Question

A seller on eBay is being investigated for selling counterfeit cell phones. It would be acceptable for a seller to accidentally sell a knock-off phone once or twice, but if more than 10% of the sales were shown to be counterfeit, the seller would be banned from the marketplace. Out of a sample of 57 phone sales, there were 10 complaints from customers that were later shown to have been sold counterfeit phones. A hypothesis test was performed to determine if the true proportion of counterfeit phones was greater than the 10% threshold at the 0.05 significance level. The test had an outcome of 0.0295, which is less than the significance level, so the decision was to reject the null hypothesis that the true proportion of counterfeit phones sold by the seller is less than 10%. After eBay banned the seller, a subsequent raid of the seller’s warehouse where they stored all of their phones showed that 25% of the phones were counterfeit.

What is the value of p, written to two decimal places?

Answer:

What is the value of p0, written to two decimal places?

Answer:

What is the value of p^, written to two decimal places?

Answer:

What is the p-value, written to two decimal places?

Answer:

Answer 1

Given that,
possibile chances (x)=10
sample size(n)=57
success rate ( p )= x/n = 0.1754
success probability,( po )=0.1
failure probability,( qo) = 0.9
null, Ho:p<0.1  
alternate, H1: p>0.1
level of significance, ? = 0.05
from standard normal table,right tailed z ?/2 =1.64
since our test is right-tailed
reject Ho, if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.17544-0.1/(sqrt(0.09)/57)
zo =1.8985
| zo | =1.8985
critical value
the value of |z ?| at los 0.05% is 1.64
we got |zo| =1.898 & | z ? | =1.64
make decision
hence value of | zo | > | z ?| and here we reject Ho
p-value: right tail - Ha : ( p > 1.8985 ) = 0.02882
hence value of p0.05 > 0.02882,here we reject Ho
ANSWERS
---------------
null, Ho:p<0.1
alternate, H1: p>0.1
test statistic: 1.8985
critical value: 1.64
decision: reject Ho
p-value: 0.0295

the true proportion of counterfeit phones was greater than the 10%
What is the value of p, written to two decimal places?

Answer: 0.1754

What is the value of p0, written to two decimal places?

Answer: 0.10

What is the value of p^, written to two decimal places?

Answer: 0.90

What is the p-value, written to two decimal places?

Answer: 0.02882