Mathematics, 30.05.2020 22:00 war86

An statistics Instructor is trying to figure out the percentage of students that still listen to Nirvana. The statistics Instructor is pretty out of touch, so he doesn't know what
percentage of students listen to Nirvana. How many students should the statistics instructor sample if he wants to be within 2% of the actual percentage of students who listen to
Nirvana with a 98% confidence level. (Round the z value to 2 decimal places)

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Answer from: vadrian4056

Step-by-step explanation:

Hello!

The variable of study is

X: number of students in the statistics class that listen to Nirvana.

He wants to calculate a sample size to estimate the percentage of students that listen to nirvana with a 98% Confidence level and a margin of error no greater than 2%.

The parameter of interest is the population proportion of the students that still listen to Nirvana.

The formula for the CI of the sample proportion is

p' ± $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'(1-p')}{n} }$

p': represents the sample proportion. Of course since he hasn't taken a sample yet, there is no known value of the sample proportion. Normally there is a pilot sample taken to calculate it or you have to assume the "worst case scenario", when working with a binomial variable, this scenario is that the proportion of "successes" is equal to the proportion of "failures"

So I'll assume worst case scenario and work with a sample proportion of 50%

The Z value is $Z_{1-\alpha /2}= Z_{1-0.02/2}= Z_{0.99}= 2.33$

The margin of error of the interval is

d= $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'(1-p')}{n} }$

Now you clear n:

$\frac{d}{Z_{1-/2}}$ = $\sqrt{\frac{p'(1-p')}{n} }$

$(\frac{d}{Z_{1-/2}})^2$ = $\frac{p'(1-p')}{n}$

$n*(\frac{d}{Z_{1-/2}})^2$ = p'(1-p')

n= $[p'(1-p')]*(\frac{Z_{1-\alpha /2}}{d} )^2$

n= (0.5*0.5)* $(\frac{2.33}{0.02} )^2$

n= 3393.0625= 3394

The professor has to take a sample of 3394 to estimate the percentage of students that still listen to Nirvana with a 98% confidence level and a margin of error within 2%.

I hope this helps!

Answer from: Quest

hdjd

step-by-step explanation:

Answer from: Quest

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

ac ≅ ab (given)< cax ≅ < bax (given)ax ≅ ax (common side)

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

ac ≅ ab (given)< cay ≅ < bay (since < cax ≅ < bax is given and xy is the extension of line ax)ay ≅ ay (common side)

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

Use a paragraph, flow chart, or two-column proof to prove the angle congruency. given: ∠cxy ≅ ∠bxy

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