Solve for the line, Thank you!

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 t

bogdanovich [222]

Answer:

a) $\sigma_{\bar x} = 1.414$

b) $\sigma_{\bar x} = 1.414$

c) $\sigma_{\bar x} = 1.414$

d) $\sigma _{\bar x} = 1.343$

Step-by-step explanation:

Given that:

The random sample is of size 50 i.e the population standard deviation =10

Size of the sample n = 50

a) The population size is infinite;

The standard error is determined as:

$\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}$

$\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}$

$\sigma_{\bar x} = 1.414$

b) When the population size N= 50000

n/N = 50/50000 = 0.001 < 0.05

Thus ; the finite population of the standard error is not applicable in this scenario;

Therefore;

The standard error is determined as:

$\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}$

$\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}$

$\sigma_{\bar x} = 1.414$

c) When the population size N= 5000

n/N = 50/5000 = 0.01 < 0.05

Thus ; the finite population of the standard error is not applicable in this scenario;

Therefore;

The standard error is determined as:

$\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}$

$\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}$

$\sigma_{\bar x} = 1.414$

d) When the population size N= 500

n/N = 50/500 = 0.1 > 0.05

So; the finite population of the standard error is applicable in this scenario;

Therefore;

The standard error is determined as:

$\sigma _{\bar x} = \sqrt{\dfrac{N-n}{N-1} }\dfrac{\sigma}{\sqrt{n} } }$

$\sigma _{\bar x} = \sqrt{\dfrac{500-50}{500-1} }\dfrac{10}{\sqrt{50} } }$

$\sigma _{\bar x} = 1.343$

7 0

3 years ago

What is the equation of this line?

Oduvanchick [21]

Answer:

y=4/3x-3

Step-by-step explanation:

+4x-(-3y)=1-1/3

5 0

3 years ago

PLZ HELP!! NEED QUICKLY!!<br> Given: ∆ABC ≅ ∆DEF. Find DF and m∠B.

Sergeu [11.5K]

Answer:

DF = 3

m<B = 28 degrees

Step-by-step explanation:

Hope that helps!

4 0

3 years ago

Ten tiles numbered 1 through 10 are placed in a bag. You randomly choose one tile. Without replacing the first tile, you randoml

ruslelena [56]

You would have one tenths (1/10) of a chance to get a 4 on the first go. you would have four ninths (4/9) of a chance to get a number less than 5 out of the bag on the second go.

the overall probability would be two forty-fifths (2/45)

7 0

3 years ago

Solve the system of equations using the linear combination method. {9x+5y=35 2x+5y=0 Enter your answers in the boxes.

Vikentia [17]

9x+ 5y=35
2x + 5y=0 |* -1

9x +5y= 35
-2x -5y= 0
-----------------
7x / = 35
x=35:7
x=5

2x+5y=0
2*5+5y=0
10+5y=0
5y=-10
y= -10:5
y=-2

5 0

3 years ago