For election polling, a simple random sample of 850 registered voters in District X shows that 58% favor Candidate A, and a simple random sample of 1400 registered voters in District Y shows that 53% favor Candidate A
If District Y is Group 2, what are the values of tcrit, pˆ2 , and n2 for a 90% confidence interval?

- Daniellelovee

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- schrodinger

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- Daniellelovee

@Directrix

- Directrix

|dw:1450240669064:dw|

- Directrix

^^^^

##### 1 Attachment

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## More answers

- Daniellelovee

.02155.

- Daniellelovee

no wait I got 0.69

- Daniellelovee

@Directrix

- Directrix

What is .58 - .53 =
This would be d.

- Directrix

Use the difference between the sample proportions and the
margin of error to construct the confidence interval
(d− margin of error, d+ margin of error)
Is that this:
(.05 - .69, .05 + .69)
I will double-check the .69 just in case.

- Directrix

Look at this.
I got .035 where you got >>no wait I got 0.69
The Wolf cranked out:
http://www.wolframalpha.com/input/?i=1.64*sqrt%28%28.58%28.42%2F850%29%29+%2B+%28.53%28.47%29%29%2F1400%29%29

##### 1 Attachment

- Directrix

Use the difference between the sample proportions and the margin of error to construct the confidence interval (d− margin of error, d+ margin of error)
Is that this: (.05 - .035, .05 + .035) =
(.015 , .085)

- Daniellelovee

i can give you my options if that helps

- Directrix

tcrit, pˆ2 , and n2 for a 90% confidence interval?
1.64, .53, 1400

- Directrix

Post them and let's see. I do not have an intuitive feel for what is going on with this problem.

- Daniellelovee

(1.5, 8.5)
(0.3, 9.7)
(0.8, 9.2)
(2.8, 7.2)

- Daniellelovee

@Directrix

- Directrix

On my first attempt, I got this;
(.015 , .085)

- Directrix

My decimal points are off.

- Daniellelovee

yeah and the first number seems odd compared to my options

- Directrix

Maybe you can find my error.
I think you made an error on the first calculation of the giant square root.

- Daniellelovee

is possible is that the square got cut off and I couldnt see the number you marked there

- Daniellelovee

can you put the equation again just smaller? @Directrix

- Directrix

Smaller Equation Attached

##### 1 Attachment

- Daniellelovee

oh ok then I got 0.02155 @Directrix

- Directrix

I don't see an error here:
http://www.wolframalpha.com/input/?i=1.64*sqrt%28%28.58%28.42%2F850%29%29+%2B+%28.53%28.47%29%29%2F1400%29%29

- Daniellelovee

then B is the best choice based on that calculator

- Daniellelovee

right?

- Daniellelovee

@Directrix

- Directrix

When you cranked out the square root "thing," did you do the square roots individually and then add? The square root of a sum is not the sum of the square roots.
The Wolf sometimes messes up.

- Daniellelovee

ok im going to check one more time lets see if I get a good answer this time

- Daniellelovee

I got 0.35 this time

- Directrix

Read the text.
This has to be done to get the answer:
margin of error to construct the confidence interval
(d− margin of error, d+ margin of error)
That square root "thing" is the margin of error.

- Daniellelovee

(0.05 - 0.035, 0 .05 + 0.035) =(0.015 , 0.085)

- Daniellelovee

@Directrix

- Directrix

That is not an option.
(.015 , .085) is what I got on the first round.

- Daniellelovee

then idk :(

- Directrix

Look at the problem you posted.
Is the confidence interval supposed to be 95%? You wrote 90%.

- Directrix

From @Teddy_the_Tudor_Brit
Construct a 95% confidence interval for the difference between the percent of all registered voters in District X and District Y who prefer Candidate A.
(0.3, 9.7)
(0.8, 9.2)
(1.5, 8.5)
(2.8, 7.2)
Edit
Answer: ANS:-
For District X,
N = 850
P = 0.58
Mean = np = 850*0.58 = 493
Sd = sqrt(n*p*(1-p)) = sqrt(850*0.58*(1-0.58)) = 14.39
For District Y,
N = 1400
P = 0.53
Mean = np = 1400*0.53 = 742
Sd = sqrt(n*p*(1-p)) = sqrt(1400*0.53*(1-0.53)) = 18.68
So 95% confidence interval for the difference between the percent of all registered voters in District X and District Y who prefer Candidate A is
(742-498) +/- 1.64*sqrt((850*14.39+1140*18.68)/(1140+850))
= (0.8, 9.2)
http://tutorteddy.com/site/free_stat_help1.php/NjM3Nw==/For-election-polling-a-simple-random-sample-of-850-registered-voters-in-District-X-shows-that-58--f

- Directrix

Teddy the Brit Tudor has this option in his list as do you:
(1.5, 8.5)

- Daniellelovee

that name reminded me of the Tudors and can that person prove it?

- Daniellelovee

that A is the correct choice?

- Directrix

Play on the word Tudor to remind us of our fuzzy studies.

- Daniellelovee

lol yeah but I did love the Tudors story and Elizabeth's diary

- Directrix

Teddy the Brit Tudor can't prove anything.
I think there is a step to our calculations that is missing.

- Daniellelovee

so then he/she just guessed?

- Directrix

Did you not see the work?

- Daniellelovee

omg no sorry hold on let me check it

- Daniellelovee

omg i messed up big time those where the option for the next question omg im so terribly sorry

- Daniellelovee

zcrit=1.64, ^p2=53%, n2=742
zcrit=2.58, ^p2=57%, n2=742
zcrit=1.64, ^p2=53%, n2=1400
zcrit=3.58, ^p2=53%, n2=1400

- Daniellelovee

zcrit=1.64, ^p2=53%, n2=742
zcrit=2.58, ^p2=57%, n2=742
zcrit=1.64, ^p2=53%, n2=1400
zcrit=2.58, ^p2=53%, n2=1400
@Directrix

- Directrix

An hour ago, I posted this as the answer to the question as it appeared in the first region:
tcrit, pˆ2 , and n2 for a 90% confidence interval?
1.64, .53, 1400

- Daniellelovee

thank you for your help and again im so sorry for messing up

- Directrix

zcrit=1.64, ^p2=53%, n2=1400
OMG! It's okay.
I think we may have part of the answer to the next question. Not sure.

- Directrix

Now, you can sleep.

- Daniellelovee

lol no I still have more question if you don't mind this lesson was pretty hard

- Directrix

I lost an hour and a half of my life on this problem.
You can post the new problem in a new thread. This thread is jinxed.

- Daniellelovee

lol that actually made me laugh, im sorry, and I was planning on doing a new thread either way

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