consider the population of all students at your school. A certain portion support mandatory national service following high school. Your friend randomly sampled 20 students from the school, and uses the sample proportion who support MNS to predict the population at the school. You take your own, separate sample of 20 students, and find the sample that supports MNS. a) for the two studies, are the population the same? b) for the two studies, are the sample proportions necessarily the same? explain.
a) In this scenario, the population refers to all students at your school. So, for both studies, the population is the same since it consists of the entirety of students at your school.
b) The sample proportions may or may not be the same in the two studies. The sample proportion is the proportion of students in the sample who support mandatory national service (MNS). Since the two samples are taken separately and randomly, it is possible that the sample proportions in each study could differ. The reason for this is that the composition of each sample might differ due to random chance.
To further explain, the sample proportion is calculated by dividing the number of students in the sample who support MNS by the total number of students in the sample. Since the two samples are taken independently, there is no guarantee that they will have the same distribution of characteristics as the population. As a result, the sample proportion in each study could vary, leading to different estimates of the proportion of students who support MNS in the population.
It's worth noting that while the sample proportions may differ, they should still be indicative of the underlying population proportion. However, it is important to keep in mind the potential sampling variability and the need for larger sample sizes to increase the accuracy of the estimates.