# Hypothesis testing ad confidance intervals

• June 14th 2008, 11:09 PM
kate204
Ok so im a little stressed out I have an exam on thurs and no idea about this stuff. This was the example on the practice examination! HELP

scientists believe that 40% of industries are heavy polluters. They found that 30 out of 80 are heavy polluters.

ok so here is what i need help with,
What is the variable?
what hypothesis test do i need to do??
and if i have a 95% confidance interval, (standard error of 0.05), what sample size do i need??

Im Lost!
• June 14th 2008, 11:45 PM
CaptainBlack
Quote:

Originally Posted by kate204
Ok so im a little stressed out I have an exam on thurs and no idea about this stuff. This was the example on the practice examination! HELP

scientists believe that 40% of industries are heavy polluters. They found that 30 out of 80 are heavy polluters.

ok so here is what i need help with,
What is the variable?

the proportion of industries that are heavy polluters, call it $p$

Quote:

what hypothesis test do i need to do??
Your null hypothesis is that $p=0.4$, under this hypothesis the expected number of heavy polluters in a sample of $80$ is $p\times 80=32$.

Quote:

and if i have a 95% confidance interval, (standard error of 0.05), what sample size do I need
The sample size is not your problem you are given a sample of size $80$, also you appear to be confusing hypothesis testing with construction of a confidence interval. With a confidence interval we construct an interval from the experimental results that will contain the true value the proscribed proportion of the time, with a hypothesis test we assume the null hypothesis and compute the probability that we would get a result at least as extreme as that observed by chance given that the null hypothesis is true, and accept or reject the null hypothesis on the basis of this probability.

RonL
• June 15th 2008, 04:55 AM
kate204
Back again, so this is the exact question,
a) perform an appropriate hypothesis test ie, p=0.4
b) If i want to be 95% confident that the error of estimate to be within 0.05 of the true proportion of heavy polluters, what sample size is required?

I have so far go up too

Ho: (p)=0.04
and my expected value =32.
the sd of approx 4.381
But... i have no idea why i need to find the sd or what the equation below is in relation to?
http://www.mathhelpforum.com/math-he...31aa5b74-1.gif
Im an arts major so this is NOT my area of expertise! Can you please explain the process not just the equation?
• June 15th 2008, 07:19 AM
CaptainBlack
Quote:

Originally Posted by kate204
Back again, so this is the exact question,
a) perform an appropriate hypothesis test ie, p=0.4
b) If i want to be 95% confident that the error of estimate to be within 0.05 of the true proportion of heavy polluters, what sample size is required?

I have so far go up too

Ho: (p)=0.04
and my expected value =32.
the sd of approx 4.381

Part (a) is a hypothesis test (using the sample data given in the question), that is you compute an appropriate test statistics and compute its p-value under the null hypothesis and if this is small enough (less than 0.05 is usual) you reject the null hypothesis. If we are using a normal approximation to the binomial here the test stastistic will be the z-score.

Part (b) you want to take a sample of size N so that a 95% confidence interval for the proportion polluting is of length 0.1 (though this looks circular to me as you are going to have to use the assumption that the true proportion is 0.4 in order to estimate the standard error of the sample mean).

RonL