A land surveyor places two stakes 500 ft apart and creates a perpendicular to the line that connects these two stakes. He needs

The 99% confidence interval for the actual mean difference between average mail-order and internet purchase amounts falls within [$(-31.82), $12.02].

Step-by-step clarification:

For internet sales, a random sample of 9 receipts gives a mean sale amount of $84.40 with a standard deviation of $21.25.

The pivotal value utilized for constructing a 99% confidence interval for the true mean difference is given by;

 ~

= sample mean of mail-order sales = $74.50

= standard deviation for mail-order sales = $17.25

= standard deviation for internet sales = $21.25

= number of mail-order sales receipts = 16

= number of internet sales receipts = 9

 =   = 18.74

The actual mean difference between average mail-order and internet purchases is denoted by (

Thus, the 99% confidence interval for () is expressed as;

      = Here, the t critical value at the 0.5% significance level with 23 degrees of freedom is 2.807.           =

          = [$-31.82, $12.02]