Given N, p, find S, Mean, compare hpothesis..

• Dec 6th 2007, 01:02 AM
Given N, p, find S, Mean, compare hpothesis..
ok guys..not here to ask you to do my homework, im seriously working my butt off pass this last test

im given a question, where N=1369, 53% of population is in favor.

i have to

A. ID the shape, mean, and standard deviation of the distribution of the sampling statistic, p' (p-hat)

B. COmpute a 95% confidence interval for the population proportion in favor

C. Based on confidence interval, which hypothesis would i beleive?

H0:P=.50 or H1 P!=.50

THus far, if im right, i got .013 for a standard deviation using: σp = sqrt[ P * ( 1 - P ) / n ]

Now how the heck would i find the mean ?

I found the confidence interval ala TI-83+, giving me .5031-.556..and yet now i have no idea do i reject hypothesis 0 or 1?

any help would be greatly appreciated. Thanks in advance!
• Dec 6th 2007, 06:57 AM
colby2152
You have a sample mean of .53 or 725.57 people. This is a binomial distribution, so the variance is np(1-p) or 341.02 people which leads to a standard deviation of 18.47 people.

A 95% confidence interval leads to a range to about two standard deviations away from the mean. The exact amount is 1.96 SD's away, so the range of values to be 95% confident that the population mean is within that range is:

$\displaystyle 725.56 \pm 1.96(18.47) = 725.56 \pm 36.19$
$\displaystyle (689.37, 761.75)$

Our null hypothesis claims a mean of 684.5 (50% of 1369). That hypothesized mean is not within our range, so we must fail to accept the null hypothesis (aka accept the alternate).

BTW. 1369 is 37 squared, and 13 squared is 169
• Dec 6th 2007, 11:16 AM