4. A paranormal investigator invites couples who believe they have a telepathic connection to participate in a trial. With each couple one person looks at a card with one of five shapes on it and the other person says which of the shapes they think it is. This is repeated six times and the number of correct answers recorded. The results from 120 couples are given below.
| Number Correct | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Number of Couples | 26 | 56 | 28 | 8 | 2 | 0 | 0 |
The investigator wishes to see if this data fits a binomial distribution with parameters \(n = 6\) and \(p = \frac { 1 } { 5 }\) and calculates to 2 decimal places the expected frequencies given below.
| Number Correct | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Expected Frequency | | | | 9.83 | 1.84 | 0.18 | 0.01 |
- Find the other expected frequencies.
- Stating your hypotheses clearly, test at the \(5 \%\) level of significance whether or not the distribution is an appropriate model.
- Comment on your findings.