Question

5. Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct the 95% confidence interval for the true proportion of all voters in the state who favor approval.

0.438 < p < 0.505
0.444 < p < 0.500
0.471 < p < 0.472
0.435 < p < 0.508

Answer 1

here a 95% confidence level corresponds to a 1.96*sigma, where sigma is the standard deviation

Answer 2

\[ C.I=p\pm z\cdot \sqrt{\frac{p(1-p)}{n}}\]

Answer 3

Ok, guys I"m not sure how to use that to get the answer?

Answer 4

The sample proportion \(p\) is the proportion of voters in favour. Do you think you can find this?

Answer 5

honestly no.. but I can try.. ok whats C

Answer 6

oh C.I. i just wrote to mean "confidence interval", which is the formula for the confidence interval for a proportion

Answer 7

(Hmm maybe you saw the \(p\) written as \(\hat{p}\)). The formula still works the same, although technically \(\hat{p}\) means the calculated proportion (found in your data), and \(p\) is the true population proportion

Answer 8

I got sigma = 0.5 @kirbykirby

Answer 9

Almost. I see where you get that number, but don't forget the divided by "n" in the formula, where \(n\) is the sample size (how many voters there are in total).

Answer 10

ok!

Answer 11

this stuff is hard for me

Answer 12

the mean value is:
408/865 = 0.472

Answer 13

did you manage to find your proportion \(p\)? Basically it is:
\[ \frac{number ~of~people~in~favour}{total~number~of~people}\]

Answer 14

im working on it

Answer 15

well hes saying he got 0.471 < 0 < 0.472

Answer 16

or would it be 0.43

Answer 17

because I got n divided to get 0.471 ... is that right

Answer 18

I'm not sure I understand what you mean :S But \(p=\dfrac{408}{865}=0.472\) as @Michele_Laino mentioned . That it just the value of p.

Then, z=1.96 (the z-value for a 95% confidence interval when using the normal distribution)

Answer 19

oh see I didnt realize that srry

Answer 20

so tell me what I need to be trying to figure out?

Answer 21

\[C.I=p\pm z\cdot \sqrt{\frac{p(1-p)}{n}}\]
You have p, you have z, and \(n=865\). You have all the ingredients to use the formula

Answer 22

ok give me one sec dont leave.. so u can tel me if im right ok

Answer 23

p=?
z=?

Answer 24

what is p ans z

Answer 25

ok so is it C or not?

Answer 26

I got C

Answer 27

\[C.I=\frac{408}{865}\pm 1.96\cdot \sqrt{\frac{\frac{408}{865}(1-\frac{408}{865})}{865}}\]

Answer 28

ok give me a sec to solve that

Answer 29

ok

Answer 30

how do i type that =- sign

Answer 31

+-

Answer 32

oh that means you need to do 2 operations. First you do + then do -. But it is really saying you have 2 equations to type

Answer 33

first one i got 0.472

Answer 34

\[\frac{408}{865}+ 1.96\cdot \sqrt{\frac{\frac{408}{865}(1-\frac{408}{865})}{865}}\]
\[\frac{408}{865}- 1.96\cdot \sqrt{\frac{\frac{408}{865}(1-\frac{408}{865})}{865}}\]

Answer 35

second one i got 0.47054517

Answer 36

so the answer is C

Answer 37

hm I don't get that :s

Answer 38

how dont u??????????????

Answer 39

round it to 0.471

Answer 40

oh I think I know why you get that. The 865 has to be in the square root sign

Answer 41

If you have trouble typing it on the calculator you could try doing this: (which is the same)

Answer 42

i got 0.438 and i dont use a cal

Answer 43

yeah I get 0.438 too

Answer 44

then i got 0.505

Answer 45

yeah :)

Answer 46

awesome