Explain the meaning of 'opportunity sampling'. Give one reason why it might be used and state one disadvantage of using it.
A market researcher is conducting an 'on-street' survey in a busy city centre, for which he needs to stop and interview 100 people. For each interview the researcher counts the number of people he has to ask until one agrees to be interviewed. The data collected are as follows.
No. of people asked
1
2
3
4
5
6
7 or more
Frequency
26
19
17
13
11
8
6
A model for these data is proposed as follows, where \(p\) (assumed constant throughout) is the probability that a person asked agrees to be interviewed, and \(q = 1 - p\).
No. of people asked
1
2
3
4
5
6
7 or more
Probability
\(p\)
\(p q\)
\(p q ^ { 2 }\)
\(p q ^ { 3 }\)
\(p q ^ { 4 }\)
\(p q ^ { 5 }\)
\(q ^ { 6 }\)
Verify that these probabilities add to 1 whatever the value of \(p\).
Initially it is thought that on average 1 in 4 people asked agree to be interviewed. Test at the \(10 \%\) level of significance whether it is reasonable to suppose that the model applies with \(p = 0.25\).
Later an estimate of \(p\) obtained from the data is used in the analysis. The value of the test statistic (with no combining of cells) is found to be 9.124 . What is the outcome of this new test? Comment on your answer in relation to the outcome of the test in part (iii).