2. A small internet mail-order company keeps track of the number of orders it fills per day for many years and determines that the distribution of the variable "orders filled per day" is right-skewed and has the following five-number summary: Minimum - 20 Median - 46 Maximum - 80 Q₁ - 32 Qs -63 Suppose we take random samples of size 40 from this distribution and calculate the range for each of our samples. Below is a dotplot of the range of 50 such samples. 53 54 55 56 57 58 59 60 Sample range (a) There are two dots on the graph at 53. Explain what these values represent. (b) Does the simulation provide evidence that the sample range is a biased estimator of the population range? Use the dotplot above to justify your answer.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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2. A small internet mail-order company keeps track of the number of orders it fills per day for many years and
determines that the distribution of the variable "orders filled per day" is right-skewed and has the following
five-number summary:
Qs - 63
Minimum - 20
0₁ - 32
Median - 46
Suppose we take random samples of size 40 from this distribution and calculate the range for each of our
samples. Below is a dotplot of the range of 50 such samples.
*******
53
******
54 55
56 57
Sample range
(a) There are two dots on the graph at 53. Explain what these values represent.
**********
Maximum - 80
58 59 60
(b) Does the simulation provide evidence that the sample range is a biased estimator of the population
range? Use the dotplot above to justify your answer.
Transcribed Image Text:2. A small internet mail-order company keeps track of the number of orders it fills per day for many years and determines that the distribution of the variable "orders filled per day" is right-skewed and has the following five-number summary: Qs - 63 Minimum - 20 0₁ - 32 Median - 46 Suppose we take random samples of size 40 from this distribution and calculate the range for each of our samples. Below is a dotplot of the range of 50 such samples. ******* 53 ****** 54 55 56 57 Sample range (a) There are two dots on the graph at 53. Explain what these values represent. ********** Maximum - 80 58 59 60 (b) Does the simulation provide evidence that the sample range is a biased estimator of the population range? Use the dotplot above to justify your answer.
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