# Is 0 Red / 10 White vs 3 Red / 8 White Significantly Different? **URL:** \ **Category:** Factual Questions\ **Created:** [March 2, 2004, 10:37pm UTC](https://boards.straightdope.com/t/is-0-red-10-white-vs-3-red-8-white-significantly-different/232179 "2004-03-02T22:37:38Z")\ **Posts on this page:** 14\ **Page:** 1
**Author:** ![Biere](https://avatars.discourse-cdn.com/v4/letter/b/b9bd4f/32.png) [@Biere](https://boards.straightdope.com/u/Biere)\ **Post date:** [March 2, 2004, 10:37pm UTC](https://boards.straightdope.com/t/is-0-red-10-white-vs-3-red-8-white-significantly-different/232179/1 "2004-03-02T22:37:38Z")
The problem: There are 2 large containers ( A & B ) both filled with white and red marbles. 10 marbles are randomly drawn from container A; 0 red and 10 white. 11 marbles are drawn randomly from container B; 3 red and 8 white. Based on these samples, can it be concluded that the population of red marbles in container B is significantly (p=0.95) different from that in container A? Also, if a “statistic” is utilized in the solution, show that it is valid at these sample sizes. Help, I have already submitted 3 solutions, all rejected … ---
**Author:** ![x-ray\_vision](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/x-ray_vision/32/351_2.png) [@x-ray\_vision](https://boards.straightdope.com/u/x-ray_vision)\ **Post date:** [March 2, 2004, 10:57pm UTC](https://boards.straightdope.com/t/is-0-red-10-white-vs-3-red-8-white-significantly-different/232179/2 "2004-03-02T22:57:17Z")
No definite conclusions can be made. Are you asking us to help you win a contest? ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [March 2, 2004, 11:20pm UTC](https://boards.straightdope.com/t/is-0-red-10-white-vs-3-red-8-white-significantly-different/232179/3 "2004-03-02T23:20:42Z")
Is this homework? ---
**Author:** ![Biere](https://avatars.discourse-cdn.com/v4/letter/b/b9bd4f/32.png) [@Biere](https://boards.straightdope.com/u/Biere)\ **Post date:** [March 2, 2004, 11:47pm UTC](https://boards.straightdope.com/t/is-0-red-10-white-vs-3-red-8-white-significantly-different/232179/4 "2004-03-02T23:47:28Z")
> [@x-ray vision](#): > > Are you asking us to help you win a contest? > [@ultrafilter](#): > > Is this homework? Sorry, couldn’t figure out how to get back here. Both somewhat correct. Probability class extra credit. Is that ok to post? ---
**Author:** ![BaldTaco](https://avatars.discourse-cdn.com/v4/letter/b/47e85d/32.png) [@BaldTaco](https://boards.straightdope.com/u/BaldTaco)\ **Post date:** [March 3, 2004, 12:22am UTC](https://boards.straightdope.com/t/is-0-red-10-white-vs-3-red-8-white-significantly-different/232179/5 "2004-03-03T00:22:43Z")
Univeristy is kind of a haze, but I think you might be missing a variable or two. See if this [calculator](http://www.surveysystem.com/sscalc.htm) works. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [March 3, 2004, 1:12am UTC](https://boards.straightdope.com/t/is-0-red-10-white-vs-3-red-8-white-significantly-different/232179/6 "2004-03-03T01:12:02Z")
> [@Biere](#): > > Sorry, couldn’t figure out how to get back here. Both somewhat correct. Probability class extra credit. Is that ok to post? Not as you’ve posted it. We have a standing policy against doing homework for people. However, if you post what you’ve done so far, and where you’re stuck, you can usually get some hints. ---
**Author:** ![Biere](https://avatars.discourse-cdn.com/v4/letter/b/b9bd4f/32.png) [@Biere](https://boards.straightdope.com/u/Biere)\ **Post date:** [March 3, 2004, 1:56am UTC](https://boards.straightdope.com/t/is-0-red-10-white-vs-3-red-8-white-significantly-different/232179/7 "2004-03-03T01:56:47Z")
Hoping I don’t screw this up too … > [@BaldTaco](#): > > Univeristy is kind of a haze, but I think you might be missing a variable or two. > > See if this [calculator](http://www.surveysystem.com/sscalc.htm) works. Thanks for the link, but as I understand it, to obtain a 0.95/0.95 confidence/significance level, as in the poll calculator you linked me to, the sample size would be set to obtain a 0.95 confidence level at a 0.95 significance. In this problem the sample size is 10 vs 11 … > [@ultrafilter](#): > > Not as you’ve posted it. We have a standing policy against doing homework for people. > > However, if you post what you’ve done so far, and where you’re stuck, you can usually get some hints. This is only for extra credit … ---
