Suppose a simple random sample of size 50 is selected from a population with σ=10σ=10. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).
a. The population size is infinite.
b. The population size is N=50,000.N=50,000.
c. The population size is N=5000.N=5000.
d. The population size is N=500.N=500.

Answer:

a= 0

b= [tex]-\frac{\sqrt{42} }{12}[/tex]

Step-by-step explanation:

We can rewrite the expression to be:

[tex]\frac{i\sqrt{7} }{i^{2}\sqrt{24} }[/tex]

We then can cancel out the i and we get

[tex]\frac{\sqrt{7} }{\sqrt{24} i}[/tex]

Can be rewritten as

[tex]\frac{\sqrt{7} }{2\sqrt{6} i}[/tex]

We then rationalize and get

[tex]-\frac{\sqrt{42} }{12} i[/tex]

Answer:

[tex]9\dfrac{5}{6}[/tex]

Step-by-step explanation:

[tex]5\dfrac{1}{6}+4\dfrac{2}{3}=\\\\5\dfrac{1}{6}+4\dfrac{4}{6}=\\\\9\dfrac{5}{6}[/tex]

Hope this helps!

Answer:

Null hypotheses = H₀ = σ₁² ≤ σ₂²

Alternative hypotheses = Ha = σ₁² > σ₂²

Test statistic = 1.9

p-value = 0.206

Since the p-value is greater than α therefore, we cannot reject the null hypothesis.

So we can conclude that the night shift workers don't show more variability in their output levels than day workers.

Step-by-step explanation:

Let σ₁² denotes the variance of night shift-workers

Let σ₂² denotes the variance of day shift-workers

State the null and alternative hypotheses:

The null hypothesis assumes that the variance of night shift-workers is equal to or less than day-shift workers.

Null hypotheses = H₀ = σ₁² ≤ σ₂²

The alternate hypothesis assumes that the variance of night shift-workers is more than day-shift workers.

Alternative hypotheses = Ha = σ₁² > σ₂²

Test statistic:

The test statistic or also called F-value is calculated using

Test statistic = Larger sample variance/Smaller sample variance

The larger sample variance is σ₁² = 38

The smaller sample variance is σ₂² = 20

Test statistic = σ₁²/σ₂²

Test statistic = 38/20

Test statistic = 1.9

p-value:

The degree of freedom corresponding to night shift workers is given by

df₁ = n - 1

df₁ = 9 - 1

df₁ = 8

The degree of freedom corresponding to day shift workers is given by

df₂ = n - 1

df₂ = 8 - 1

df₂ = 7

We can find out the p-value using F-table or by using Excel.

Using Excel to find out the p-value,

p-value = FDIST(F-value, df₁, df₂)

p-value = FDIST(1.9, 8, 7)

p-value = 0.206

Conclusion:

p-value > α    

0.206 > 0.05   ( α = 1 - 0.95 = 0.05)

Since the p-value is greater than α therefore, we cannot reject the null hypothesis corresponding to a confidence level of 95%

So we can conclude that the night shift workers don't show more variability in their output levels than day workers.

Answer:

x = 22

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the interior angles

6x+1 = 79+ 2x+10

Combine like terms

6x+1 = 2x+89

Subtract 2x from each side

4x+1 = 89

Subtract 1 from each side

4x = 88

Divide by 4

4x/4 = 88/4

x = 22

Answer:

The answer is

Step-by-step explanation:

We can cross out A. So it has to be either B, C, or D.

Answer:

Due to the higher z-score, Norma should be offered the job

Step-by-step explanation:

Z-score:

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 question:

Whoever has the higher z-score should get the job.

Norma:

Norma got a score of 84.2; this version has a mean of 67.4 and a standard deviation of 14.

This means that [tex]X = 84.2 \mu = 67.4, \sigma = 14[/tex]

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{84.2 - 67.4}{14}[/tex]

[tex]Z = 1.2[/tex]

Pierce:

Pierce got a score of 276.8; this version has a mean of 264 and a standard deviation of 16.

This means that [tex]X = 276.8, \mu = 264, \sigma = 16[/tex]

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{276.8 - 264}{16}[/tex]

[tex]Z = 0.8[/tex]

Reyna:

Reyna got a score of 7.62; this version has a mean of 7.3 and a standard deviation of 0.8.

This means that [tex]X = 7.62, \mu = 7.3, \sigma = 0.8[/tex]

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{7.62 - 7.3}{0.8}[/tex]

[tex]Z = 0.4[/tex]

Due to the higher z-score, Norma should be offered the job

Answer:

7/3

Step-by-step explanation:

Write this symbolically as:

  7/9

 -------

   1/3

Invert the denominator fraction and then multiply:

(7/9)(3/1)

Reducing this, we get 7/3

Answer:

the answer as a mixed number is 2 and 1/3  (2 1/3)

and as a normal fraction its 7/3

As the x values go up, the y values go down which means the line is higher on the left side than it is on the right side.

