The auditor for a large corporation routinely monitors cash disbursements. As part of this process, the auditor examines check request forms to determine whether they have been properly approved. Improper approval can occur in several ways. For instance, the check may have no approval, the check request might be missing, the approval might be written by an unauthorized person, or the dollar limit of the authorizing person might be exceeded.
(a) Last year the corporation experienced a 5
percent improper check request approval rate. Since this was
considered unacceptable, efforts were made to reduce the rate of
improper approvals. Letting p be the proportion of all
checks that are now improperly approved, set up the null and
alternative hypotheses needed to attempt to demonstrate that the
current rate of improper approvals is lower than last year's rate
of 5 percent. (Round your answers to 2 decimal
places.)
H_{0}: p > versus H_{a}: p < .
(b) Suppose that the auditor selects a random
sample of 630 checks that have been approved in the last month. The
auditor finds that 19 of these 630 checks have been improperly
approved. Use critical values and this sample information to test
the hypotheses you set up in part a at the .10, .05, .01,
and .001 levels of significance. How much evidence is there that
the rate of improper approvals has been reduced below last year’s 5
percent rate? (Round your answers to 2 decimal places.
Negative value should be indicated by a minus
sign.)
z | |
–z_{.01} | |
–z_{.001} | |
Reject H_{0} at α = (Click to
select)none.1, and .05.1, .05 and .01.10, .05, .01, and .001 ,
(Click to select)someextremely strongnovery strongstrong
evidence.
(c) Find the p-value for the test of
part b. Use the p-value to carry out the test by
setting a equal to .10, .05, .01, and .001. Interpret your results.
(Round your answer to 4
decimal places.)
p-value
Reject H_{0} at α = (Click to select)none.1, .05 and .01.1, and .05.10, .05, .01, and .001.
(d) Suppose the corporation incurs a $10 cost to
detect and correct an improperly approved check. If the corporation
disburses at least 2 million checks per year, does the observed
reduction of the rate of improper approvals seem to have practical
importance?
Probably | |
Not probably |
thank you.
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