Velvetleaf is a particularly annoying weed in corn fields. It produces lots of s

Question

Velvetleaf is a particularly annoying weed in corn fields. It produces lots of seeds, and the seeds wait in the soil for years until conditions are right. The velvetleaf seed beetle feeds on the seeds and might be a natural weed control. Here are the total seeds, seeds infected by the beetle, and percent of seeds infected for 28 velvetleaf plants.

a. Do a complete analysis of the percent of seeds infected by the beetle. (Round your answers to four decimal places.)

x=_____

s=_____

b. Include a 90% confidence interval for the mean percent infected in the population of all velvetleaf plants. (Round your answers to two decimal places.)  

_____% to _____%

Seeds
Infected
Percent 2450
137
5.6 2504
101
4.0 2114
77
3.6 1110
25
2.3 2137
123
5.8 8015
190
2.4 1623
32
2.0 1531
46
3.0 2008
73
3.6 1716
12
0.7 Seeds
Infected
Percent 721
28
3.9 863
42
4.9 1136
43
3.8 2819
81
2.9 1911
84
4.4 2101
85
4.0 1051
42
4.0 218
0
0.0 1711
65
3.8 164
6
3.7 Seeds
Infected
Percent 2228
158
7.1 363
33
9.1 5973
238
4.0 1050
90
8.6 1961
136
6.9 1809
90
5.0 130
3
2.3 880
22
2.5

Explanation / Answer

X = 2062

n = 52297

P = X/n= 2062/52297 = 0.03942

b)
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=2062
Sample Size(n)=52297
Sample proportion = x/n =0.039
Confidence Interval = [ 0.039 ±Z a/2 ( Sqrt ( 0.039*0.961) /52297)]
= [ 0.039 - 1.645* Sqrt(0) , 0.039 + 1.65* Sqrt(0) ]
= [ 0.038,0.04]

2450 137 2504 101 2114 77 1110 25 2137 123 8015 190 1623 32 1531 46 2008 73 1716 12 721 28 863 42 1136 43 2819 81 1911 84 2101 85 1051 42 218 0 1711 65 164 6 2228 158 363 33 5973 238 1050 90 1961 136 1809 90 130 3 880 22 Total 52297 2062

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