4B.5 An experiment was conducted to compare the performance of two potato peelers, and in particular to discover whether the typical user might be able to peel potatoes faster with one rather than the other. Ten volunteers were used, and each was given both peelers for a period before the experiment in order to gain familiarity with them. In the experiment the volunteer subjects used both peelers on standardised amounts of potatoes, and then repeated the experiment with the peelers used in the opposite order, so as to eliminate any effect due to ordering. The table below gives, for each subject, the mean of the natural logarithms of time (in seconds) needed to complete the tasks. Subject Peeler A B 1 2-33 2.34 2 2-76 2-79 3 1.91 1.91 4 2-62 2.60 5 2.01 2.03 6 1.77 1.80 7 1.81 1.81 8 1.99 2.00 9 1.97 1.98 10 2-26 2.30 Use Student's t-test, at the 5% level of significance, to test whether the peelers differ in their efficiency.
4B.5 An experiment was conducted to compare the performance of two potato peelers, and in particular to discover whether the typical user might be able to peel potatoes faster with one rather than the other. Ten volunteers were used, and each was given both peelers for a period before the experiment in order to gain familiarity with them. In the experiment the volunteer subjects used both peelers on standardised amounts of potatoes, and then repeated the experiment with the peelers used in the opposite order, so as to eliminate any effect due to ordering. The table below gives, for each subject, the mean of the natural logarithms of time (in seconds) needed to complete the tasks. Subject Peeler A B 1 2-33 2.34 2 2-76 2-79 3 1.91 1.91 4 2-62 2.60 5 2.01 2.03 6 1.77 1.80 7 1.81 1.81 8 1.99 2.00 9 1.97 1.98 10 2-26 2.30 Use Student's t-test, at the 5% level of significance, to test whether the peelers differ in their efficiency.
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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