Answer:
80% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases () is [-9.132 , 23.332].
Step-by-step explanation:
We are given that a random sample of 7 sales receipts for mail-order sales results in a mean sale amount of $81.70 with a standard deviation of $18.75.
A random sample of 11 sales receipts for internet sales results in a mean sale amount of $74.60 with a standard deviation of $28.25.
Firstly, the Pivotal quantity for 80% confidence interval for the difference between population means is given by;
P.Q. = ~
where, = sample mean sales receipts for mail-order sales = $81.70
= sample mean sales receipts for internet sales = $74.60
= sample standard deviation for mail-order sales = $18.75
= sample standard deviation for internet sales = $28.25
= size of sales receipts for mail-order sales = 7
= size of sales receipts for internet sales = 11
Also, =
= 25.11
<em>Here for constructing 80% confidence interval we have used Two-sample t test statistics as we don't know about population standard deviations.</em>
<em />
So, 80% confidence interval for the difference between population means, () is ;
P(-1.337 < < 1.337) = 0.80 {As the critical value of t at 16 degree
of freedom are -1.337 & 1.337 with P = 10%}
P(-1.337 < < 1.337) = 0.80
P( <
<
) = 0.80
P( < (
) <
) = 0.80
<u>80% confidence interval for</u> () =
[ ,
]
= [ ,
]
= [-9.132 , 23.332]
Therefore, 80% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases () is [-9.132 , 23.332].