Question

In 1996, 6% of people used cocaine. This year, a company wishes to use their employment drug screening to test a claim. They take a simple random sample of 2045 job applicants and find that 118 individuals fail the drug test for cocaine. They want to test the claim that the proportion of the population failing the test is lower than 6%. Use .005 for the significance level. Round to three decimal places where appropriate. Hypotheses: H o : p = 6 % H 1 : p < 6 % Test Statistic: z = Critical Value: z = p-value: Conclusion About the Null: Reject the null hypothesis Fail to reject the null hypothesis Conclusion About the Claim: There is sufficient evidence to support the claim that the proportion of the population failing the test is lower than 6% There is NOT sufficient evidence to support the claim that the proportion of the population failing the test is lower than 6% There is sufficient evidence to warrant rejection of the claim that the proportion of the population failing the test is lower than 6% There is NOT sufficient evidence to warrant rejection of the claim that the proportion of the population failing the test is lower than 6% Do the results of this hypothesis test suggest that fewer people use cocaine? Why or why not?

Answer 1

Given that,
possible chances (x)=118
sample size(n)=2045
success rate ( p )= x/n = 0.058
success probability,( po )=0.06
failure probability,( qo) = 0.94
null, Ho:p=0.06
alternate, H1: p<0.06
level of significance, alpha = 0.05
from standard normal table,left tailed z alpha/2 =1.645
since our test is left-tailed
reject Ho, if zo < -1.645
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.0577-0.06/(sqrt(0.0564)/2045)
zo =-0.438
| zo | =0.438
critical value
the value of |z alpha| at los 0.05% is 1.645
we got |zo| =0.438 & | z alpha | =1.645
make decision
hence value of |zo | < | z alpha | and here we do not reject Ho
p-value: left tail - Ha : ( p < -0.43763 ) = 0.33083
hence value of p0.05 < 0.33083,here we do not reject Ho
ANSWERS
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null, Ho:p=0.06
alternate, H1: p<0.06
test statistic: -0.438
critical value: -1.645
decision: do not reject Ho
p-value: 0.33083
we do not have enough evidence to support the claim that the proportion of the population failing the test is lower than 6%