please help me about some statistics O/X quiz...

Dear everyone

With all due respect, may I ask a help for some O/X quiz?

1)Suppose two random variables X and Y are negatively correlated. If X is above its mean, then Y is always below its mean.

(I know that when two are negatively correlated, if X gose up, Y goes down. However, I am not sure about the relation with mean)

2)Suppose X is a binomial random variable. Then 1000X is approximately a normal random variable.

(I know when n is bigger, it would be a normal distribution. However, I am not sure about 1000X..)

3)The polling agency should take a larger sample if the population is larger.

(I think that sample would be not affect whether the population is larger.. but not sure)

4)Linear regression framework can be applied to capture the decreasing marginal returns between two variables.

(I think it is O)

I deeply appreciate your help in advance.

Re: please help me about some statistics O/X quiz...

1) If X is at its mean then Y is at its mean. Like you say when X goes up from its mean then Y will go down from its mean.

2) 1000X is not normally distributed. If X's population was {1,0,0,1,0,1} then 1000X's population would be {1000,0,0,1000,0,1000} it still only has two values.

3) We correct for things such as standard error for a finite population with a "finite correction factor" $\displaystyle \sqrt{\frac{N-n}{N-1}}$ (Where N is population size and n is sample size) if N increases then you do need to increase n to maintain the same accuracy.

You can read more about this here http://courses.wcupa.edu/rbove/Beren...section7_3.pdf

4) Decreasing marginal returns tends asymptotically to zero. You cannot use a linear relationship to model that.

Re: please help me about some statistics O/X quiz...

I deeply appreciate your teaching.

May I ask one thing?

As for the question 1, the questions says 'always', so can that be false, because a value of Y can sometimes be above its mean even if a value of X is also above its mean?

Have a great day.

Re: please help me about some statistics O/X quiz...

y will always be below its mean when increasing x. If the slope of the regression line has a slope m which is negative then when x increases by an amount d, y will change by an amount md. Since m is negative md is negative and y decreases.

Re: please help me about some statistics O/X quiz...

Many thanks for your reply.

May I have the last question..?

Because the real regression equation has an error - Y = a + mX + error, could there sometimes be a thing that occurs out of scope?

I do apologise for keeping bothering you.

Re: please help me about some statistics O/X quiz...

If you are measuring X and Y then the error is only due to measurement and a regression line predicting Y for X would have some error. But their actual values without measurement error would fit some line perfectly.

Re: please help me about some statistics O/X quiz...

If X is [2, 3, 4, 5, 6], so E[X] is 4, and Y is [6. 2, 4, 3, 5] so E[Y] is 4, then Cov(X+Y), E[(X-E(X))(Y-(E(Y)], has s negative covariance. However, when X is 6 which is above its mean 4, Y is also 5 which is above its mean 4. Would I understand totally wrong? Deeply appreciate it!