The 4th graph would be the correct one

Answer:

-3

Step-by-step explanation:

Because -3x-3=9 and 9+8= 17. 17 is greater than 14

Answer:

Population = 34.27336

Step-by-step explanation:

Given:

Population function (t) = 34(1.00804)^t

Number of year = 2000

Find:

Number of citizen in year 2000

Computation:

We know that, base year is 2000

So, t = 1

Population function (t) = 34(1.00804)^t

Population function (1) = 34(1.00804)^1

Population = 34(1.00804)

Population = 34.27336

Therefore, Population is 34.273636 million

Answer:

Terrance is 25.5

Step-by-step explanation:

Answer:

Hello There. The correct answer is 26

T = 3.5 + 22.5 = 26

Hope It Helps!

Answer:

slope = -3, y intercept = 3

Step-by-step explanation:

The y intercept is where it crosses the y axis

y intercept is 3

The slope is found by taking two points (0,3) and (1,0) and using the slope formula

m = (y2-y1)/(x2-x1)

   = (0-3)/(1-0)

   -3/1

  =-3

Answer:

B=25

Step-by-step explanation:

Answer:

NO

Step-by-step explanation:

The objective of this surveys is to determine if the two surveys will reach a similar conclusion.

From the data given, we have  two test surveys here:

The survey is to measure the effect of an advertising campaign for a certain brand of detergent.

Now in the first survey; interviewers ask house- wives whether they use that brand of detergent and in the second survey  the interviewers ask to see what detergent is being used.

Let assume that the brand name of the detergent is KLIN ;

From this disparities of statement ; we anticipate that they will reach different conclusion. This is because; from the first survey people will either respond to the fact that they use the brand detergent (KLIN) or do not used the brand detergent. But in the second survey; when being asked to see what detergent that is being used. There are greater chance that they will bring out the detergent that is commonly used  which will eventually result to the same detergent .

Answer:

g(x)= 1/4 |x-2| + 1

Step-by-step explanation:

line:

points on same line:

slope based on the points

And the line is moved to the right by 2 units:

So the function becomes:

Considering movement up by 1 unit as well:

This is the final of equation for the line.

Answer:

-8,-6,-4,-2 is an Arithmetic sequence, because there common difference is 2.

Answer:

16

Step-by-step explanation:

The right triangle shown is a 30:60:90 triangle.

30:60:90 right triangles have a 1:sqrt(3):2 ratio between their sides.

Since the side opposite from the 30 degree is 8, and x is opposite from the 90 degree angle, 8 and x have a 1:2 ratio, or 8:16.

Answer:

(A)Decay

(b)0.8

(c)First Term

(d)[tex]f(t)=2000(0.8)^t[/tex]

(e)$819.20

Step-by-step explanation:

The exponential function for modelling growth or decay is given as:

[tex]A(t)=A_o(1\pm r)^t[/tex],

Where:

Plus indicates growth and minus indicates decay.

[tex]A_o$ is the Initial Value\\r is the growth/decay rate\\t is the time period[/tex]

For a powerful computer that was purchased for $2000, but loses 20% of its value each year.

(a)Since it loses value, it is a decay.

(b)Multiplier

Its value decays by 20%.

Therefore, our multiplier(1-r) =(1-20&)=1-0.2

Multiplier =0.8

(c)$2000 is our First term (or Initial Value [tex]A_o[/tex])

(d)The function for this problem is therefore:

[tex]f(t)=f_o(1- r)^t\\f(t)=2000(1- 0.2)^t\\\\f(t)=2000(0.8)^t[/tex]

(e)Since we require the worth of the computer after 4 years,

t=4 years

[tex]f(4)=2000(0.8)^4\\f(4)=\$819.20[/tex]

Answer:

[tex] E(100 Y^2) =100 E(Y^2)[/tex]

And we have that :

[tex] E(Y^2) =\sum_{i=1}^n X^2_i P(X_i)[/tex]

And replacing we got:

[tex] E(Y^2) =0^2 *0.6 + 1^2 *0.25 +2^2*0.10 +3^2 *0.05 = 1.1[/tex]

And finally we have:

[tex] E(100 Y^2) =100 *1.1 = 110[/tex]

Step-by-step explanation:

For this case we have the following probability masss function given:

Y         0           1              2             3

p(Y)    0.6        0.25      0.10         0.05

And we can define the surcharge with this expression [tex] 100Y^2[/tex]

We want to find the expected value for the last expression and we can do it on this way:

[tex] E(100 Y^2) =100 E(Y^2)[/tex]

And we have that :

[tex] E(Y^2) =\sum_{i=1}^n X^2_i P(X_i)[/tex]

And replacing we got:

[tex] E(Y^2) =0^2 *0.6 + 1^2 *0.25 +2^2*0.10 +3^2 *0.05 = 1.1[/tex]

And finally we have:

[tex] E(100 Y^2) =100 *1.1 = 110[/tex]

Answer:

L = 3/4

Option A. The Root Test says that the series converges absolutely.

