Question

STATS HELP?! :(

Answer 1

The circumference of a particular species of tree was thought to be different depending on certain geographical factors. An SRS of 60 trees is selected in Sequoyah National Forest, where it is found that = 6 meters with a standard deviation = 3 meters. A second SRS of size 40 is independently selected in Yellowstone National Forest, and it is found that = 4 meters with a standard deviation = 2 meters. Let μ1 and μ2 represent, respectively, the true mean circumferences of this particular species of tree. Assume the two-sample t procedures are safe to use.


A 95% confidence interval for μ1 – μ2 is
A. 2 ± 0.50 m.
B. 2 ± 0.84 m.
C. 2 ± 0.99 m.
D. 2 ± 1.34 m.

Answer 2

You know the difference of means is 2, so it's really a matter of finding the margin of error.
Margin of error, ME=t*SE ; SE = standard error. You choose t* based on the confidence level. You'll have to determine the degrees of freedom, and here because the 2 sample sizes are different, that can be tricky. Sometimes you can make a simplifying assumption, though..

Answer 3

The standard error is a sample size-corrected estimate of the standard deviation. For a sum or difference of variables, the new standard deviation is always found by \[\sigma_z=\sqrt{\sigma_x^2+\sigma_y^2}\] Think pythagorean theorem.

Answer 4

for standard error, you need to divide the variance by the sample size. i.e. \[SE=\sqrt{\sigma_1^2/n_1+\sigma_2^2/n_2}\]

Answer 5

check out stattrek.com for some good explanations of how to find the critical t-score when you have unequal variances.