Question

Suppose a sample of 80 with a sample proportion of 0.58 is taken from a population. Which of the following is the approximate 68% confidence interval for that population parameter?

A. (0.525, 0.635)
B. (0.470, 0.690)
C. (0.359, 0.801)
D. (0.414, 0.746)

Answer 1

what is you attempt/process ?

Answer 2

@amistre64 I was going to use the standard deviation formula but I don't think that is the right way to solve this problem. I am not sure?

Answer 3

a confidence interval is similiar to a devition formula: assuming you mean

\[z=\frac{\bar x-\mu}{\sigma}\]
we have some alterations but its mainly solving for x
\[\mu\pm z\sigma=\bar x\]
all your options have different boundary values, so we only need to pick one bound, lets do
\[\mu+ z\sigma=\bar x\]
we need to modify this to suit our needs

Answer 4

u = .58 , the sample proportion

o~ is evaluated as: sqrt(pq/n)

such that p=.58, q=1-p, and n is the sample size

Answer 5

the value of z, is an approximation of 68%, which tells us that its alluding to the empirical rule 1 sd gives us 68% centered about the mean. so z=1 in this case

so lets figure it out

.58 + sqrt(.58(.42)/80) should give us our upper bound

Answer 6

@amistre64 I got .58 + sqrt(.58(.42)/80)=0.635 (which would be A.) but how would you find the lower bond?

Answer 7

instead of +, do -, of course.

Answer 8

middle + A = upper

middle - A = lower

Answer 9

so just put .58 - sqrt(.58(.42)/80)

Answer 10

yep, this gives us the spread about the sample statistic that gives us a range for the population statistic.

Answer 11

I got 0.525 thank you for your help :)

Answer 12

youre welcome