# AP Stats Questions

• May 21st 2008, 01:11 PM
David_is_a_LOSTaway
AP Stats Questions
I don't get how to do these two inter-related problems. I have the answer to the first one, but not the second. The questions are:

1. A random sample of 4 Herefords, each with a frame size of three (on a one-to-seven scale), gave a sample mean weight of 452 kg. The known population standarad deviation is 12 kg. A 95% confidence interval for the average weight of all Herefords of this frame size is (using an "exact" confidence interval):

The answer is (432.9, 471.1), but I was getting (440.2, 463.8). How do you get the right answer?

2. Referring to the previous question, about how many animals should be sampled (in total) in order to be 95% confident of determining the true mean weight WITHIN 2 kg?

The answer is either 138, 139, 140, 550, or 190. Keep in mind if you get a non-whole answer (which you will), you must round up, no matter what.

• May 21st 2008, 02:06 PM
mr fantastic
Quote:

Originally Posted by David_is_a_LOSTaway
I don't get how to do these two inter-related problems. I have the answer to the first one, but not the second. The questions are:

1. A random sample of 4 Herefords, each with a frame size of three (on a one-to-seven scale), gave a sample mean weight of 452 kg. The known population standarad deviation is 12 kg. A 95% confidence interval for the average weight of all Herefords of this frame size is (using an "exact" confidence interval):

The answer is (432.9, 471.1), but I was getting (440.2, 463.8). How do you get the right answer?

2. Referring to the previous question, about how many animals should be sampled (in total) in order to be 95% confident of determining the true mean weight WITHIN 2 kg?

The answer is either 138, 139, 140, 550, or 190. Keep in mind if you get a non-whole answer (which you will), you must round up, no matter what.

• May 21st 2008, 02:09 PM
CaptainBlack
Quote:

Originally Posted by David_is_a_LOSTaway
I don't get how to do these two inter-related problems. I have the answer to the first one, but not the second. The questions are:

1. A random sample of 4 Herefords, each with a frame size of three (on a one-to-seven scale), gave a sample mean weight of 452 kg. The known population standarad deviation is 12 kg. A 95% confidence interval for the average weight of all Herefords of this frame size is (using an "exact" confidence interval):

The answer is (432.9, 471.1), but I was getting (440.2, 463.8). How do you get the right answer?

T-distribution 3 degrees of freedom and standard error of 12/sqrt(4) gives an
interval of +/- 3.18 standard errors about the sample mean.

RonL
• May 22nd 2008, 07:32 PM
David_is_a_LOSTaway
Thanks for all your help, I get it now. I was using the wrong formula, one that didn't apply.

How do I do the second part of the problem?
Quote:

2. Referring to the previous question, about how many animals should be sampled (in total) in order to be 95% confident of determining the true mean weight WITHIN 2 kg?

The answer is either 138, 139, 140, 550, or 190. Keep in mind if you get a non-whole answer (which you will), you must round up, no matter what.
• May 22nd 2008, 07:49 PM
mr fantastic
Quote:

Originally Posted by David_is_a_LOSTaway
Thanks for all your help, I get it now. I was using the wrong formula, one that didn't apply.

How do I do the second part of the problem?
Quote:
2. Referring to the previous question, about how many animals should be sampled (in total) in order to be 95% confident of determining the true mean weight WITHIN 2 kg?

The answer is either 138, 139, 140, 550, or 190. Keep in mind if you get a non-whole answer (which you will), you must round up, no matter what.

You want the value of n such that the 95% confidence interval is $\displaystyle 452 \pm 2$.

Therefore $\displaystyle 2 = z_{\alpha/2} \frac{\sigma}{\sqrt{n}} = z_{0.025} \frac{12}{\sqrt{n}}$. You look up $\displaystyle z_{0.025}$ in a table of critical values. Substitute. Solve for n.