4. Luka wants to carry out a survey of students at his school.
He obtains a list of all 280 students.
- Explain how he can use this list to select a systematic sample of 40 students.
Luka is trying to make his own random number table. He generates 400 digits to put in his table. Figure 1 shows the frequency of each digit in his table.
\begin{table}[h]
| Digit generated | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Frequency | 36 | 42 | 33 | 41 | 44 | 43 | 48 | 38 | 32 | 43 |
\captionsetup{labelformat=empty}
\caption{Figure 1}
- Determine the conclusion of this test.
(3)
The digits generated by Luka are taken two at a time to form two-digit numbers.
Figure 2 shows the frequency of two-digit numbers in his table.
\begin{table}[h]
| Two-digit numbers generated | \(00 - 19\) | \(20 - 39\) | \(40 - 59\) | \(60 - 79\) | \(80 - 99\) |
| Frequency | 31 | 49 | 30 | 42 | 48 |
\captionsetup{labelformat=empty}
\caption{Figure 2}
- Test, at the \(10 \%\) level of significance, whether the two-digit numbers generated by Luka follow a uniform distribution. You should state the hypotheses, the degrees of freedom and the critical value used for this test.
There are 70 students in Year 12 at his school.
- State, giving a reason, the advice you would give to Luka regarding the use of his table of numbers for generating a simple random sample of 10 of the Year 12 students.