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For this case we must simplify the following expression
We know that, by definition:
So, rewriting the expression we have:
We add similar terms taking into account that:
- Equal signs are added and the same sign is placed.
- Different signs are subtracted and the major's sign is placed:
Answer:
Answer:
99% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases is [$(-31.82) , $12.02].
Step-by-step explanation:
We are given that a random sample of 16 sales receipts for mail-order sales results in a mean sale amount of $74.50 with a standard deviation of $17.25.
A random sample of 9 sales receipts for internet sales results in a mean sale amount of $84.40 with a standard deviation of $21.25.
The pivotal quantity that will be used for constructing 99% confidence interval for true mean difference is given by;
P.Q. = ~
where, = sample mean for mail-order sales = $74.50
= sample mean for internet sales = $84.40
= sample standard deviation for mail-order purchases = $17.25
= sample standard deviation for internet purchases = $21.25
= sample of sales receipts for mail-order purchases = 16
= sample of sales receipts for internet purchases = 9
Also, =
= 18.74
The true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases is represented by ().
Now, 99% confidence interval for () is given by;
=
Here, the critical value of t at 0.5% level of significance and 23 degrees of freedom is given as 2.807.
=
= [$-31.82 , $12.02]
Hence, 99% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases is [$(-31.82) , $12.02].
Most of the time for coordinate planes, they are asking you to plot the point correctly, and to state which quadrant the point falls into.
The Quadrant points start at (+ , +) for Quadrant I, and moves clockwise. See attached picture.
Quadrant I: (+ , +)
Quadrant II: (+ , -)
Quadrant III: (- , -)
Quadrant IV: (- , +)
Remember, the point is split into two parts, in which the first one is x (which signifies the placement for the horizontal line), while the other is y (which signifies the placement for the vertical line).
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