Sampling frames and populations

1 A magazine conducted a survey about the sleeping time of adults. A random sample of 12 adults was chosen from the adults travelling to work on a train.

1. Give a reason why this is an unsatisfactory sample for the purposes of the survey.
2. State a population for which this sample would be satisfactory. A satisfactory sample of 12 adults gave numbers of hours of sleep as shown below.
   \(4.6 \quad 6.8\)
   5.2
   6.2
   5.7
   \(\begin{array} { l l } 7.1 & 6.3 \end{array}\)
   5.6
   7.0
   \(5.8 \quad 6.5\)
   7.2
3. Calculate unbiased estimates of the mean and variance of the sleeping times of adults.

1. (a) State one characteristic of a population that would make a census a practical alternative to sampling.

A leisure centre has 2500 members.
It asks a sample of 300 members for their opinions on the fees it charges for using the centre. For the sample,
(b) (i) identify a suitable sampling frame,
(ii) identify a sampling unit. The leisure centre has the following pieces of information.
\(A\) is the list of the different types of membership that can be paid for by members.
\(B\) is the mean of the membership fees paid by all 2500 members.
\(C\) is the number in the sample of 300 members who are satisfied with the fees they pay.
(c) State the piece of information that is a statistic. Give a reason for your answer.

2. (a) Explain what you understand by (i) a population and (ii) a sampling frame. The population and the sampling frame may not be the same.
(b) Explain why this might be the case.
(c) Give an example, justifying your choices, to illustrate when you might use

1. a census,
2. a sample.