1. A university professor wants to study the factors that aect the likelihood of a student to succeed in his class.
He thinks that the high school GPA of a student might be one of those factors. He has a list of his 100 students
ordered by randomly generated student identication numbers. He decides to select a sample of 25 students
using systematic sampling and he ascertains the high school GPA of the selected students. He obtains a sample
mean high school GPA of 3.5 with standard deviation 0.5. We want to estimate the variance of the sample mean.
(a) What important hypothesis is required to compute an estimate of the variance of the sample mean
in this context?
(b) What is the estimate of the variance of the sample mean GPA?
2. A large university class has 160 students. All 160 students attend the lectures together, but the
students are divided into 4 groups, each of 40 students, for tutorial sections administered by dierent teaching
assistants. The professor wants to conduct a survey about how satised the students are with the course. He
plans to select 40 students at random and he believes that the tutorial section a student is in might aect the
student's overall satisfaction with the course. What is the most appropriate sampling design here: simple random
sampling, cluster sampling, or stratied sampling? Justify your choice.
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