Chapter 5
Exercises: 5.21, 5.23(e)
Also:
A newspaper article in 1965 reported that a high school student observed 9207 heads and 8743 tails in 17,950 coin tosses.
If $\pi$ is the probability of tossing a head, test the hypothesis that $H_0 : \pi = \frac{1}{2}$.
It turned out that the student had tossed groups of five coins at a time, with the results as shown in the table below. Test the hypothesis that the observations are from a binomial distribution with probability of heads being $\pi = \frac{1}{2}$.
Test the hypothesis that the observations are from a binomial distribution (that is, the coins each have the same probability of heads, but this probability is not necessarily $\frac{1}{2}$).
| Number of Heads | Frequency |
| 0 | 100 |
| 1 | 524 |
| 2 | 1080 |
| 3 | 1126 |
| 4 | 655 |
| 5 | 105 |