7 The following table shows observed frequencies, where \(x\) is an integer, from an experiment to test whether or not a six-sided die is biased.
| Number on die | 1 | 2 | 3 | 4 | 5 | 6 |
| Observed frequency | \(x + 6\) | \(x - 8\) | \(x + 8\) | \(x - 5\) | \(x + 4\) | \(x - 5\) |
A goodness of fit test is conducted to determine if there is evidence that the die is biased.
- Write down suitable null and alternative hypotheses for this test.
It is found that the null hypothesis is not rejected at the \(5 \%\) significance level.
- Hence
- find the minimum value of \(x\)
- determine the minimum number of times the die was rolled.