Question

a tad confused

Answer 1

http://prntscr.com/b1vslo this part is the most confusing

Answer 2

@inkyvoyd

Answer 3

She knows based on her current data that 30% like Rocky Road

However, this is NOT a perfect representation of the entire population. That 30% only represents her previous customers. It doesn't include other people who are potential future customers. Which is why there's a margin of error.

She's 95% confident that the true proportion of those who like Rocky Road is somewhere between 17.26% and 42.74%

To find those last two percentages listed, you would subtract and add the margin of error to the center

30% - 12.74% = 17.26% which is the lower end of the confidence interval
30% + 12.74% = 42.74% which is the upper end of the confidence interval

Answer 4

So if she were to sample everyone in the population, and get the true proportion p, then p would probably be between 17.26% and 42.74%

If she made 100 confidence intervals, then 95 of them would have p between 17.26% and 42.74%

Answer 5

>> She's 95% confident that the true proportion of those who like Rocky Road is somewhere between 17.26% and 42.74%

how do you get these percents?

Answer 6

30% is the center. It's the sample proportion

to get the lower bound, subtract the margin of error from this center

30% - 12.74% = 17.26%

Answer 7

0.1274 = 12.74% is the margin of error

Answer 8

between 30 ± 12.74 or between 17.26% and 42.74%.

Answer 9

what made them get these percents

Answer 10

the way they wrote `30 ± 12.74` is a bit odd

they meant 30% plus/minus 12.74%

Answer 11

do you see how 30% was found?

Answer 12

30% represents rocky road

Answer 13

from 15/50 = 0.30

15 like rocky road
50 total in the sample

Answer 14

yes

Answer 15

do you see how they got `12.74%` ?

Answer 16

plugging in 50 from the sample space and proportion in the sample into the formula

Answer 17

sample proportion = 0.30
margin of error = 0.1274

lower bound of confidence interval = (sample proportion) - (margin of error)
lower bound of confidence interval = (0.30) - (0.1274)
lower bound of confidence interval = 0.1726
lower bound of confidence interval = 17.26%

Answer 18

make sense?

Answer 19

i believe so. how did they get 42.74% by adding the two? oh okay. much better.

Answer 20

yep

sample proportion = 0.30
margin of error = 0.1274

upper bound of confidence interval = (sample proportion) + (margin of error)
upper bound of confidence interval = (0.30) + (0.1274)
upper bound of confidence interval = 0.4274
upper bound of confidence interval = 42.74%

Answer 21

wow. thanks for clearing that up. this will be less painful now.

Answer 22

no problem