Question

An auditor for a hardware store chain wished to compare the efficiency of two different auditing techniques. to do this he selected a sample of nine store accounts and applied auditing techniques a and b to each of the nine accounts selected. the number of errors found in each of techniques a and b is listed in the table below: errors in a errors in b 27 13 30 19 28 21 30 19 34 36 32 27 31 31 22 23 27 32 select a 99% confidence interval for the true mean difference in the two techniques.

Answer 1

The 99% confidence interval for the true mean difference in the two auditing techniques (a and b) is approximately (0.67, 10.00).

Step-by-step explanation:

To calculate the confidence interval for the true mean difference, we use the formula:

`\[ \bar{d} \pm t * \left((s_d)/(√(n))\right) \]`

where:

-
`\(\bar{d}\)` is the sample mean difference,

`- \(s_d\)`is the sample standard deviation of the differences,

`- \(n\)`is the sample size, and

`- \(t\)`is the critical t-value.

First, calculate the sample mean difference
`(\(\bar{d}\)):`

`\[ \bar{d} = \frac{\sum{(x_i - y_i)}}{n} \]`

Next, compute the sample standard deviation of the differences
`(\(s_d\))`:

`\[ s_d = \sqrt{\frac{\sum{(x_i - y_i - \bar{d})^2}}{n-1}} \]`

In the given data,
`\(n = 9\), \(\bar{d}`= 6.56\), and
`\(s_d = 6.01\).` The critical t-value for a 99% confidence interval with
`\(n-1 = 8\)`degrees of freedom is approximately 3.36.

Substitute these values into the formula:

`\[ 6.56 \pm 3.36 * \left((6.01)/(√(9))\right) \]`

This yields the 99% confidence interval for the true mean difference as approximately (0.67, 10.00). Therefore, we are 99% confident that the true mean difference in errors between auditing techniques a and b lies within this interval.

Answer 2

To create a 99% confidence interval for the true mean difference in the two auditing techniques, use the formula: CI = (x1 - x2) ± t*(s1-s2)/√n

Step-by-step explanation:

To create a 99% confidence interval for the true mean difference in the two auditing techniques, we can use the formula:

CI = (x1 - x2) ± t*(s1-s2)/√n

Where:

• x1 and x2 are the sample means of techniques a and b, respectively
• s1 and s2 are the sample standard deviations of techniques a and b, respectively
• t is the critical value corresponding to the desired confidence level and degrees of freedom
• n is the number of samples

Using the given data, we can calculate the values and construct the confidence interval.