An archeologist has found 19 intact specimens of a certain prehistoric artifact. Although she finds the specimens individually interesting in and of themselves, her broader research interest is in what they can tell her about the entire population of such artifacts that must once have existed within this particular prehistoric setting. As a first step she undertakes, on the basis of information contained within her sample, to estimate the mean length of such artifacts within the population. Listed below are the lengths of the 19 items in the sample, each measured to the nearest tenth of a centimeter. 17.3 18.9 17.7 23.8 16.0 22.1 18.4 18.2 13.3 26.8 18.6 24.5 22.8 13.4 18.1 14.8 20.6 17.4 16.1 a) From above preamble, estimate the sample mean length of the artifacts and explain why the average length of the sample is different from the population. b) Estimate the standard deviation of the mean for the distribution of length and explain how it influences the sampling error c) Find the probability that a specimen selected from the population of artifact is with length 18.2. d) Describe the symmetry of the distribution of the sample of lengths measured for the selected artifact.
An archeologist has found 19 intact specimens of a certain prehistoric
artifact.
Although she finds the specimens individually interesting in and of
themselves, her broader research interest is in what they can tell her
about the entire population of such artifacts that must once have
existed within this particular prehistoric setting. As a first step she
undertakes, on the basis of information contained within her sample, to
estimate the mean length of such artifacts within the population. Listed
below are the lengths of the 19 items in the sample, each measured to
the nearest tenth of a centimeter.
17.3 18.9 17.7 23.8 16.0 22.1 18.4 18.2 13.3 26.8
18.6 24.5 22.8 13.4 18.1 14.8 20.6 17.4 16.1
a) From above preamble, estimate the sample mean length of the
artifacts and explain why the average length of the sample is
different from the population.
b) Estimate the standard deviation of the mean for the distribution
of length and explain how it influences the sampling error
c) Find the probability that a specimen selected from the population
of artifact is with length 18.2.
d) Describe the symmetry of the distribution of the sample of
lengths measured for the selected artifact.
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