Question 2 Fourth Standard students of primary schools in the Eastern Caribbean
ID: 3046101 • Letter: Q
Question
Question 2 Fourth Standard students of primary schools in the Eastern Caribbean sit Proficiency Tests in English and Mathematics. The scores obtained in both tests by 225 students, drawn randomly, are processed using MINITAB and some preliminary results are shown in Exhibit 1 below. Exhibit I N Variable English Math 225 225 Mean Median 63.26 64.00 70.20 70.00 TrMean 63.00 70.00 StDev 19.44 14.805 Variable English Math = Minimum 10.00 25.00 Maximum 100.00 100.00 Qi Q3 50.00 79.00 61.00 79.00 Page 19 of 37Explanation / Answer
(a) A stratifiied random sampling design is a design by which the population is first divided into separate groups (or strata) and sampling is done from each group. This division into groups can be on the basis of gender, age, race, country, or any such factor. Each member of the population will belong to exactly one of the groups.
(b) Two differences between simple random sampling design and stratifiied random sampling design are:
1) Taking separate samples from each group ensures that all groups are represented adequately in our survey. No group will get accidentally left out.
2) A stratified random sample can lead to saving of time and money as there is more focus on the kind of information from members of each group. We can even get the kind of results we require by having smaller sample sizes within each group.
(c) The advantages in this case are:
1) We are ensuring that all countries are there in the survey. Each country will have adequate participation.
2) We can focus on getting the required data from each country within Eastern Caribbean.
3) In case results are different across countries, we already have one difference to explain the difference.
(d) On the one hand, we are ensuring that all countries are represented in the samples.
On the other hand, a country may probably not be an explanatory variable. In that case, grouping by country and sampling from each country separately will lead to loss of time and energy without any real benefit.
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