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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].
Answer:
See attached pictures.
Step-by-step explanation:
The sine and cosine functions have the forms: and
. A is the amplitude for each function. The period is found by dividing 2π the absolute value of B or
. C shifts the function up and down.
The sine function always starts and ends on the x-axis.
The cosine function always starts and ends at the y=A.
6.) The sine function starts at (0,0) then peaks at 5. Comes down to 0 and down to -5 before returning to 0.
The amplitude is 5.
The period is
7.) Here A=3 so the amplitude is 3, B is 1/2 so the period is 4π. Start at (3,0) and descend down to (2π, 0). Go back up to (4π, 3).
8.) Here A = 2 so the amplitude is A. B is 2π so the period is 1. C is 1 so the graph is shifted up a unit.
Start the graph at (0,1) and go up to (0.25,3) and down to (0.5,1) and continue downward to (0.75, -3) then back up to (1,1).
