Velvetleaf is a particularly annoying weed in corn fields It

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 _____%

Solution

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]