A weed scientist is conducting an experiment to determine if a herbicide could a

Question

A weed scientist is conducting an experiment to determine if a herbicide could achieve control of at least 70% a certain weed species when applied at one-half of the label rate. In a greenhouse, 200 seeds from the species were planted in individual pots and at the recommended time after emergence sprayed with the herbicide at one-half of its label rate. One week later 153 of the seedlings were dead.

a) Define the random variable(s) of interest and their probability distribu- tion(s).

b) Test an appropriate set of hypotheses to determine if 70% control had been attained. Obtain a p-value and interpret its numerical value in the context of the problem. Use = .03 to make your decision.

c) Are the assumptions that were made to obtain the p-value in part (c) satisfied? Briefly explain your answer.

Explanation / Answer

a) here variable of interest is the proportion of dead seedings when applied at one-half of the label rate.

b) here p=0.7 ; n=200

std error =(p(!-p)/n)1/2 =0.0324

also phat =(153/200)=0.765

hence test stat z=(phat-p)/std error =2.0059

for above test stat p value =0.0224

as p value is less then 0.03 ; we reject null hypothesis, and conclude that herbicide could achieve control of at least 70% a certain weed species when applied at one-half of the label rate.

c) as np>10 and n(1-p)>10 and sample size is large assumptions are satisfied

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