2. Accuracy and Precision. Five students measured the mass of a rock sample thre

Question

2. Accuracy and Precision. Five students measured the mass of a rock sample three times and recorded the values below. Their teacher said the value of the rock’s mass was 39.3 g (grams). Trial 1 Trial 2 Trial 3 Student A 35.4 g 37.7 g 42.1 g Student B 39.4 g 39.5 g 39.3 g Student C 34.8 g 34.8 g 34.8 g Student D 39.2 g 41.2 g 36.3 g Student E 38.4 g 39.4 g 40.4 g (a) Ignoring accuracy, rank the five students from best precision to least precision. (b) Identify the two students who measure with the same amount of accuracy. (c) Between the two students in part (b), which one took a “better” sample in a statistical sense?

3. True or False? For each of the following statements, circle either true or false. T F Increasing the sample size is the best way to eliminate bias and to decrease sampling variability when estimating an unknown population parameter. T F When taking a simple random sample (SRS), every member of the population is equally likely to be chosen. T F Systematic sampling gives a representative sample when the order of the list could be associated with the responses. T F The value of a statistic may change from sample to sample, i.e., in repeated sampling. T F A sampling frame is a list of all of the items in the sample. T F If every member of the population has the same chance of being chosen, then we will automatically obtain a simple random sample (SRS).

Explanation / Answer

A) From best Precision to least precision

1- Student B and E

3- Student D

4- Student A

5- Student C

B) The students with the same amount of accuracy are B and E with an Average Deviation of -0.1 from the real value

C) The best sample was taken by the the student B, in his third sample he measured the exact value of the rock mass, the best value statistically speaking.

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Rock mass 39.3 Measure Deviation Average Deviation Average Measure Student A 35.4 3.9 0.9 38.4 37.7 1.6 42.1 -2.8 Student B 39.4 -0.1 -0.1 39.4 39.5 -0.2 39.3 0 Student C 34.8 4.5 4.5 34.8 34.8 4.5 34.8 4.5 Student D 39.2 0.1 0.4 38.9 41.2 -1.9 36.3 3 Student E 38.4 0.9 -0.1 39.4 39.4 -0.1 40.4 -1.1

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