Question

Describe in detail how you would construct a 95% confidence interval for a set of 30 data points whose mean is 20 and population standard deviation is 3. Be sure to show that you know the formula and how to plug into it.
Also, clearly state the margin of error.

Answer 1

@perl

Answer 2

i don't think were making one i think we are just describing how to make it since we aren't given 30 points to use

Answer 3

@perl

Answer 4

$$
\Large Confidence~ Interval = Point~ estimate \pm Margin~of~Error

$$

Answer 5

for margin of error i got 5.88

Answer 6

wait what?

Answer 7

how did you get 5.88 for margin of error

Answer 8

critical value times standard deviation

Answer 9

oh okay what is the formula

Answer 10

one moment, checking

Answer 11

ok

Answer 12

$$

\Large{
\text{confidence interval for sample mean is: } \\
\bar x \pm z^* \frac{\sigma }{\sqrt n}

\\~\\
\text{confidence interval for sample proportion is: } \\
\hat p \pm z^* \sqrt{\frac{\hat p (1 - \hat p ) }{ n} }




}
$$

Answer 13

we're trying to find confidence mean?

Answer 14

would we look for the confidence proportion since we don't have any knowledge as to what the population size is?

Answer 15

it depends on the problem, what you are sampling.
if you are sampling yes/no to a political survey , then you would want proportion. if you are sampling say mean height of freshman college students, you would use sample mean.

Answer 16

the problem doesn't say :/

Answer 17

i think this problem from the context you can tell they want a confidence interval for the sample mean

Answer 18

since it says 'the mean is 20' , they mean the sample mean is 20

Answer 19

okay, so how do we find that without population

Answer 20

if they wanted proportion it would be different , it would say the sample proportion is say 60%

Answer 21

how do we calculate this? I'm confused

Answer 22

$$

\Large{
\text{confidence interval for sample mean is: } \\
\bar x \pm z^* \frac{\sigma }{\sqrt n}

\\\therefore\\

20 \pm 1.96 \cdot \frac{3 }{\sqrt {30}}



}
$$

Answer 23

oh we would use 30 for the population??

Answer 24

\(\large \sigma \) is the population standard deviation.
n is the size of your sample

Answer 25

20 +/- 1.073536

Answer 26

\( \large \bar x \) is the sample mean (of the 30 data points)

Answer 27

yes thats correct :)

Answer 28

okay thank you so much!! i was so stuck

Answer 29

you're the best

Answer 30

wait sorry @perl is my margin of error of 5.88 or no?