# variances

1. ### Help with rules of variances

I'm working on a problem where you have a normally distributed population with a mean of 60 and variance of 130. The question is, if you were to take 3 individuals from this population and take their average, what would be the mean value and vari? I know that the average would just be...
2. ### Help with data pooling (Means and variances)

Hey everyone, I've attached a question to this post, I've spent what seems like forever trying to figure it out, anyone have any ideas? Any help would be much appreciated!! (Nod)
3. ### Calculating Variances and Regression Coefficients

This first part I am just looking for confirmation that I am working it correctly: I have 30 observations and sumX=30, sumX2=150, sumY=120, sumY2=1830 and sumXY=480. I found the variance of X to be V[X]= E[X2] - (E[X])2= (150/30) - (12) = 5 - 1 = 4 the variance of X to be V[Y]= E[Y2] - (E[Y])2=...
4. ### Comparing Variances of the Sample Means

Hi, "Suppose that two populations have equal population variances but have different sizes: N_1=100,000, N_2=10,000,000 . Compare the variances of the sample means for a sample of size n=25 . Is it easier to approximate the mean of a smaller population?" Where do I even begin? :(
5. ### ANOVA and different variances

I know that one of the key conditions of performing an ANOVA test is that the variances of the groups has to be broadly similar. I have some data sets that I need to compare and the variance of some of them is very different to the rest. Surely this in itself proves (indicates?) that the samples...
6. ### Comparing Variances Question Help

The McBurger company's management is interested in whether there is a difference in the standard deviation in services times for customers who use the drive-through window versus those who go inside to the service counter. A sample of 13 drive-through customers and a sample of 9 inside-counter...
7. ### Residualized Coefficient Using Solely Variances and Covariances

I just want to confirm that I'm on the right track. I need to derive an expression for b^Y1.2 that refers solely to variances and covariances (that is, only to bi-variate and mono-variate terms). I have come up with the following: b-hatY1.2 = (CovY1)/(Var1) -...
8. ### ANOVA: how can variances tell us if the means are different

in anova (specifically one-way anova), the variance within each group and the variance between groups are calculated, and then their ratio yields the f-statistic, which tells us if the population means are the same or different. question is, how does the ratio of the variances tell us if the...
9. ### Reference for combining correlated estimates with unequal variances

Hello, I am attempting to understand the theory behind combining correlated estimates which have unequal variances. All the estimates are unbiased estimates of one true mean. I've been reading the paper "Almost linearly-optimum combination of unbiased estimates" by Max Halperin. (If my...
10. ### Test of equality of means and variances with correlated samples

Say that I have n samples from a parameter generated from a MCMC-algorithm, the samples are therefore correlated with eachother. I want to test if the sample distribution that i have obtained of this parameter are equal to the true distribution of that parameter. The sample distribution are...
11. ### two-sample test for equality of means assuming unequal variances

a. Comparison of GPA for randomly chosen college juniors and seniors: = 3.05, s1 = .20, n1 = 15, = 3.25, s2 = .30, n2 = 15, α = .025, left-tailed test. b. Comparison of average commute miles for randomly chosen students at two community colleges: = 15, s1 = 5, n1 = 22, = 18, s2 = 7, n2 =...
12. ### Confidence Interval for Variances

I understand that \frac{(n-1)S^2}{\sigma ^2} = \frac{(n-1)\frac{1}{n-1}\sum_{i=1}^{n}(x_i - \bar{x})^2}{\sigma ^2} ~ \chi ^2(n-1) I do not understand why \frac{n\hat{\sigma}^2}{\sigma ^2} = \frac{n\frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2}{\sigma ^2} ~ \chi ^2(n-2)
13. ### Expected values and Variances

Question 1: Let where Xi's be i.i.d. Normal with mean 10 and variance 4 for i=1,2,...,16 and Yj's be i.i.d. Normal with mean 15 and variance 12 for j=1,2,...,10 and Ix & Yj are independent for all i & j. What is the value of E[W] and Var(W)? Question 2: Let Y= where Xi's be i.i.d. Normal...
14. ### Sample size for ratio of variances

Want to find the sample size required for alpha=0.05 and beta =0.05 (power 95%) in testing the equality of two normal population variances, when actually one variance is 25.5 times larger than the other. The right tail of the F distribution is chosen for the rejection region. I believe this...
15. ### How to test if 4 variances are the same?

Hello, I know how to test 2 variances, but how should I go about testing 4? Here's the whole problem: You want to see the effect of drugs on the reaction time. 4 independent samples of 7 people has been tested, one with no drug and the three others with a different drug each. No drug...
16. ### Variances and covariance - needs help!!!

Express var(X+Y), var(X-Y), and cov(X+Y),X-Y) in terms of the variances and covariance of X and Y.
17. ### Testing equality of variances using the F distribution.

I have a question where I have to test the equality of two variances using the F distribution at 5% level of significance. H0 is the variances are equal H1 is the variances are not equal. I woked my p-value out to be 1.19 and I have to use an F29,29 distribution. Do I have to use the 2.5...
18. ### Test for the equality of two variances

Hi, my question is; Which of the following is/are assumptions underlying the test for the equality of two variances? 1) The samples are independent 2) Both populations are normally distributed 3) Both populations have the same mean 4) 1 and 2 5) 1 and 3 6) 1,2 and 3 Thanks!
19. ### Testing two variances is the same as testing two means?

That is false right because you use the f-test for variances and t-test for means...?
20. ### Inference for variances

question 1: past experience indicates that the time required for high school seniors to complete a standardized test is a normal random variable with a standard deviation of 6 minutes. Test the hypothesis that after i calculated the chi-square values σ =6 against the alternative that σ<6 if a...