Evaluate 2√((p(1-p))/(n)) for the given values of p and n Round to the nearest thousandth if nec

Evaluate 2√((p(1-p))/(n)) for the given values of p and n...

Key Concepts

Standard Error of a Proportion

This concept refers to the measurement of variability in an estimated proportion. It is calculated using the formula ?(p(1-p)/n), where 'p' represents the sample proportion and 'n' is the sample size. The standard error quantifies how much the sample proportion is expected to fluctuate due to random sampling variability.

Margin of Error

Often used in confidence interval calculations, the margin of error represents the amount added to and subtracted from an estimate to form a range within which the true population parameter is expected to lie. Multiplying the standard error by a factor (such as 2) provides an approximate margin of error for the estimate.

Rounding

Rounding is the process of adjusting a numerical value to a specified degree of precision to simplify the number or conform it to a certain format. In the context of the problem, rounding to the nearest thousandth means expressing the final numerical result with three decimal places based on standard rounding rules.

Transcript

00:01 Okie -dokey.

00:03 So we have been asked to evaluate an expression and it says in this expression that p equals 0 .25.

00:13 Oh come on.

00:14 It doesn't want to write that 5 for some reason.

00:17 There we go.

00:19 And that n equals 500.

00:23 So if i want to evaluate this expression, all i need to do is plug in p where i see p.

00:28 And i'm plugging 0 .25 where i see p and plug in 500 where i see n.

00:34 So the expression itself is 2 square root of p times 1 minus p all over n.

00:43 Well, remember that p is 0 .25, 0 .25, and that n equals 500.

00:54 So all i'm going to do is replace them with what they equal.

00:58 So i get 2 square root of 0 .25, because that's what p equals times 1 minus p, which is, again, 0 .25, and then n equals 500.

01:16 So we're going to replace n in the bottom of 500.

01:23 Now all i have to do is simplify what's in my square root first, because you can think about this as a big old set of parentheses.

01:29 Then i can take my square root, then i can multiply by two.

01:33 So let's simplify in here.

01:35 Well, in here we have to do parentheses first because of order operations.

01:39 Paranthases, exponents, multiplication, division, additions, subtraction, right? pemdas.

01:47 So i am going to take 1 minus 0 .25 and simplify that first.

01:55 So i get 0 .25 times 1 minus 0 .025 .0 .25 is 0 .75 .75...

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