Question

In the united states, paper currency often comes into contact with cocaine directly, during drug deals or usage, or in counting machines where it wears off from one bill to another. A forensic survey collected fifty $1 bills and measured the cocaine content of the bills. Forty-six of the bills had measurable amounts of cocaine on them. Assume that the sample of bills was a random sample. Please answer the following questions.

1. (a) Suppose that the US Treasury Department claims that 4 out of 5 circulating American 1$ bills contain residues of cocaine. Is there any evidence based on these results that the claim is incorrect? Note: find the p-value using pbinomor dbinom.

2. (b) For the test in (a), is there evidence of incorrectness at level 0.01? Explain, briefly.

3. (c) What sort of error could you be making in (a)? Explain briefly, in the context of the problem.

Answer 1

a)

Ho :   p = 4/5 = 0.8                  
H1 :   p ╪   0.8       (Two tail test)          
                          
Level of Significance,   α =    0.05                  
Number of Items of Interest,   x =   46                  
Sample Size,   n =    50                  
                          
Sample Proportion ,    p̂ = x/n =    0.9200                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0566                  
Z Test Statistic = ( p̂-p)/SE = (   0.9200   -   0.8   ) /   0.0566   =   2.121
                          
  
p-Value   =   0.0339

Decision:   p-value<α , reject null hypothesis

there is enough  evidence based on these results that the claim is incorrect at 0.05

B)

at 0.01 significance level ,

p value> 0.01 , so do not reject Ho

there is not enough evidence of incorrectness at level 0.01

c)

in part at a we reject the null hypothesis so we are maiking type 1 error

type error occurs when we reject a true null hypothesis

here,we are rejecting that 4 out of 5 circulating American 1$ bills contain residues of cocaine while it is true

revert back for doubt