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# Stat 3507 Exercise Questions Solutions

• Date Submitted: 04/11/2016 04:13 AM
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STAT 3507 Exercise Questions Solutions

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Bernoulli Sampling Questions
Cluster Sampling Questions
Ratio, Regression and Difference Estimation
Stratified Random Sampling
Systematic Sampling
Two-stage Cluster Sampling Questions

1-A university professor who is correcting 600 written examinations decides to get a preliminary idea of the passing rate on the test. He decides to use a simple randomized scheme to single out a smaller number of exam copies for first-hand correction. In passing through the pile of exams, he tosses an ordinary six-sided die, once for each exam copy. If the die shows a 6, he corrects the corresponding exam, otherwise not. Suppose the sample selected in this way consists of 90 students and that 60 out of these are found to have passed.
a. Identify the sampling design implemented.
b. Estimate the total number of students who passed the exams
c. Compute a 95% confidence interval, based on the normal approximation, for the number of passing students (among the 600).
d. Repeat (b) and (c) using the alternative (improved) estimator.

2-
Table: Number of Employees and Range
Division Number of employees Cumulative range
1 1200 1— 1200
2 450 1201 —1650
3 2100 1651— 3750
4 860 3751— 4610
5 2840 4611 — 7450
6 1910 7451— 9350
7 390 9361 — 9750
8 3200 9751 - 12950
12950

i. Suppose 2011, 7972 and 10281 are the random numbers generated between 1 and 12950. Using this information what are the clusters selected?
ii. Suppose the total number of sick days used by the three sampled divisions during the past quarter are respectively, y, = 4320 y2 = 4160 y3 = 5790 .
Estimate the average number of sick clays used per person for the entire firm and place a bound on the error of estimation.

Ratio and Regression Estimators (Examples) under Simple Random Sampling Without Replacement
Set 1: Estimation of Ratio...