7 A random sample of 80 observations of the continuous random variable \(X\) was taken and the values are summarised in the following table.
| Interval | \(2 \leqslant x < 3\) | \(3 \leqslant x < 4\) | \(4 \leqslant x < 5\) | \(5 \leqslant x < 6\) |
| Observed frequency | 36 | 29 | 9 | 6 |
It is required to test the goodness of fit of the distribution having probability density function f given by
$$f ( x ) = \begin{cases} \frac { 3 } { x ^ { 2 } } & 2 \leqslant x < 6
0 & \text { otherwise. } \end{cases}$$
Show that the expected frequency for the interval \(2 \leqslant x < 3\) is 40 and calculate the remaining expected frequencies.
Carry out a goodness of fit test, at the \(10 \%\) significance level.