle-shaped picture frame has a length of 4b cm and an area of 12ab² square cm. Find the width. *

Answers

Answer:

3ab

Step-by-step explanation:

area = length * width

width = area/length

width = (12ab^2)/(4b)

width = 3ab

Find the solution of the given initial value problem. ty' + 2y = sin t, y π 2 = 9, t > 0 y(t) =

Answers

For the ODE

[tex]ty'+2y=\sin t[/tex]

multiply both sides by t so that the left side can be condensed into the derivative of a product:

[tex]t^2y'+2ty=t\sin t[/tex]

[tex]\implies(t^2y)'=t\sin t[/tex]

Integrate both sides with respect to t :

[tex]t^2y=\displaystyle\int t\sin t\,\mathrm dt=\sin t-t\cos t+C[/tex]

Divide both sides by [tex]t^2[/tex] to solve for y :

[tex]y(t)=\dfrac{\sin t}{t^2}-\dfrac{\cos t}t+\dfrac C{t^2}[/tex]

Now use the initial condition to solve for C :

[tex]y\left(\dfrac\pi2\right)=9\implies9=\dfrac{\sin\frac\pi2}{\frac{\pi^2}4}-\dfrac{\cos\frac\pi2}{\frac\pi2}+\dfrac C{\frac{\pi^2}4}[/tex]

[tex]\implies9=\dfrac4{\pi^2}(1+C)[/tex]

[tex]\implies C=\dfrac{9\pi^2}4-1[/tex]

So the particular solution to the IVP is

[tex]y(t)=\dfrac{\sin t}{t^2}-\dfrac{\cos t}t+\dfrac{\frac{9\pi^2}4-1}{t^2}[/tex]

or

[tex]y(t)=\dfrac{4\sin t-4t\cos t+9\pi^2-4}{4t^2}[/tex]

2) Find the diameter.
4) If the diameter is equal to 3 inches ,d=

Answers

Answer:

d = 3 in

Step-by-step explanation:

Since we are trying to find the diameter, and the diameter is given to us as 3 in, our diameter is 3 in.

What is the value of X in equation? 1/3 X - 2/3 = - 18

Answers

Answer:

x=-52

Step-by-step explanation:

1/3x=-17 1/3

x=-52

3.A man answers 10 maths problems, one after the other. He answers the first problem correctly and the second problem incorrectly, for each of the remaining 8 problems the probability that he answers the problem correctly equals to the ratio of the number of problems that he has already answered correctly to the total number of problems that he has already answered. What is the probability that he answers exactly 5 out of 10 problems correctly​

Answers

Answer:

Probability of answering 5out of 10 correctly= 0.246

Step-by-step explanation:

Total question answered= 2

Question answered correctly= 1

Probability of answered correctly= 1/2

Probability of answered correctly= 0.5

Probability of answered incorrectly = 0.5

Probability of answering 5out of 10 correctly= 10C5(0.5)^5(0.5)^5

Probability of answering 5out of 10 correctly = 10!/5!5!(0.5)^5(0.5)^5

Probability of answering 5out of 10 correctly = 252(0.03125)(0.03125)

Probability of answering 5out of 10 correctly= 0.246

Dairy cows at large commercial farms often receive injections of bST (Bovine Somatotropin), a hormone used to spur milk production. Bauman et al. (Journal of Dairy Science, 1989) reported that 12 cows given bST produced an average of 28.0 kg/d of milk. Assume that the standart deviation of milk production is 2.25 kg/d.

Requried:
a. Find a 99% confidence interval for the true mean milk production.
b. If the farms want the confidence interval to be no wider than ± 1.25 kg/d, what level of confidence would they need to use?

Answers

Answer:

a) 26.33 kg/d and 29.67 kg/d

b) 94.5%

Step-by-step explanation:

a. Find a 99% confidence interval for the true mean milk production.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575*\frac{2.25}{\sqrt{12}} = 1.67[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 28 - 1.67 = 26.33 kg/d

The upper end of the interval is the sample mean added to M. So it is 28 + 1.67 = 29.67 kg/d

The 99% confidence interval for the true mean milk production is between 26.33 kg/d and 29.67 kg/d

b. If the farms want the confidence interval to be no wider than ± 1.25 kg/d, what level of confidence would they need to use?

We need to find z initially, when M = 1.25.

[tex]M = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]

[tex]1.25 = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]

[tex]2.25z = 1.25\sqrt{12}[/tex]

[tex]z = \frac{1.25\sqrt{12}}{2.25}[/tex]

[tex]z = 1.92[/tex]

When [tex]z = 1.92[/tex], it has a pvalue of 0.9725.

1 - 2*(1 - 0.9725) = 0.945

So we should use a confidence level of 94.5%.

