Question

For this question, you will flip fair coin to take some samples and analyze them. First, take any fair coin and flip it 12 times. Count the number of heads out of the 12 flips. This is your first sample. Do this 4 more times and count the number of heads out of the 12 flips in each sample. Thus, you should have 5 samples of 12 flips each. The important number is the number of heads in each sample (this can be any whole number between 0 and 12). Then answer the following questions:

1) HTHHHHHTTTHT
2) TTTTHTHTTTTT
3) HHTTTHTHHTTH
4) TTHHHHTTTHTH
5) THHHHHTHHHTT 

1) If you had a very large number of samples, what value(s) should the mean and median have? Why?

2) For each of your 5 samples of 12 flips, use the binomial distribution to test the null hypothesis that the coin is fair, using p = .05 (two-tailed). (The alternative hypothesis is that the coin is not fair.) For each sample, calculate the p value (the probability of getting the number of heads you did or a more extreme number of heads (“two-tailed”) purely by chance). Show your work and organize the data into a small table. For each sample indicate the number of heads out of 12, the p value, your decision about the null hypothesis, and the explicit reason for your decision, in terms of the decision rule. Show your work computing the p values.

3) In general, what proportion of samples of fair coin flips (when N is sufficiently large that rejection region of the binomial distribution exists) should result in rejecting the null hypothesis (p = .05,two-tailed)?

Answer 1

(1) Here is possible outcomes is Head and Tail either Success and failure so the probability will be 1/2 for number of head and number and number of tail. so this distribution is Binomial distribution. but the data is very large then Binomial distribution is follows Normal distribution with mean np and variance is npq.

Here is the mean= np= 12*0.5=6

median will be half of the data