Velvetleaf is a particularly annoying weed in corn fields. It produces lots of s
ID: 3022183 • Letter: V
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: Do a complete analysis of the percent of seeds infected by the beetle. (Round your answers to four decimal places.) Include a 90% confidence interval for the mean percent infected in the population of all velvetleaf plants. (Round your answers to two decimal places.) Do you think that the beetle is very helpful in controlling the weed? The beetle infects more than 5% of seeds, so it is likely to be effective in controlling velvetweed. The beetle infects more than 15% of seeds, so it is likely to be effective in controlling velvetweed. The beetle infects less than 15% of seeds, so it is unlikely to be effective in controlling velvetweed. The beetle infects less than 5% of seeds, so it is unlikely to be effective in controlling velvetweed.Explanation / Answer
a)
Using technology,
X = sample mean = 4.042857143 [ANSWER]
s = sample standard deviation = 2.030038965 [ANSWER]
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b)
We use t distrbution because we only have n = 28 < 30.
Note that
Lower Bound = X - t(alpha/2) * s / sqrt(n)
Upper Bound = X + t(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.05
X = sample mean = 4.042857143
t(alpha/2) = critical t for the confidence interval = 1.703288446
s = sample standard deviation = 2.030038965
n = sample size = 28
df = n - 1 = 27
Thus,
Lower bound = 3.389405343
Upper bound = 4.696308943
Thus, the confidence interval is
( 3.39 , 4.70 ) [ANSWER]
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c)
As the whole confidence interval is less than 5%, then
OPTION C: The beetle infects less than 15% of seeds, so it is unlikely to be effective in controlling velvetweed. [ANSWER, C]
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