Stat problem: Some guidance needed

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danny89

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4. A survey at SRA of 125 workers showed that 75 of them belonged to a union. A similar survey taken at Columbia Nitrogen showed that of 100 workers questioned 38 were union members. Develop a 95% confidence interval for the true difference between the proportions of union members.


Do I break these down into the fractions? I know I take various fraction samples but this seems really confusing.
 
Heya, Danny.

Look up "confidence interval for the difference of two proportions".

The two populations are SRA workers and Columbia Nitrogen workers.

The proportion of SRA workers belonging to a union is 75/125, for example.

Apply the formula.
 
Okay thanks, heres what I have so far. P is 75/125 belong to union 50/125 do not; and 38/100 belong to Cn and 62/100 do not. Ok then I know the size of sample one is n=125 and 2 is n=100. Now all I need is the Z number this is my problem area. So I take the difference of the two means 75/100-38-100=.37 my z value At 99% confidence. I see .3 on the z table and .4 but I dont know which row to look in this is where I always get stuck.
 
Check that you compute the correct difference of proportions: that should be mu1 = 75/125 (not 75/100 but you had it correct earlier in the post).

The question asks for a 95% confidence interval. But if it was 99%:

0.99/2 = 0.4950.

Scan the inside of the standard normal distribution tables and you can see 0.4949, which is as close to 0.4950 we can initially get, corresponds to a Z-score of 2.57. We need to add 0.001 to this to get 0.4950, so look under the Differences column for 1. There are a few options; my Statistics teacher once said it was best to go with the "middle" one which corresponds to 6 at the top, and we have 2.576. That's what I've always used but I've seen 2.574 used. Not something to be concerned about, really.

I'm sorry that I can't help you with your other questions.
 
Its okay, so I'm assuming if it was at a 95 CI that it would be .475 that I look up , then I think when I do my difference of mean which is .37 I dont know what I do next although I do know that I need this diff. to find the Z value or look it up.

I think - this shouldnt be so confusing but my professor never really showed me the "correct" way.
 
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