What number is 408% of 568?

Answers

Answer:

2317.44

Step-by-step explanation:

Solution for What is 408 percent of 568:

408 percent *568 =

(408:100)*568 =

(408*568):100 =

231744:100 = 2317.44

Answer:

2317.44

Step-by-step explanation:

what is u over 4-4= -20

Answers

u/4 - 4 = -20

Add 4 to both sides:

u/4 = -16

Multiply both sides by 4:

u = -64

Answer:

u=-64

Step-by-step explanation:

u/4 -4 = -20

First add 4 to both sides.

u/4=-16

Now multiply both sides by 4

u=-64

Round 2826 to the nearest hundred.

Answers

Answer:

2800

Step-by-step explanation:

2826 to the nearest hundred is 2800

The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Suppose a box in the shape of a rectangular prism has length (2a + 11), width (5a – 12), and height (a + 6). Which expression represents the volume of the box?

Answers

Answer:

Volume = 10a³ + 91a² + 54a - 792

Step-by-step explanation:

In the absence of answer choices, let's find the expression for the volume.

Given: Volume = length×width×height

V = lwh

length =(2a + 11)

width =(5a – 12)

height= (a + 6)

V =  (2a + 11)(5a – 12) (a + 6)

Expand the first two brackets using distributive property

V = (10a² -24a +55a - 132)(a + 6)

Collect like terms

V = (10a² + 31a -132)(a + 6)

Expand the two brackets using distributive property

V = 10a³ + 31a² - 132a + 60a² + 186a - 792

Collect like terms

V = 10a³ + 91a² + 54a - 792

The expression that represents the volume of the box = 10a³ + 91a² + 54a - 792

Answer:

Volume = 10a³ + 91a² + 54a - 792

Step-by-step explanation:

In 1998, as an advertising campaign, the Nabisco Company announced a "1000 Chips Challenge," claiming that every 18-ounce bag of their Chips Ahoy cookies contained at least 1000 chocolate chips. Dedicated statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips. Some of their data are given below. 1219 1214 1087 1200 1419 1121 1325 1345 1244 1258 1356 1132 1191 1270 1295 1135 Find a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies.

Answers

Answer:

A 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

Step-by-step explanation:

We are given that statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips.

Some of their data are given below; 1219, 1214, 1087, 1200, 1419, 1121, 1325, 1345, 1244, 1258, 1356, 1132, 1191, 1270, 1295, 1135.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                          P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean number of chocolate chips = [tex]\frac{\sum X}{n}[/tex] = 1238.2

            s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex]  = 94.3

            n = sample of car drivers = 16

            [tex]\mu[/tex] = population mean number of chips in a bag

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.131 < [tex]t_1_5[/tex] < 2.131) = 0.95  {As the critical value of t at 15 degrees of

                                             freedom are -2.131 & 2.131 with P = 2.5%}  

P(-2.131 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.131) = 0.95

P( [tex]-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                   = [ [tex]1238.2-2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] , [tex]1238.2+2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] ]

                                   = [1187.96, 1288.44]

Therefore, a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

Select the correct interpretation of the probability of getting an 11 when a pair of dice is rolled. Interpret an event as significant if its probability is less than or equal to 0.05. Select one: a. Significant at .055 b. Not significant at .945 c. Not significant at .055 d. Significant at .028

Answers

Answer:

c. Not significant at .055

Step-by-step explanation:

When a pair of dice is rolled, we have 6²=36 possible outcomes. Only 2 of these outcomes have a total score of 11:

When the first dice is 5 and the second is 6.When the first dice is 6 and the second is 5.

Then, we can calculate the probability of getting 11 as the quotient between the successs outcomes and the total outcomes.

Then, the probability of getting 11 is:

[tex]P=\dfrac{X}{N}=\dfrac{2}{36}=0.055[/tex]

This probability is not equal or less than 0.05, so it is not significant at 0.055.

Given X= 5+ V16 select the value(s) of x. Check
all of the boxes that apply.
-11
1
9
21

Answers

Answer:

[tex]x = 9\ or\ x = 1[/tex]

Step-by-step explanation:

Given

[tex]x = 5 + \sqrt{16}[/tex]

Required

Find the value of x

[tex]x = 5 + \sqrt{16}[/tex]

We start by taking the square root of 16; Square root of 16 is +4 or -4; So, we have:-

[tex]x = 5 \±4[/tex]

The expression above can be split into two; This is as follows

[tex]x = 5 + 4\ or\ x = 5 - 4[/tex]

[tex]x = 9\ or\ x = 1[/tex]

