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# MCQs: Probability and Stratified Sampling

1. A researcher plans to use a simple random sample to determine population mean &#956;. She has determined that using a simple random sample of size 400, she can determine &#956; within ±0.2*&#956; at a 99% level of confidence. The researcher is assuming that:

(a) &#963; &#8776; 1.55
(b) &#963; &#8776; 2.04
(c) &#963;/&#956; &#8776; 1.55
(d) &#963;/&#956; &#8776; 2.04
(e) &#960; &#8776; 0.5

2. At University X, all students visit the library from time to time. A researcher visited the library and collected a sample of 200 students. The respondents were asked how many times a week they visit the library. Based on frequency of visits, the researcher divided the sample into two sub-samples:

? Light users: There were 50 light users in the sample.
? Heavy users: There were 150 heavy users in the sample.

Based on frequency of visits, the researcher estimated that any given heavy user is five times as likely to be selected in the sample as any given light user. Let N denote the size of the student population at University X, N1 the number of light users, and N2 the number of heavy users in this population. Then, N2/N is approximately equal to:
(a) 0.25
(b) 0.375
(c) 0.5
(d) 0.625
(e) 0.75
Scenario for problems 5 and 6: At University X, the expenditure by a student on text books during the academic year 2009-2010 was normally distributed with population mean (&#956;) \$800, and population standard deviation (&#963;) \$250.

3. What is the probability that a student, randomly drawn from the student population at University Z, spent more than \$830 on text books during academic year 2009-2010?

(a) 0.0478
(b) 0.1151
(c) 0.3849
(d) 0.4522
(e) 0.7698

6.(1 pt) Suppose you have drawn a simple random sample of size 100 from the student population of University Z. What is the probability that the average expenditure on text books by this sample during academic year 2009-2010 was more than \$830?

(a) 0.0478
(b) 0.1151
(c) 0.3849
(d) 0.4522
(e) 0.7698

#### Solution Summary

The solution provides answers to multiple choice questions on probability.

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