Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (V). (Enter your answers in set notatio
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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:
We know a random sample of 16 mail-order sales receipts shows a mean sale amount of $74.50 and a standard deviation of $17.25.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;
P.Q. =~
where, = 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]