There's no way I can figure it out! Please see attachment below..thanks.

2. Thats actually a fun problem.
I assume that the population varainces are unknow and you need to pool.
You have to figure out the chi-squares and obtain a t distribution.
I will be back tonight if you need help.
IF we assume we know the pop variances then it's a normal distribution.

$3\bar X-2\bar Y$

But I do need to know if the pop variances are known, I assume not.

3. It is def a normal distribution. But we never did anything like this in class that I have no idea how to start.

4. I know that, but I see a few problems.
In part two do you really want a CI for $\mu_1-\mu_2$
or $3\mu_1-2\mu_2$?
THEN, I think your instructor messed up with the relationship between the pop variances.
It works either way, but the algebra is nicer if we switch the 2 and the 3.

$3\bar X-2\bar Y$ is unbiased for $3\mu_1-2\mu_2$

and it's variance is $9\sigma^2_1+4\sigma^2_2$

It's normal hence

${(3\bar X-2\bar Y)-(3\mu_1-2\mu_2)\over \sqrt{9\sigma^2_1+4\sigma^2_2}}\sim N(0,1)$

Next use the relationship between the sigma's
BUT I keep asking, are they known?
If they are this is the test stat and you use a st normal table putting half of alpha in each table.

MORE likely the sigma's are unknown and you use the relationship and derive a t stat.
Here you need to pool the sample variances and obtain the chi-square distribution which replaces the $\sigma^2$s

5. Originally Posted by matheagle
I know that, but I see a few problems.
In part two do you really want a CI for $\mu_1-\mu_2$
or $3\mu_1-2\mu_2$?
THEN, I think your instructor messed up with the relationship between the pop variances.
It works either way, but the algebra is nicer if we switch the 2 and the 3.

$3\bar X-2\bar Y$ is unbiased for $3\mu_1-2\mu_2$

and it's variance is $9\sigma^2_1+4\sigma^2_2$

It's normal hence

${(3\bar X-2\bar Y)-(3\mu_1-2\mu_2)\over \sqrt{9\sigma^2_1+4\sigma^2_2}}\sim N(0,1)$

Next use the relationship between the sigma's
BUT I keep asking, are they known?
If they are this is the test stat and you use a st normal table putting half of alpha in each table.

MORE likely the sigma's are unknown and you use the relationship and derive a t stat.
Here you need to pool the sample variances and obtain the chi-square distribution which replaces the $\sigma^2$s
The variables are not known...I asked the professor. Only hint given. Now what do you do though...I'm completely stuck

6. Replace one variance with the other using the relationship
Next obtain a Chi-square distribution.
Then obtain a t density.

And I asked last week, is there a typo in part 2?
WHAT exactly do you want the CI for?