A company that stocks shelves in supermarkets is considering expanding the suppl
ID: 3067460 • Letter: A
Question
A company that stocks shelves in supermarkets is considering expanding the supply that it delivers. Items that are not sold must be discarded at the end of the day, so it only wants to schedule additional deliveries if stores regularly sell out. A break-even analysis indicates that an additional delivery cycle will be profitable if items are selling out in more than 56 % of markets. A survey during the last week in 43 markets found the shelves bare in 37.
Complete C
(a) State the null and alternative hypotheses. Choose the correct answer below.
B. H0 :p?0.560.56 vs. Ha>0.56
Your answer is correct.
(b) Describe a Type I error and a Type II error in this context. Choose the correct answer below.
B. Choosing to schedule additional deliveries when less than 56 % of markets regularly sell out is a Type I error. Choosing not to schedule additional deliveries when more than 56 % of markets regularly sell out is a Type II error.
Your answer is correct.
(c) Find the p-value of the test. Do the data reject the null hypothesis if the ?-level is 0.05 ?
p-value=____ (Round to four decimal places as needed.)
Explanation / Answer
Given that,
possibile chances (x)=37
sample size(n)=43
success rate ( p )= x/n = 0.8605
success probability,( po )=0.56
failure probability,( qo) = 0.44
null, Ho:p<=0.56
alternate, H1: p>0.56
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=0.86047-0.56/(sqrt(0.2464)/43)
zo =3.9692
| zo | =3.9692
critical value
the value of |z ?| at los 0.05% is 1.64
we got |zo| =3.969 & | z ? | =1.64
make decision
hence value of | zo | > | z ?| and here we reject Ho
p-value: right tail - Ha : ( p > 3.96925 ) = 0.00004
hence value of p0.05 > 0.00004,here we reject Ho
ANSWERS
---------------
null, Ho:p<=0.56
alternate, H1: p>0.56
test statistic: 3.9692
critical value: 1.64
decision: reject Ho
p-value: 0.00004
analysis indicates that an additional delivery cycle will be profitable if items are selling out in more than 56 % of markets
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