Use the given data to find the minimum sample size required to estimate the population proportion. margin of error: 0.045; confidence level: 96%; and unknown

The formula to find the minimum sample size while testing population proportion is

n =

Where p is sample proportion. If there is no information about sample proportion then we take it as 0.5

ME = Margin of error = 0.045

z (α/2) = Critical z score value

This is z score such that P(Z < - z (α/2)) = α/2 and P(Z > z (α/2)) = α/2

α = 1 -confidence level = 1- (96/100) = 0.04

α/2 = 0.04/2 = 0.02

So we have to find z score such that

P(Z < -z (α/2)) = 0.02 and P(Z > z (α/2)) = 0.02

Using z score table to find probability exactly or close to 0.02

Probability value 0.0202 is closest probability value and the corresponding z score is -2.05

It means P(Z < -2.05) =0.02 and P(Z > 2.05) = 0.02

So we have z (α/2) = 2.05

Using all the given values into formula to find sample size

n = 0.5 * (1-0.5) (2.05/0.045)^2

= 0.25 * (45.5556)^2

= 0.25 * 2075.313

n = 518.82

Round the sample size to nearest integer we get

n =519

The minimum sample size is 519

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

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step-by-step explanation:

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