I was unable to attend the review lectures and now I'm working through the tests and I'm stuck on the very first step.

On the Stats 2B03 Sample Test for Sections 9.2-9.5, 9.7, 10.2-10.4, 11.2, 13.4, 13.6
Could someone just help me get started with the first question... how I'm supposed to fill in the unknowns? I know how to take it from there but that's just got me stumped :$

Thank you
and good luck studying all!

hey!

For Q.1

You are looking for the confidence interval.
This is the equation:


X= 17.6
95% CI
x bar = 17.03
y hat = 10.7 + 4.06 (17.6)
sxx = sum of xi2 –nxbar2
H0: B1 = 0 y = B0 + B1x
T = B hat / s/√ sxx = 6.46

where sxx is missing

6.46 = 4.06 / √ 12 / √ sxx
0.6284 = 3.46 / √ sxx
sxx = 30.308

Now that you have sxx you can put into the missing numbers to find the CI

y+/- t8, 0.0975 3.46 √1+ 1/10 + (17.6 -17.03)2 /30.308

y+/- 8.4087

plug in 17.6 into the equation as the x value to find y

y =10.7 + 4.06 x
y= 10.7 + 4.06(17.6)
y= 82.156

CI:

82.156 + 8.4087
= 90. 56

82.156 – 8.4087
= 73.74

The answers are close enough to the exact ones. There might have been some rounding errors
I hope this helps

do you want to teach me the last part of the class while you're at it? lol

and am i the only one who keeps getting confused with probability?

Originally Posted by Sm:)e

T = B hat / s/√ sxx = 6.46

where sxx is missing

6.46 = 4.06 / √ 12 / √ sxx
0.6284 = 3.46 / √ sxx
sxx = 30.308

Sorry, can I ask you a question about this? You'd be my hero, haha!

From the Minitab output, it says s = 3.46409, so wouldn't we sub that in to the equation? When I do that, I get Sxx = 2.35, which is way off from what you have.

I know 12 is the MSE, so is there some relationship between MSE and s that I'm missing? Why do we use root 12 over 3.46409?

Originally Posted by _Mike

Sorry, can I ask you a question about this? You'd be my hero, haha!

From the Minitab output, it says s = 3.46409, so wouldn't we sub that in to the equation? When I do that, I get Sxx = 2.35, which is way off from what you have.

I know 12 is the MSE, so is there some relationship between MSE and s that I'm missing? Why do we use root 12 over 3.46409?

s (=3.46409) is the square root of 12. I assume it's 0.00001 off as a result of some rounding error somewhere.

Edit: for further clarification, use the relationship MSE = SSE/(n-2) to get SSE = 96. From the definition of s, you see that s = sqrt (MSE), which we already established to be 12.

If your Sxx is 2.35, you're doing something else wrong; the problem isn't with s.

I rearranged the equation to be:

sqrt(Sxx) = (s)(t8)/(B1)
= (3.4641)(6.46)/(4.06)
= 5.5118

And Sxx is just the square of that. You're use the MSE and SSE and stuff later on though.

Originally Posted by Entropy

s (=3.46409) is the square root of 12. I assume it's 0.00001 off as a result of some rounding error somewhere.

If your Sxx is 2.35, you're doing something else wrong; the problem isn't with s.

I rearranged the equation to be:

sqrt(Sxx) = (s)(t8)/(B1)
= (3.4641)(6.46)/(4.06)
= 5.5118

And Sxx is just the square of that. You're use the MSE and SSE and stuff later on though.

Whoops! I took the root of 5.5118 instead of squaring it! Thank you.

How do you find the F-Value in the same table?