Plant spacing can have both a positive and negative effect on crop yield. For example, closer spacing increases the number of plants and hence the yield per acre, but it also increases plant competition for available nutrients and moisture, thereby reducing the yield per plant. For an investigation of the effect of raw spacing on the production of garden peas, equal-sized fields at seven different locations were available. At each location, the field was divided into three square, equal- sized plots. Peas were planted at each location by randomly assigning one plot to be sown in a 4 inch row spacing, a second plot to be sown in an 8 inch row spacing and the third plot to be sown in a 12 inch row spacing. All plots were planted on the same date, and the plots at each location were treated the same except for row spacing. The yields of peas in bushels/ acre for each plot is given in the data table. The image below provide the following details : (1) Table on the left represents yield of a crop taken from 7 different locations. Row spacing denotes the spacing of plants. From each location, three different yield values are taken with 3 different plant spacing (2) The table on the right provides summary statistics of each sample based on the 'row-spacing'.   How do we select the best(optimal) plant spacing for this crop, by interpreting the summary statistics of the table?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
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Plant spacing can have both a positive and negative effect on crop yield. For example, closer spacing increases the number of plants and hence the yield per acre, but it also increases plant competition for available nutrients and moisture, thereby reducing the yield per plant. For an investigation of the effect of raw spacing on the production of garden peas, equal-sized fields at seven different locations were available. At each location, the field was divided into three square, equal- sized plots. Peas were planted at each location by randomly assigning one plot to be sown in a 4 inch row spacing, a second plot to be sown in an 8 inch row spacing and the third plot to be sown in a 12 inch row spacing. All plots were planted on the same date, and the plots at each location were treated the same except for row spacing. The yields of peas in bushels/ acre for each plot is given in the data table.

The image below provide the following details :

(1) Table on the left represents yield of a crop taken from 7 different locations. Row spacing denotes the spacing of plants. From each location, three different yield values are taken with 3 different plant spacing

(2) The table on the right provides summary statistics of each sample based on the 'row-spacing'.

 

How do we select the best(optimal) plant spacing for this crop, by interpreting the summary statistics of the table?

Can I have a step-by-step explanation on that?

Thank you!

Location
Row Spacing
4"
8"
12'
4"
8"
12'
110
114
118
Mean
103.5714286 Mean
108.1428571 Mean
111.8571429
104
108
112
Standard Error
3.987224496 Standard Error
3.467046028 Standard Error
3.71886165
106
108
98
88
Median
104 Median
108 Median
112
4
94
98
Mode
#N/A
Mode
114 Mode
#N/A
5
112
114
120
Standard Deviation
10.54920444 Standard Deviation
9.172941575 Standard Deviation
9.839183086
6
102
Sample Variance
Kurtosis
95
100
111.2857143 Sample Variance
84.14285714 Sample Variance
96.80952381
7
118|
121
125
-1.05729079 Kurtosis
-0.515458563 Kurtosis
-1.307413656
Skewness
-0.141107806 Skewness
-0.257382078 Skewness
-0.155316243
Range
30 Range
27 Range
27
Minimum
88 Minimum
94 Minimum
98
Maximum
118 Maximum
121 Maximum
125
Sum
725 Sum
757 Sum
783
7 Count
118 Largest(1)
7 Count
121 Largest(1)
94 Smallest(1)
Count
7
Largest(1)
125
88 Smallest(1)
Smallest(1)
Confidence Level(95.0%)
98
9.756386873 Confidence Level(95.0%)
8.483556015 Confidence Level(95.0%)
9.099726644
Transcribed Image Text:Location Row Spacing 4" 8" 12' 4" 8" 12' 110 114 118 Mean 103.5714286 Mean 108.1428571 Mean 111.8571429 104 108 112 Standard Error 3.987224496 Standard Error 3.467046028 Standard Error 3.71886165 106 108 98 88 Median 104 Median 108 Median 112 4 94 98 Mode #N/A Mode 114 Mode #N/A 5 112 114 120 Standard Deviation 10.54920444 Standard Deviation 9.172941575 Standard Deviation 9.839183086 6 102 Sample Variance Kurtosis 95 100 111.2857143 Sample Variance 84.14285714 Sample Variance 96.80952381 7 118| 121 125 -1.05729079 Kurtosis -0.515458563 Kurtosis -1.307413656 Skewness -0.141107806 Skewness -0.257382078 Skewness -0.155316243 Range 30 Range 27 Range 27 Minimum 88 Minimum 94 Minimum 98 Maximum 118 Maximum 121 Maximum 125 Sum 725 Sum 757 Sum 783 7 Count 118 Largest(1) 7 Count 121 Largest(1) 94 Smallest(1) Count 7 Largest(1) 125 88 Smallest(1) Smallest(1) Confidence Level(95.0%) 98 9.756386873 Confidence Level(95.0%) 8.483556015 Confidence Level(95.0%) 9.099726644
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