Hence, the solution to [tex]x = 5 + \sqrt{16}[/tex] is B. 1 and C. 9

Answer:

its b and c

Step-by-step explanation:

the guy who answered first said so

also i just did it

Find the area of the yellow region.
Round to the nearest tenth.
15 cm
15 cm
Area = [ ? ] cm2

Answers

Answer:

48.3 cm²

Step-by-step explanation:

Let A be the area of the yellow region

A= the area of the square - the area of the quarter square

A= 15²-(15²*π)/4= 48.28≈ 48.3 cm²

Find the range of y=3/2cos4x-1

Answers

Answer:

Range = [- 2.5, 0.5] = [ - 5/2, 1/2]

Step-by-step explanation:

Smallest value of cos α = - 1,

largest value of cos α = 1.

When cos 4x = - 1,  y=3/2cos4x-1 = 3/2*(-1) - 1 = - 5/2 = - 2 1/2 = - 2.5

When cos 4x = 1,  y=3/2cos4x-1 = 3/2*1 - 1 = 1/2 = 0.5

Range = [- 2.5, 0.5] = [ - 5/2, 1/2]

Which expression is equivalent to 3m + 1 - m? 2 + m - 1 + m 1 + m 3m - 1 3m

Answers

Answer:

2m + 1

Step-by-step explanation:

Simply combine like terms. m terms go with m terms and constants go with constants.

Answer:

2m + 1

Step-by-step explanation:

3m + 1 - m =

= 3m - m + 1

= 2m + 1

A simple random sample of 44 adults is obtained from a normally distributed​ population, and each​ person's red blood cell count​ (in cells per​ microliter) is measured. The sample mean is 5.31 and the sample standard deviation is 0.51 . Use a 0.05 significance level and the given calculator display to test the claim that the sample is from a population with a mean less than 5.4 comma which is a value often used for the upper limit of the range of normal values. What do the results suggest about the sample​ group?

Answers

Answer:

There is not enough evidence to support the claim that the population mean is significantly less than 5.4.

This result suggest we may be making a Type II error, where a true alternative hypothesis does not have enough evidence to be supported.

If the same outcome would have been obtained with a bigger sample size, the power of the test is bigger and there is a higher probability of rejecting the null hypothesis.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the population mean is significantly less than 5.4.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=5.4\\\\H_a:\mu< 5.4[/tex]

The significance level is 0.05.

The sample has a size n=44.

The sample mean is M=5.31.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.51.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.51}{\sqrt{44}}=0.077[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{5.31-5.4}{0.077}=\dfrac{-0.09}{0.077}=-1.171[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=44-1=43[/tex]

This test is a left-tailed test, with 43 degrees of freedom and t=-1.171, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-1.171)=0.124[/tex]

As the P-value (0.124) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the population mean is significantly less than 5.4.

This result suggest we may be making a Type II error, where a true alternative hypothesis does not have enough evidence to be supported.

If the same outcome would have been obtained with a bigger sample size, the power of the test is bigger and there is a higher probability of rejecting the null hypothesis.

Simply the expression 3.4-1/2(0.75)

Answers

Answer:

3.025

Step-by-step explanation:

3.4-1/2(0.75)

3.4-0.375

3.025

Simplify: |2-5|-(12 ÷4-1)^2

Answers

The value of the expression when simplified is -13

How to determine the value

It is important to note:

PEDMAS is a mathematical acronym that representing;

P for ParenthesesE for exponentsD for divisionM for multiplicationA for additionS for subtraction

Also, we should note that absolute value of a number is the non-negative value of that number. It s the value of a number irrespective of its direction from zero.

It is denoted with the symbol '| |'

Given the expression;

|2-5|-(12 ÷4-1)^2

Solve the bracket

|-3| - (12 /3)^2

Solve further

|-3| - 4^2

Find the absolute value

3 - 4^2

Find the square

3 - 16

-13

The value is - 13

Thus, the value of the expression when simplified is -13

Learn more about PEDMAS here:

https://brainly.com/question/345677

#SPJ1

In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample was $112. The population standard deviation is known to be $16.

a. Which form of the hypotheses should be used to test whether or not the average room price is significantly different from $108.50?

H0:
-mu is greater than or equal to $108.50
mu is greater than $108.50
mu is less than $108.50mu is less than or equal to $108.50
mu is equal to $108.50mu is not equal to $108.50

Ha: -
-mu is greater than or equal to $108.50
mu is greater than $108.50mu is less than $108.50
mu is less than or equal to $108.50
mu is equal to $108.50mu is not equal to $108.50

b. Test to determine if whether or not the average room price is significantly different from $108.50, using an alpha level of .05.


