THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
An auditor is faced with reviewing 1,098 invoices.From a random sample of 134 of these accounts,he found that the average amount was $548 with a standard deviation of $129.He also found that 42 out of the 134 in the sample were from out-of-state suppliers.
-Find a 95% confidence interval for the total dollar value of these invoices.
A)60,1704 ± 10258.15
B)60,1704 ± 8168.36
C)60,1704 ± 15987.64
D)60,1704 ± 22481.79

Question

Quizplus · Accepted Answer

To find the confidence interval for the total dollar value of the invoices, we need to use the formula:

Sample mean ± (t-value x standard error)

where the t-value is based on a 95% confidence level with 133 degrees of freedom (since we used a sample of 134).

The sample mean from the information given is $548, and the standard error is calculated as:

Standard error = sample standard deviation / √sample size 
= $129 / √134 
= $11.13

Using a t-table or calculator with a t-distribution function, we can find the t-value as 1.977.

Therefore, the confidence interval for the total dollar value of the invoices is:

$60,170.4 ± (1.977 x $11.13 x √1,098) 
= $60,170.4 ± $22,481.79

So the answer is D, $60,170.4 ± 22481.79.