Not Excel. Problem 2. You are in charge of a new accounting client, and as you s

Question

Not Excel. Problem 2. You are in charge of a new accounting client, and as you speak with the client, you have the sense that there may be a substantial proportion (p) of invoices that have been incorrectly entered into the books. To estimate p, you gather a sample of 100 invoices at random from over sixty thousand, and find that 18 were misfiled. a. What is the sample proportion of misfiled invoices? b. Is your sample size large enough to use the normal distribution to approximate the sampling distribution for p-hat? c. What is the standard error? d. Use a confidence level of 99%, what is the margin of error? e, write down the 99% confidence interval for p. f. In a single sentence, write down the correct conclusion based on the CI reported above g. What is the probability that the true proportion of all invoices is within the confidence interval you reported above? h. If you wish to drive down the margin of error to 0.05 (i.e. five percentage points), retaining the 99% confidence level, what sample size would you require? If your boss insisted on a 0.05 margin of error, but without any increase in sample size (so n remains 100), can you satisfy this requirement? If so, how? i.

Explanation / Answer

2)
a ) p^ = X/n = 18/100 = 0.18
b)
np = 18> 5 , nq = 82 > 5
hence it is large enough

c)
standard error = sqrt(pq/n)
= sqrt(0.18 * 0.82/100)
= 0.03841874542

d)
z for 99% confidence interval = 2.576
hence
margin of error = z * standard error
= 2.576* 0.03841874542
=0.09896
e)
(0.18 - 2.576 * 0.03841874542 , 0.18 + 2.576* 0.03841874542)
= (0.081033 , 0.278966)

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