Reject H0
or
Fail to reject H0

Answers

Answer:

Step-by-step explanation:

H0: mu is equal to $108.50

Ha: mu is not equal to $108.50

This test is a two tailed test and using the z tat formula, we can ascertain if there is a difference.

z = x-u / sd/√n

Where x is $112, u is $108.50 sd is $16 and n is 64

z = 112-108.50 / 16/√64

z = 3.5/(16/8)

z = 3.5/2

z = 1.75

To help us arrive at a conclusion, we need to find the p value using alpha id = 0.05. The p value is 0.08. Since the p value is great than 0.05, we fail to reject the null and conclude that there is not enough statistical evidence to prove that the average room price is significantly different from $108.50

From Statistics and Data Analysis from Elementary to Intermediate by Tamhane and Dunlop, pg 265. A thermostat used in an electrical device is to be checked for accuracy of its design setting of 200◦F. Ten thermostats were tested to determine their actual settings, resulting in the following data: 202.2 203.4 200.5 202.5 206.3 198.0 203.7 200.8 201.3 199.0 Perform the t-test to determine if the mean setting is different from 200◦F. Use α = 0.05

Answers

Answer:

[tex]t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

The p value for this case is given by:

[tex]p_v =2*P(t_{(9)}>2.32)=0.0455[/tex]    

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

Step-by-step explanation:

Information given

data: 202.2 203.4 200.5 202.5 206.3 198.0 203.7 200.8 201.3 199.0

We can calculate the sample mean and deviation with the following formulas:

[tex]\bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]\sigma=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

[tex]\bar X=201.77[/tex] represent the sample mean    

[tex]s=2.41[/tex] represent the sample standard deviation    

[tex]n=10[/tex] sample size    

[tex]\mu_o =200[/tex] represent the value that we want to test    

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.    

t would represent the statistic

[tex]p_v[/tex] represent the p value for the test

Hypothesis to test

We want to determine if the true mean is equal to 200, the system of hypothesis are :    

Null hypothesis:[tex]\mu = 200[/tex]    

Alternative hypothesis:[tex]\mu = 200[/tex]    

The statistic for this case is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)    

The statistic is given by:

[tex]t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

The p value for this case is given by:

[tex]p_v =2*P(t_{(9)}>2.32)=0.0455[/tex]    

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

evaluate 25.1 * 2.51 in two decimal places​

Answers

Answer:

63.00

Step-by-step explanation:

25.1 × 2.51

Multiply.

= 63.001

Round to two decimal places.

63.00

Answer:

63.00

Step-by-step explanation:

when u multiply 25.1 by 25.1 you get 630.01. Then u have to move the decimal over to the left once and then u get 63.00

I’m Confused On The Question

Answers

The answer is A but check desmos first to make sure

factorise 12x² + x - 20​

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

(3x + 4) * (4x - 5)

▹ Step-by-Step Explanation

12x² + x - 20

Rewrite

12x² + 16x - 15x - 20

Factor out

4x(3x + 4) - 15x - 20

4x(3x + 4) - 5(3x + 4)

Factor

(3x + 4) * (4x - 5)

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

How do you write 416.7 in scientific notation? ___× 10^____

Answers

Answer:

4.167(10²)

Step-by-step explanation:

Step 1: Put number into proper decimal form

416.7 = 4.167

Step 2: Figure out exponent

Since we are moving the decimal places 2 places to the right, our exponent is 2

Answer:

4.167 × 10^2

Step-by-step explanation:

= 4.167 × 10^2

(scientific notation)

= 4.167e2

(scientific e notation)

= 416.7 × 10^0

(engineering notation)

(one)

= 416.7

(real number)

If you average your costs over your total production, you get the average cost, written C: C(x, y) = C(x, y) x + y . Find the average cost for the cost function C(x, y) = 200,000 + 5,700x + 4,200y − 100,000e−0.01(x + y).

Answers

Answer:

Average cost

= [200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾] ÷ (x + y)

Step-by-step explanation:

Average cost is the cost per unit of production. It is expressed mathematically as the total cost divided by the total number of units produced.

If total cost = C(x, y)

Average cost = C(x, y) ÷ (x+y)

For this question, total cost function is

C(x, y) = 200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾

The average cost is simply this total cost function divided by the total number of units produced.

Average cost

= [200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾] ÷ (x + y)

If numerical values are then provided, this can then be worked around. But as the numerical values are absent, the average cost function just remains in this its raw form.

Hope this Helps!!!

Factor completely 5x(x + 3) + 6(x + 3). (1 point)

Answers

Answer:

The answer is ( 5x + 6 ) ( x + 3 )

Step-by-step explanation:

5x(x + 3) + 6(x + 3)

The final answer is

( 5x + 6 ) ( x + 3 )

Hope this helps you

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