I Need Help

#1
All,

I am struggling with Statistics in all areas. I'm great with numbers, however, I'm lost with this. Can someone help? Here are the following questions on estimates and samples,confidence intervals and critical value:

1.
The confidence interval: 5.06 < sigma2 < 23.33 is for the population variance based on the following sample statistics:

n = 25, x-bar = 41.2, and s = 3.1

What is the degree of confidence? Use only integers, no % sign and no decimal places.

2. Find the margin of error. 95% confidence interval; n = 91 ; x-bar = 55,
s = 5.4

Round to the nearest two decimal places.

3. Find the critical value Chi squared R corresponding to a sample size of 3 and a confidence level of 95 percent.

Round to the nearest three decimal places.

4. Find the appropriate minimum sample size: You want to be 95% confident that the sample variance is within 40% of the population variance. Remember, sample size must be an integer.


Thanks,
 
#2
Hi,

Let's work with one problem at a time. For #1, how far did you get? Please show some work we'll be glad to help with specific questions.
 
#3
Quark,

Actually, I haven't gotten anywhere. I understand what confidence level is (1-a((lower case Greek alpha)) and the most common is 95%. However, all of the other stuff looks foreign. I've been lost since the beginning of the course (5 weeks). The only part I did pretty well was on Standard Deviation and that was week one. By week 2, I was lost. Especially with probabilities. I beleive I get a pretty good handle things at first and have been good with numbers, but for some reason, when I try and put the formulas to use, the numbers aren't correct. I think some times I use the wrong formula and other times, I feel like I've missed something from the prior week.

Anyway, on question 1, I'm sot sure what formula to use. According to question 1, 5.06<Sigma^2<23.33 and n=25, x-bar=41.2 s=31. So,

5.06<3.1^2<23.33 - right? I don't know what x-bar is. And where does n fit in? Please help, I feel so lost.
 
#4
1NAMILL,

x-bar is the sample mean, it,s redundant information for this problem. Since the CI for sigma^2 is given, and (n-1)sd^2/sigma^2 is distributed as chi square with (n-1) degrees of freedom. You can calculate the chi-square values from the confidence limits


3.1^2/chisq = 23.33

and you can find the corresponding confidence level from the chi square table with df=n-1=24
 
#5
ok. So, my question is. How do I find the confidence level with the information given. Is there a formula for this? What am I missing?
 
#6
You can find the chi square value from the table, and locate the corresponding column heading. If it's chis-quared(0.975), then your confidence level is 95%. chis-quared(0.975) indicates that the probability in each tail is 1-0.975=0.025, thus you have a 95% CI.
 
#7
Quark,

I understand.However, is the CI the same as the degree of confidence. For example, question 1's CI is 95% - so is that the same as the degree of confidence. Just wanted to know.