Was wondering if someone could go over these homework answers with me before I turn this in.

- theopenstudyowl

Was wondering if someone could go over these homework answers with me before I turn this in.

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- theopenstudyowl

Which of the following represents the information you need in order to find the sample size necessary for a confidence interval for a single population proportion with a given margin of error and confidence level?
z*, n,
t*, m, p*
t*, n, p*
z*, m, p*
z*, m, s

- theopenstudyowl

I think it's C

- Michele_Laino

sorry can you write the meaning of z, m, s, t, p?

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## More answers

- theopenstudyowl

sure, one sec...

- theopenstudyowl

Z or z refers to a standardized score, also known as a z score.

- Michele_Laino

ok!

- theopenstudyowl

its ok, I think I known the answe to this one, could I ask another one in the same thread??

- Michele_Laino

ok!

- theopenstudyowl

A company wants to find out what kinds of transportation its employees use to get to work. It conducts a survey of 537 employees, and 243 say they ride the bus. Construct a 95% confidence interval for the proportion of employees who ride the bus to and from work.
(.411, .495)
(.4521, .4539)
(2.168, 2.252)
(.3962, .5098)
(.4316, .4744)
I think it's C

- anonymous

I'm sure it's b

- theopenstudyowl

prove it

- Michele_Laino

we have a probability 243/537 for going with bus, and a probability of 1-(243/537) for not going with bus

- Michele_Laino

oops...1- (243/537)

- Michele_Laino

I think that we have to use the binomial distribution

- Michele_Laino

so the standard deviation is:
\[\Large \sigma = \sqrt {Npq} = \sqrt {537\frac{{243}}{{537}}\left( {1 - \frac{{243}}{{537}}} \right)} = ...\]

- Michele_Laino

whereas the mean is:
\[\Large m = Np = 243\]

- Michele_Laino

then we can write:
\[\begin{gathered}
m = Np = 243 \hfill \\
\hfill \\
\sigma = 11.534 \hfill \\
\end{gathered} \]

- theopenstudyowl

ok

- Michele_Laino

next, a confidence level of 95% mean a distance about 1.96* sigma

- theopenstudyowl

oh ok

- theopenstudyowl

I think my answer is right! Thanks

- Michele_Laino

ok! Thanks!

- theopenstudyowl

is it right?

- theopenstudyowl

did u get the same result?

- Michele_Laino

please I continue then

- theopenstudyowl

ok

- theopenstudyowl

sorry

- Michele_Laino

referring to our sample of population, we have:
mean value= 243/537=0.452
and
1.96*sigma= 1.96*(11.534/537)=0.04
so our interval, is:
0.452-0.04=0.412 left value
0.452+0.04= 0.492 right value, or
\[\Large \left( {0.412,\quad 0.492} \right)\]

- theopenstudyowl

huh, looks like the closest answer is A???

- Michele_Laino

yes!

- theopenstudyowl

wow! thanks! And thnxs for walking me through the steps

- Michele_Laino

thanks! :)

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