Q T4.10. A researcher wishes to compare t... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 4: Q T4.10. (page 275)

A researcher wishes to compare the effects of 2 fertilizers on the yield of soybeans. She has 20 plots of land available for the experiment, and she decides to use a matched pairs design with 10 pairs of plots. To carry out the
random assignment for this design, the researcher should
(a) use a table of random numbers to divide the 20 plots into 10 pairs and then, for each pair, flip a coin to assign the fertilizers to the 2 plots.
(b) subjectively divide the 20 plots into 10 pairs (making the plots within a pair as similar as possible) and then, for each pair, flip a coin to assign the fertilizers to the 2 plots.
(c) use a table of random numbers to divide the 20 plots into 10 pairs and then use the table of random numbers a second time to decide upon the fertilizer to be applied to each member of the pair.
(d) flip a coin to divide the 20 plots into 10 pairs and then, for each pair, use a table of random numbers to assign the fertilizers to the 2 plots.
(e) use a table of random numbers to assign the 2 fertilizers to the 20 plots and then use the table of random numbers a second time to place the plots into 10 pairs.

Short Answer

Expert verified

The correct option is (b).

Step by step solution

Given information

The effects of two fertilizers on soybean yield are being compared by a researcher.

Concept

When random sampling is not used, bias or systematic flaws in the way the sample represents the population can occur. Voluntary response samples, in which respondents choose their own respondents, and convenience samples, in which people who live nearby are included in the sample, are particularly biassed.

Explanation

As indicated in the inquiry, a researcher wants to compare the effects of two fertilizer's on soybean yield. She has twenty plots of land for the experiment, with ten of them being used in a matched-pair scheme. To carry out the random assignment for this matched pairs design, one plot from each pair must be assigned to the first group and the other plot to the second group. In a matched pairs design, pairings should be as comparable as possible to avoid unnecessary elements, hence answer (b) is the correct option.