Mathematics, 07.05.2020 14:58 operrt

Using the traditional formula, a 95% CI for p1 − p2 is to be constructed based on equal sample sizes from the two populations. For what value n (= m) will the resulting interval have width at most 0.4 irrespective of the results of the sampling? (Round your answer up to the nearest whole number.)

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Answer from: sanic123

The minimum sample size required is 49.

Step-by-step explanation:

The (1 - α)% confidence interval for the difference between two proportions is:

$CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\ \sqrt{\frac{\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})}{n}}$

*The sample size is considered equal in this case.

The width of the interval is at most 0.40.

Then the margin of error of the interval will be:

MOE = Width ÷ 2 = 0.20

The formula of the margin of error is:

$MOE= z_{\alpha/2}\ \sqrt{\frac{\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})}{n}}$

Assume that the two sample proportion values are 0.50.

The critical value of z for 95% confidence level is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

Compute the sample size required as follows:

$MOE= z_{\alpha/2}\ \sqrt{\frac{\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})}{n}}$

$n=[\frac{z_{\alpha/2}\times \sqrt{\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})}}{MOE}]^{2}$

$=[\frac{1.96\times \sqrt{0.50(1-0.50)+0.50(1-0.50)}}{0.20}]^{2}\\\\=48.02\\\\\approx 49$

Thus, the minimum sample size required is 49.

Answer from: Quest

answer: 20

step-by-step explanation:

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

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Using the traditional formula, a 95% CI for p1 − p2 is to be constructed based on equal sample sizes...

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