1. Explain, in your own words, the meaning of “bias” in statistics? Give an exam
ID: 3069677 • Letter: 1
Question
1. Explain, in your own words, the meaning of “bias” in statistics? Give an example. 2. Imagine we had a need to gather data in the following situation: After receiving the same lesson, a class of 100 students was randomly divided into two groups of 50 students each. One group was given a multiple-choice exam covering the material, the other an essay exam. The average scores on the tests for the two groups were then compared. Is this an experiment, or an observational study? Why? 3. What does it mean to say we are going to make an inference about a parameter based on the value of a statistic? Include in your answer what “parameter” and “statistic” mean, and give an example. 4. Consider the following set of numbers: 8 4 35 21 29 -3 7 What is the mean of this group, what is the median, and what is the mode? If it is impossible to identify one of these values, explain why that is the case? 5. Amanda collects 10 leaves, and measures their lengths, in centimeters. Here are her results: 5, 6, 5, 2, 4, 5, 8, 7, 5, 4 Fill in the following frequency and relative frequency chart: Length of leaf (cm) Frequency Relative Frequency 2 3 4 5 6 7 8 6. Again referring to Amanda’s leaf collection above, calculate the mean length of the leaves she collected. 7. By hand or using technology (if you use technology, insert a screen capture or picture of the spreadsheet/calculator screen you used to find the value), compute the standard deviation of the lengths of the leaves Amanda collected. 8. Combine the concepts of the mean and standard deviation of the leaves Amanda collected. What do you infer or deduce from the value of the mean and the standard deviation? What do those values, in other words, tell you about the lengths of the leaves in the collection? 9. Should Amanda use the dataset from her collection to speculate on the mean leaf length of the trees in a forest near her home? Why or why not?
Explanation / Answer
Answer to question# 1)
Bias: is the difference of actual and predicted value. When the sample is not formed randomly or it fails to represent the true population bias occurs in the data
Example: Suppose if the research relates to 100 students in the class, and the sample is to be formed by randomly selecting 10 students from the class. But the researcher simply gets in touch with first 10 students and includes them in the sample. This will lead to bias since the entire class of 100 students was not even considered during the selection of the sample.
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