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:

In R, do a complete analysis of the percent of seeds infected by the beetle.
#R Code

hist(Percent)
mean(Percent)
sd(Percent)
t.test(Percent, mu = 5.0, conf.level = 0.90)

Researchers would like to test whether the average percent of seeds infected is different than 5 percent. What is the null and alternative hypothesis for this test?

H0: ? > 5 percent

Ha: ? < 5 percent

H0: ? = 5 percent

Ha: ? ? 5 percent

    

H0: p ? 5 percent

Ha: p = 5 percent

H0: p = 5 percent

Ha:p ? 5 percent

H0: ? < 5 percent

Ha: ? = 5 percent

What is the average and standard deviation for the percent of seeds that are infected? (Round your answers to four decimal places.)

According to the R output, the test statistic and p-value are: (Round your answers to four decimal places.)

Given a significance level of 0.10. What can we conclude from the hypothesis test?

Fail to reject the null hypothesis. Reject the null hypothesis.    

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  %

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 less than 5% of seeds, so it is unlikely 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 more than 15% of seeds, so it is likely to be effective in controlling velvetweed.

Seeds
Infected
Percent 2450
135
5.6 2504
101
4.0 2114
76
3.4 1110
24
2.0 2137
121
5.9 8015
189
2.6 1623
31
1.8 1531
44
3.0 2008
73
3.7 1716
12
0.9 Seeds
Infected
Percent 721
27
3.8 863
40
4.5 1136
41
3.8 2819
79
2.7 1911
82
4.4 2101
85
4.2 1051
42
4.0 218
0
0.0 1711
64
3.8 164
7
4.4 Seeds
Infected
Percent 2228
156
7.1 363
31
8.7 5973
240
4.0 1050
91
8.8 1961
137
6.9 1809
92
5.3 130
5
4.0 880
23
2.8 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: Seeds24502504 2114 1110 2137 8015 1623 1531 2008 1716 Infected 135 101 7624 121 189 31 4473 Percent 12 5.6 4.0 3.4 2.0 5.9 2.6 1.8 3.0 3.7 0.9 Seeds Infected Percent3.8 4.5 3.82.74.44.24.00.0 3.8 4.4 721 863 1136 2819 1911 2101 1051 218 1711 164 27 40 41 79 82 85 42 0 64 Seeds2228363 5973 1050 1961 1809 130 88 Infected 156 31240 91 137 92 Percent7.1 8.74.0 8.8 6.95.3 4.02.8 5 23 In R, do a complete analysis of the percent of seeds infected by the beetle. #R Code Percent 5.6, 4.0, 3.4, 2.0, 5.9, 2.6, 1.8, 3.0, 3.7, 0.9, 3.8, 4.5, 3.8, 2.7, 4.4, 4.2, 4.0, 0.0, 3.8, 4.4, 7.1, 8.7, 4.0, 8.8, 6.9, 5.3, 4.0, 2.8) hist (Percent) mean(Percent) sd (Percent) t.test(Percent, mu 5.0, conf.level 0.90) Researchers would like to test whether the average percent of seeds infected is different than 5 percent. What is the null and alternative hypothesis for this test? Ho: 5 percent Ha: ? 5 percent Ho: 5 percent Ha: 5 percent Ho: p 5 percent Hai p 5 percent Ho: p 5percent Ha:p # 5 percent HoA5 percent Ha: ? = 5 percent What is the average and standard deviation for the percent of seeds that are infected? (Round your answers to four decimal places.) According to the R output, the test statistic and p-value are: (Round your answers to four decimal places.) p-value Given a significance level of 0.10. What can we conclude from the hypothesis test? O Fail to reject the null hypothesis. O Reject the null hypothesis. 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 Do you think that the beetle is very helpful in controlling the weed? O The beetle infects more than 5% of seeds, so it is likely to be effective in controlling velvetweed O The beetle infects less than 5% of seeds, so it is unlikely to be effective in controlling velveteed O The beetle infects less than 15% of seeds, so it is unlikely to be effective in controlling velveteed O The beetle infects more than 15% of seeds, so it is likely to be effective in controlling velvetweed.

Explanation / Answer

>x=c(5.6,4.0,3.4,2.0,5.9,2.6,1.8,3.0,3.7,0.9,3.8,4.5,3.8,2.7,4.4,4.2,4.0,0.0,3.8,4.4,7.1,8.7,4.0,8.8,6.9,5.3,4.0,2.8)
> x=matrix(x)
> mu=5
> ## H0:mu=5 vs H1: mu is not equal 5
> xbar=mean(x);xbar
[1] 4.146429
> s =sd(x);s
[1] 2.037879
> n=nrow(x);n
[1] 28
> t.test(x,mu=5,conf.level=0.90)

One Sample t-test

data: x
t = -2.2164, df = 27, p-value = 0.03528
alternative hypothesis: true mean is not equal to 5
90 percent confidence interval:
3.490453 4.802404
sample estimates:
mean of x
4.146429

> alpha = 0.1

p-value = 0.03528 < alpha = 0.1

Reject the null hypothesis.

90% confidence interval for the mean percent infected in the population of all velvetleaf plants,

3.49% to 4.80%

The beetle infects more than 5% of seeds, so it is likely to be effective in controlling velvetweed.

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