Question

An accounting firm checks that accuracy of a company’s records, which contains 13 inaccurate accounts out of a total of 50 because of time constraints the accounting firm can only audit eight of the 50 accounts. The company supplied the accounting firm with eight randomly selected accounts. However, none of the eight accounts contains inaccuracies. In light of this, an investigation asks, ‘is it true that the company randomly selected the eight accounts to be audited, or did the company purposefully supply only accurate accounts on each step of the process? State the outcome of the investigation under the significant level of α=0.10

Answer 1

Let x be the accurate accounts and N is total accounts and n is randomly selected accounts.

We are given N = 50 , n = 8

The company claimed that sample was randomly selected .

So null and alternative hypothesis are :

H0 : The selection of the acconts was random.

Ha: The selection of the accounts was not random.

Test statistics : x = 37 (since there are 13 inaccurate accounts out of total 50, so remaining 37 are accurate )

To find p value of the test we need to find probability that randomly selected 8 accounts contain all accurate accounts .

So P( x = 8 ) = =    =

To find combination  and  we can use excel function =COMBIN(n,r)

=COMBIN(37,8) = 38608020

= COMBIN(50,8) = 536878650

P( x = 8 ) = 38608020/536878650

P( x = 8 ) = 0.0719

So p-value of the test is 0.0719

Decision rule : Reject H0 ,if p value is less than or equal to , otherwise fail to reject H0

We are given = 0.1

As p value ( 0.0719) is less than (0.1) , we reject the null hypothesis H0.

We rejected the H0: The selection of the acconts was random. , supposed to accept Ha : The selection of the accounts was not random.

Conclusion :

We have significant evidence that the selection of the accounts was not random at 10% level of significance.