Lab #1

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Purdue University *

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301

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Statistics

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Apr 3, 2024

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Name: Lilyhan Liao TA name/ class time: Fang, Yaxin, Fridays at 1:30-2:20pm Lecturer Name: Christina Munson Lab 1: Sampling Methods/ Bias 1. SRS #1 1 2 3 4 5 Height 61.74 66.09 59.72 68.46 65.78 2. SRS #2 1 2 3 4 5 Height 66.97 63.97 67.46 67.13 62.89 SRS #3 1 2 3 4 5 Height 71.34 70.18 63.80 68.27 65.27 SRS #4 1 2 3 4 5 Height 66.25 74.11 68.94 66.45 73.16 Table 1: Height SRSs Means SRS #1 SRS #2 SRS #3 SRS #4 Mean: 64.358 65.692 67.772 69.782 3. Mean Height: 67.766

Statistics Height N Valid 150 Missing 0 Mean 67.7657 Median 68.3600 Std. Deviation 4.31766 Range 21.75 Minimum 56.01 Maximum 77.76 4. a) In your opinion, are the sample means in Table 1 similar to or different than the mean of the fictitious “population”? Was variability due to small sample size apparent? In Table 1, the sample means are mostly more different in comparison to the sample mean given for the fictious population. In Table 1, it is quite evident that there is more of a wider range in means. There was variability due to the small sample size. There was no variability in the big sample size. b) Explain how increasing the sample size would affect how the sample means compare to the mean of the fictitious “population”. In the beginning, because a smaller group was analyzed, a range of numbers of where the mean could be was given to us. When it comes to analyzing statistics, this can lead to giving us inaccurate results. Inaccuracy can prove to be fatal to a study’s success. Higher variability means the values are less consistent. On the other hand, the fictitious population gave us one mean only. Not a range. Lower variability means the values are more consistent which leads us to more accurate results. 5. The subjects in the data set answered a call for volunteers to participate in this study. Assuming every subject who volunteered has a recorded response for every variable, what type of bias could possibly result from this sampling design? One type of bias that could arise from this type of sampling design could be voluntary sample bias. When a study is voluntary, it is likely that most subjects have strong opinions. This can lead to partial truth such as leaving out representative groups.

6. What is an alternative sampling design that could avoid the bias mentioned in question #5? Explain how it would address the bias. An alternative sampling design that could avoid voluntary bias would be using a random sampling design instead. When using random sampling such as systematic sampling, it allows every person in a population to have an equal chance of being chosen to be included in the study. A more accurate representation could be achieved this way instead of bias being involved. 7. The variables GPA and Height were measured through self-reporting. Describe the bias that could possibly result. It is a possibility that those subjects that have higher GPA’s or feel that their height is something they like to brag about were more likely to report themselves and become involved in the study. Another possibility is that the subjects could lie about either their heights or GPAs. Height and GPA could be sensitive topics for them. This is called response bias. 8. How could you avoid the type of bias mentioned in question #7? Give at least one idea for each variable. For GPA, you could ask each subject for a screenshot of their official transcripts or proof of some kind. For height, you could measure each subject personally. However, it can be inconvenient and be time consuming. 9. a) Consider the following scenario: Subjects were asked to volunteer for this study and were told they would be paid for their time spent completing a questionnaire. As part of the questionnaire, the subjects provided their own average hours slept per night. Also, some of the questions on the questionnaire asked personal questions that several subjects refused to answer. Given this information, do you think that the data from the questionnaire will provide an accurate reflection of all subjects’ average hours slept per night? Not at all. I don't believe there will be enough data to form a conclusive result. Although there was a incentive provided which could lead to an increase in survey completion, there were questions in the survey that were personal. When it comes to personal topics, the chance of the responses being truthful is very low. b) If so, explain why. If not, identify at least two flaws in the sampling method of the study. Two flaws in the sampling method of the study are the decision to involve an incentive (could be considered unethical coercion) and including personal questions in the survey (leads to inaccurate/skewed results).

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