Problem

Luka surveys 280 students.

(a) Explain how a systematic sample of 40 students could be taken from the 280 students.

A random digit table is used to generate 400 digits. The frequencies are shown below.

Digit	0	1	2	3	4	5	6	7	8	9
Frequency	36	42	33	41	44	43	48	38	32	43

Test, at the 10% level of significance, whether the digits may be regarded as uniformly distributed.

You are given that $\dfrac{(O-E)^2}{E} = 5.9$.

(b) Determine the conclusion.

The digits are then paired to form two-digit numbers. The frequencies are shown below.

Two-digit number	00-19	20-39	40-59	60-79	80-99
Frequency	31	49	30	42	48

(c) Test, at the 10% level of significance, whether the two-digit numbers may be regarded as uniformly distributed. You should state your hypotheses, degrees of freedom and critical value.

There are 70 students in Year 12.

(d) Advise Luka about using his table to select a simple random sample of 10 Year 12 students.