Which of the following SRS designs will give the most precision (smallest standard error) for estimating a population mean? Assume that each population has the same value of the population variance S^2?

1) An SRS of size 400 from a population of size 4000
2) An SRS of size 30 from a population of size 300
3) An SRS of size 3000 from a population of size 300,000,000

Design 3: An SRS of size 3000 from a population of size 300,000,000

Step-by-step explanation:

To check the SRS designs will give the most precision (smallest standard error) for estimating a population mean, we'll make use of the following formula:

V(y) = S²/n( 1 - n/N)

Where S² is a constant for the three SRS designs

Check the first design

n = 400

N = 4000

So, V(y) = S²/400 (1 - 400/4000)

V(y) = S²/400(1 - 0.1)

V(y) = 0.0025S²(0.9)

V(y) = 0.00225S²

V(y) = 2.25S²E-3

The second design

n = 30

N = 300

So, V(y) = S²/30 (1 - 30/300)

V(y) = S²/30(1 - 0.1)

V(y) = S²/30(0.9)

V(y) = 0.03S²

V(y) = 3S²E-2

The third design

n = 3,000

N = 300,000,000

So, V(y) = S²/3,000 (1 - 3,000/300,000,000)

V(y) = S²/3,000(1 - 0.00001)

V(y) = S²/3,000(0.99999)

V(y) = 0.00033333

V(y) = 3.33S²E-4

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

answer: 12

step-by-step explanation:

because yes