# Thread: 4 step method problems help

1. ## 4 step method problems help

I have some questions on some statistics problems I've worked on, if anyone can help who is good at stats it would be very much appreciated!!
"Use a significance test for proportion to see if there is strong evidence that more than 1/3 the population never use condoms.
The sample included 803 heterosexuals who reported having more than one sexual partner in the past year. We cna consider this
srs of size 803 from the population of all heterosexuals in high risk cities who have multiple partners. 304 of the respondents said they never use condoms. Is there strong evicence that more than one-third of this population never used condoms?"
I got the proportion 304/803= .3785
then I go to use the z=p-p0/sqrt(p0(1-p0)/n
However I got stuck because I forgot how to find p0. At first ?I used .005, but that wasn't right.
Can anyone explain how to get p0?
--
"use a two-sample t-test to answer is there a significant difference between the fabrics.
"
A table was given with two columns
{cotton}48.82 48.88 48.98 49.04 48.68 49.34 48.75 49.12
{Ramie}41.72 41.83 42.05 41.44 41.27 42.27 41.12 41.49

I found the proportion of the fabrics x1= 387.61/8=48.45
x2=333.19/8= 41.65
and I used the
t=x1-x2/sqrt(s1^2/n1 + s2^2/n2
plugged the numbers in and got .037628 I looked in the chart and found that P<.50 and concluded that there was strong evidence of a difference between the fabrics.

Another test for significance for comparing two populations to see if the death rate of one group was higher than the other.
"In the year 1936, there were 223 deaths among 33809 African miners and 7 deaths among 1541 European miners. consider this year as a random sample from the colonial era. Is there good evidence that the proportion of African miners who died was higher than the proportion of European miners?"

The populations proportions were 223/33,809=.00659
and 7/1541=.00454
I plugged them into z=p1-p2/sqrt(p(1-p)(1/n1 + 1/n2)
and got .08046 and found that it lies between .674 and .841 and the P<.40 and concluded there was strong evidence that one group(223 one) 's death rate was higher.
Did I do this correctly?

2. 1 the blah blah is VERY important
I need to know the null and alternative hypotheses

2 your babbling in the later parts is blah
THIS is NOT a t test
you are tesing a proportion
the underlying distribution is binomial, not normal
hence you don't have normality to do a t test

3 you will most likely use the central limit theorem to approximate the binomial
and that p0 is P under the null, see 1.
the .005 is alpha

3. EDIT: Sorry that was very stupid of me I've added in the addtional questions and details so it will be a bit more clear.

4. strong evidence that more than 1/3 the population never use condoms

should be H_a, it's what you want to 'prove'

$H_0=1/3" alt="H_0=1/3" /> vs. $H_a>1/3" alt="H_a>1/3" />

Then $p_0=1/3$ is p under the null hypothesis.

The test stat is ${\hat p-p_0\over\sqrt{p_0q_0\over n}}$

where $\hat p={304\over 803}$ and n=803

Use a one-sided z test, with the rejection region on the right tail.