random statistics sample

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May 17th 2008, 09:13 AM
bluejay

random statistics sample

According to Nielson Media Research, 75% of all US households have cable television. Erica conducts a random sample of 1000 households in DuPage County and finds that 800 of them have cable. What might Erica conclude?

I am not sure if there is work that I should be including... it seems like the sample size is not representative of the whole US... maybe 1 county is not a good representation of the whole country. I am really not sure what I am supposed to be doing with this problem. Thanks for any help!
May 17th 2008, 09:59 AM
CaptainBlack

Quote:

Originally Posted by bluejay

According to Nielson Media Research, 75% of all US households have cable television. Erica conducts a random sample of 1000 households in DuPage County and finds that 800 of them have cable. What might Erica conclude?

I am not sure if there is work that I should be including... it seems like the sample size is not representative of the whole US... maybe 1 county is not a good representation of the whole country. I am really not sure what I am supposed to be doing with this problem. Thanks for any help!

Ask the question:"Is cable telivision use in DuPage County typical of that of all US house holds".

Then the null hypothesis is that the cable usage is 75% in DuPage, and your data is that in a sample of size 1000 the observed usage is 800.

RonL
May 21st 2008, 12:36 PM
bluejay

I know I posted this question several days ago, but I am still not sure where to go from here. Since the sample size seems to indicate that 75% have cable television, then we fail to reject the null hypothesis? Is there anything that I can use to support that? Or is there something else that I need to be looking at entirely?
May 21st 2008, 01:46 PM
CaptainBlack

Quote:

Originally Posted by bluejay

I know I posted this question several days ago, but I am still not sure where to go from here. Since the sample size seems to indicate that 75% have cable television, then we fail to reject the null hypothesis? Is there anything that I can use to support that? Or is there something else that I need to be looking at entirely?

800 from 1000 is 80%.

If the null hypothesis were true you would expect 750 with a SD of 13.6. 800-750=50 which is ~3.7 sd's from expectation, normallity is an acceptable approximation so we reject the null hypothesis.

RonL
May 21st 2008, 04:23 PM
bluejay

How do you know that the standard deviation is 13.6 and that a normal standard deviation is 3.7?
May 21st 2008, 07:41 PM
CaptainBlack

Quote:

Originally Posted by bluejay

How do you know that the standard deviation is 13.6 and that a normal standard deviation is 3.7?

Because under the null hypothesis the number of cable customers has a binomial distribution and so the SD is $\sqrt{Np(1-p)}$ , where $N$ is the sample size, and $p$ is the proportion that are cable customers, in this case $N=1000$ , and $p=0.75$ .

RonL