2. The students at a high school are split roughly equally across grades 9 throu
ID: 3248135 • Letter: 2
Question
2. The students at a high school are split roughly equally across grades 9 through 12. A group of students in a statistics class at the school wishes estimate the mean time spent studying by students at the school during the previous seven days. The group decides to select a sample of 40 students from the school, to ask those students how many hours they have studied during the previous seven days, and to use the mean value for the sample as an estimate of the mean value for the school. (a) One of the students in the group thinks that they should use a simple random sample. Describe how this sample might be selected. A different student thinks that they should use stratified random sampling, with the strata being the grades (9 through 12). (The sample size will again be 40) (b) How might this stratified sample be selected?Explanation / Answer
(a)
To select the simple random sample names of all students can be put in a box and via lottery 40 students names can be selected. This would be a simple random sample since then all students will have equal probability to be selected in the sample.
(b)
From grade 9 to 12 there are 4 grades. So if we are using the straified random sampling then we should select 10 students from each grade. These 10 students can be selected randomly using the same lottery method that we have used in previous part, only this time in each lottery names of students of a single grade will be present at one time.
(c)
Students from different grades have different capabilities and stamina for reading. Also the content taught is same across a single grade. Therefore different grade levels are used as different strata for study.
(d)
If we use simple random sample then we will only get an overall idea of mean time spent by the school students on studying. Also in this process we are expected to have more variance and thus our results would be less reliable. But using the stratified sample we will have low variance. Also we will have an extra result where we can see the difference between different grade levels in time spent for studying.
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