# Thread: Coin Spin Statistical Hypothesis

1. ## Coin Spin Statistical Hypothesis

I am having a really hard time with this problem because I have no teacher to discuss it with. I am hoping someone here can help me.

The probability of observing heads is throught to be p=0.30. Three people spun a coin and recorded the number of heads out of the three spins, say x. They repeated this n=200 times, observing 0, 1, 2, and 3 heads 57, 95, 38, and 10 times, respectively. Use these date to test the hypothesis that X is b(3,0.30). Give limits for the p-value of this test. In addition, out of 600 spins, calculate the number of heads occurring and then a 95% confidence interval for p.

I'm sorry the problem is so long. I actually picked one of the shorter ones.

2. Originally Posted by larz
I am having a really hard time with this problem because I have no teacher to discuss it with. I am hoping someone here can help me.

The probability of observing heads is throught to be p=0.30. Three people spun a coin and recorded the number of heads out of the three spins, say x. They repeated this n=200 times, observing 0, 1, 2, and 3 heads 57, 95, 38, and 10 times, respectively. Use these date to test the hypothesis that X is b(3,0.30). Give limits for the p-value of this test. In addition, out of 600 spins, calculate the number of heads occurring and then a 95% confidence interval for p.

I'm sorry the problem is so long. I actually picked one of the shorter ones.
You can use Chisquare test for the hypothesis part..
57, 95, 38, and 10 are the observed and 200*B(X=0, 3,.3) ,200*B(X=1, 3,.3)... 200*B(X=3, 3,.3) are the theoretical frequencies..

Second part.. out of 600 spins... it is B(600,.3)

Mean is 600*.3 and var is 600*.3*.7 So CI is mean +/- 1.96*var

3. So i have a mean of 180, variance of 126 and the 95% confidence interval would then be 180+/-246.96? Then wouldn't it be in the negative also? (-66.96 to 426.96)

Thank you for the time you put in. I am not understanding this part of the book at all and the Chi Square / hypothesis material is really killing me.

4. sorry . it is
So CI is mean +/- 1.96*sqrt(var)
ie

So CI is mean +/- 1.96*sd

and regarding hypothesis test the following link may help
http://www.stat.yale.edu/Courses/1997-98/101/chigf.htm