Step-by-step explanation:

By using the root test equation given in the question. L = 3/4

Since L < 1, the series converges absolutely.

For clarity of expression, the detailed calculation is contained in the attached file. Check the file attached for the complete calculation to this question.

Answer:

  (0, 3/2)

Step-by-step explanation:

The equation can be put in the form ...

  x^2 = 4py

where p = 3/2.

In this form, the focus is distance "p" from the vertex in the direction the parabola opens.

The vertex is at (0, 0); the parabola opens upward. So, the focus is 3/2 units above the vertex, at ...

  focus = (0, 3/2) . . . . . matches choice A

Answer:

A, D and B must be in a straight line.

Step-by-step explanation:

If D is between A and B, than AD+DB=AB

This would mean A, D and B would be in a straight line.

Answer:

A. Schaid draws a white sock and a green sock. It did not talk about no green sock

Step-by-step explanation:

Answer:

The area of the triangle is 18.70 sq.units.

Step-by-step explanation:

It is provided that a triangle is bounded by the y-axis, the line [tex]f(x)=y=9-\frac{2}{3}x[/tex].

The slope of the line is: [tex]m_{1}=-\frac{2}{3}[/tex]

A perpendicular line passes through the origin to the line f (x).

The slope of this perpendicular line is:[tex]m_{2}=-\frac{1}{m_{1}}=\frac{3}{2}[/tex]

The equation of perpendicular line passing through origin is:

[tex]y=\frac{3}{2}x[/tex]

Compute the intersecting point between the lines as follows:

[tex]y=9-\frac{2}{3}x\\\\\frac{3}{2}x=9-\frac{2}{3}x\\\\\frac{3}{2}x+\frac{2}{3}x=9\\\\\frac{13}{6}x=9\\\\x=\frac{54}{13}[/tex]

The value of y is:

[tex]y=\frac{3}{2}x=\frac{3}{2}\times\frac{54}{13}=\frac{81}{13}[/tex]

The intersecting point is [tex](\frac{54}{13},\ \frac{81}{13})[/tex].

The y-intercept of the line f (x) is, 9, i.e. the point is (0, 9).

So, the triangle is  bounded by the points:

(0, 0), (0, 9) and [tex](\frac{54}{13},\ \frac{81}{13})[/tex]

Consider the diagram attached.

Compute the area of the triangle as follows:

[tex]\text{Area}=\frac{1}{2}\times 9\times \frac{54}{13}=18.69231\approx 18.70[/tex]

Thus, the area of the triangle is 18.70 sq.units.

Answer:

2.964

Step-by-step explanation:

Answer:

A. 20.5

Step-by-step explanation:

We can use the Pythagorean theorem to solve this equation for the missing side length, X.

a^2 + b^2 = c^2

We have a and b, we just need c, the hypotenuse.

14^2 + 15^2 = c^2

196 + 225 = c^2

421 = c^2

Now, we will square both sides:

The answer is about 20.5

Answer:

9.9

Step-by-step explanation:

remember your distribution rules.

x/3.3=3 make sure x is by itself. so take 3*3.3

When you have x divided by a number equaling a number take the number it equals to and multiply by the number that x is being divided by.

3=x/3.3

move 3.3 by multiplying it by 3 which gives you 9.9.

The solution of x in equation 3 = x / 3.3 is,

⇒ x = 9.9

We have to given that;

Expression is,

⇒3 = x / 3.3

Now, We can simplify the equation for x as;

⇒ 3 = x / 3.3

Multiply by 3.3 both side,

⇒ 3 × 3.3 = x

⇒ 9.9 = x

⇒ x = 9.9

Thus, Solution is,

⇒ x = 9.9

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Answer:

Step-by-step explanation:

a) The %tax comes from the "Rate" column on the line "up to $9525". It is 10%.

__

b) Simply compute the difference shown:

  $38,700 -$9,525 = $29,175

__

c) 22% of $9,300 is ...

  0.22 × $9,300 = $2,046

__

d) The total from the three previous calculations is ...

  $952.50 +3,501.00 +2,046.00 = $6,499.50

Answer:

10%

$29,175

$2,046

$6,499.50

got it right on ttm.  

Step-by-step explanation:

just believe me it works

Answer:

C.

Step-by-step explanation:

Diameter = 11 inches.

Radius = D/2 = 5.5 inches

Volume = 4/3πr³

= 4/3(3.14)(5.5)³

= 696.6 in.³

Answer:

work is shown and pictured

The factor of the equation x² - 9x + 14 is,

⇒ (x - 2)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ x² - 9x + 14

Now, We can find the factor of the expression as;

⇒ x² - 9x + 14

⇒ x² - 7x - 2x + 14

⇒ x (x - 7) - 2 (x - 7)

⇒ (x - 7) (x - 2)

Thus, The factor of the equation x² - 9x + 14 is,

⇒ (x - 2)

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