Question

Any ideas for this one??

A simple random sample of voters is taken from the voters in a large country. Researchers construct an approximate 99% confidence interval for the percent of the country’s voters who will vote for Candidate X. The interval goes from 37.3% to 48.7%.

A) In the sample, the percent of voters who will vote for Candidate X is equal to _%.

I found 42.8. but is not correct.

B) An approximate 95% confidence interval for the percent of the state’s voters who will vote for Candidate X goes from _% to _%.

I answered 38.44 and 47.56. Again wrong. Any ideas please?

Answer 1

@social , can I know how did you attempt the question?

Answer 2

Yes of course. 99% means +- 2.58

47.56 - 38.44 = 9.12

Answer 3

9.12 for the interval +- 2.58. In this interval we have 2.5 + 2.5 = 5 => 5x2 = 10

Answer 4

9.12/10 = 0.912, for every 0.5

Answer 5

lets say that 38.44 is on -2.58. The percent of voters who will vote for Candidate X is on 0 right? So to find the value on 0 we have to do 0.912x5= 4.56 => 38.44+4.56 = 43

Answer 6

B) the same way of thinking. The only difference now is that we have the interval -+ 1.96

Answer 7

For A, I would find the center of
37.3% to 48.7%.

i.e. (37.3 + 48.7)/2 = 43.0

the interval from 43 to 48.7 = 5.7 represents 2.58 \( \sigma\) so
5.7/2.58 = 2.21 % per σ

for B, you want 43 ± 1.96 σ = 43 ± 4.3 = 38.7% to 46.3%

Answer 8

@phi Thank you phi!!.

Answer 9

In question B, you wanted to say: from 38.7% to 47.3%. That's the correct answer ;-)

Answer 10

I don't understand what you did in the part A... 2.21% times sigma? Why? What would the solution be? Thanks.

Answer 11

43...

Answer 12

Phi your answers are wrong.. only 38.7 is correct

Answer 13

@asjara are you sure fot the 47.3 ?

Answer 14

Yes, if you take a look to the explanation of @phi, you can see that there was a little but fatal error: 43 ± 4.3 is okey... which means 38.7 and 47.3.

Answer 15

@asjara thank you... an what about the first one? i answered 42.8 but is wrong..

Answer 16

You have to give an integer number!

Answer 17

@asjara ohhh... where does it write to give an integer??? I lost 2 points because I gave 42.8.. The correct answer was 43?

Answer 18

yes, there is a typo ... it never hurts to over a post.

Answer 19

1. confidence interval = mean +- t*sd
It is a symmetrical interval, so answer is 43%, in this case you don't have to input the percent symbol.

2. I don't know why I'm right... (presented in R pseudo-code):
error1 = 5.7% = qnorm(99%) * s / sqrt(n)
error2 = x = qnorm(95%) * s / sqrt(n)
[then] x = 0.057 * qnorm(.975) / qnorm(.995)
upper = mean + x = 47.3%
lower = mean - x = 38.7%

I think a less confident interval of 95% should be wider than 99% interval, but grading system shows the answers were right.
btw: This question is from Stat2.3X of UCB at edX. Notice the honor code dude.