**Author:** ![TitoBenito](https://avatars.discourse-cdn.com/v4/letter/t/2acd7d/32.png) [@TitoBenito](https://boards.straightdope.com/u/TitoBenito)\ **Post date:** [March 3, 2004, 2:12am UTC](https://boards.straightdope.com/t/is-0-red-10-white-vs-3-red-8-white-significantly-different/232179/8 "2004-03-03T02:12:45Z")
Been awhile since stat I probibly did it wrong but Test and Confidence Interval for Two Proportions Success = 1 Variable X N Sample p b 3 11 0.272727 a 0 10 0.000000 Estimate for p(b) - p(a): 0.272727 95% CI for p(b) - p(a): (0.00954012, 0.535914) Test for p(b) - p(a) = 0 (vs not = 0): Z = 2.03 P-Value = 0.042 - NOTE \* The normal approximation may be inaccurate for small samples. Divide P by 2 and there is your p score. So yes I think its significant beyond 95% ---
**Author:** ![TitoBenito](https://avatars.discourse-cdn.com/v4/letter/t/2acd7d/32.png) [@TitoBenito](https://boards.straightdope.com/u/TitoBenito)\ **Post date:** [March 3, 2004, 2:13am UTC](https://boards.straightdope.com/t/is-0-red-10-white-vs-3-red-8-white-significantly-different/232179/9 "2004-03-03T02:13:54Z")
On second though don’t divide by two. ---
**Author:** ![Urban\_Ranger](https://avatars.discourse-cdn.com/v4/letter/u/e9c0ed/32.png) [@Urban\_Ranger](https://boards.straightdope.com/u/Urban_Ranger)\ **Post date:** [March 3, 2004, 7:17am UTC](https://boards.straightdope.com/t/is-0-red-10-white-vs-3-red-8-white-significantly-different/232179/10 "2004-03-03T07:17:53Z")
Insufficient information. How many marbles are in the containers? ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [March 3, 2004, 2:58pm UTC](https://boards.straightdope.com/t/is-0-red-10-white-vs-3-red-8-white-significantly-different/232179/11 "2004-03-03T14:58:48Z")
> [@Biere](#): > > This is only for extra credit … Why should that matter? ---
**Author:** ![Munch](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/munch/32/5281_2.png) [@Munch](https://boards.straightdope.com/u/Munch)\ **Post date:** [March 3, 2004, 3:09pm UTC](https://boards.straightdope.com/t/is-0-red-10-white-vs-3-red-8-white-significantly-different/232179/12 "2004-03-03T15:09:50Z")
> [@Urban Ranger](#): > > Insufficient information. How many marbles are in the containers? With the given as “large containers” that are “both filled”, is that necessary? I think you can safely assume an infinite amount for the purposes of the exercise. ---
**Author:** ![Biere](https://avatars.discourse-cdn.com/v4/letter/b/b9bd4f/32.png) [@Biere](https://boards.straightdope.com/u/Biere)\ **Post date:** [March 3, 2004, 7:39pm UTC](https://boards.straightdope.com/t/is-0-red-10-white-vs-3-red-8-white-significantly-different/232179/13 "2004-03-03T19:39:19Z")
> [@TitoBenito](#): > > Estimate for p(b) - p(a): 0.272727 > 95% CI for p(b) - p(a): (0.00954012, 0.535914) > Test for p(b) - p(a) = 0 (vs not = 0): Z = 2.03 P-Value = 0.042 > > - NOTE \* The normal approximation may be inaccurate for small samples. Thanks. One approach, similar to yours, used binomial proportions. p(B) - p(A) = 0.2727 with s = 0.1529 resulted in Z = 1.784, i.e. not significant at p=0.95. This solution was not accepted since I could not prove or find a proof that the statistic follows a normal distribution with this number of samples. Using your result for Z = 2.03 and Student’s-t of 2.093 with n(A) + n(B) - 2 d.f., would also indicate that the sampling results are not significant at p=0.95. However, as you mentioned, need to prove that the statistic follows a normal distribution at 10 vs 11 samples. ---
**Author:** ![muttrox](https://avatars.discourse-cdn.com/v4/letter/m/a8b319/32.png) [@muttrox](https://boards.straightdope.com/u/muttrox)\ **Post date:** [March 3, 2004, 10:22pm UTC](https://boards.straightdope.com/t/is-0-red-10-white-vs-3-red-8-white-significantly-different/232179/14 "2004-03-03T22:22:41Z")
The standard for significant results is p = 0.05, not 0.95. You got it reversed. Roughly speaking, a test that results in p=0.05 would mean that under the null hypothesis (both buckets are pretty much the same), if we repeated this experiment many times, we would see results like this only 5% of the time. Since 5% is pretty low, we conclude that the null hypothesis is false, and we accept the alternative hypothesis, namely that the buckets are different.