pts D Question 12 Sandy works for campus security and wants the opinions of the

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pts D Question 12 Sandy works for campus security and wants the opinions of the undergraduates at BGSU about campus safety at night. To get a variety of responses she takes 3 different samples. Sample 1: She sets up a table at a busy walking path on campus late at night and asks students their opinion as they pass by. She receives about 450 responses and finds that 64% of the students feel safe walking on campus at night. She calculates a margin of error for a 95% confidence interval to be 4.4%. Sample 2 She obtains a list of all the undergraduates and randomly selects 200 students. She contacts the students and finds that 54% of the 200 students feel safe walking on campus at night. She calculates a margin of error for a 95% confidence interval to be 7%. Sample 3 She obtains a list of all the undergraduates and sends an email asking their opinion. She receives many emails so she randomly picks 300 emails and finds that 45% of the 300 students feel safe walking on campus at night. She calculates a margin of error for a 95% confidence interval to be 5.6%. 1. (6pts/For each sample, explain at least one source of sampling bias or explain why there is no sampling bias. 2. apts Explain which sample result would most accurately reflect the opinions of the undergraduate students at BGSU? 3. t2ptsWhat is the probability that the interval generated from the sample you picked in part b would not include the proportion of all BGSU students that feel safe walking on campus at night. 4. (3pts)From any of the samples can you make the claim that most of the students (over 50%) at BGSU feel safe walking on campus at night? Explain your answer

Explanation / Answer

a) Find source of sampling bias, if any

SAMPLE 1: This is a convenience sample where Sandy chose people who were walking on the night without any randomization. It will create sampling bias because it is quite possible people who are not walking in the night do not feel safe.

SAMPLE 2: She is closed to unbiased random sampling. As she obtains a list of all the undergrads and randomly select 200 from them and contacted them for their opinion. As they have not mentioned that many students didn't answer thus I am excluding Nonresponse is when people chosen for the sample cannot be reached or refuse to participate.

SAMPLE 3: Voluntary response sampling, Sandy sends email to students and let members of the population choose whether or not they would be in the sample. This is a voluntary response sample, which almost always produces biased results.

2. Sample 2 most accurately reflects the opinions of the undergrads as it an unbiased sampling.

3. Since the result is 95% confidence about the result, the probability of not including is 5% or 0.05

4. Let look at all the intervals

SAMPLE 1: 64% with 4.4 % ME = [59.6% to 68.4%]

SAMPLE 2:54% with 7% ME = [47% to 61%]

SAMPLE 3: 45% with 5.6% ME = [39.4% to 50.6%]

Thus from sample 1 we can make claim that most of the students (over 50%) at BGSU feel safe walking on campus at night as its upper and lower limit are both beyond 50%.

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