In a shelter, the number of kennels is proportional to the number of dogs. The constant of proportionality in terms of dogs per
2 answers:
Answer: The correct option is (A) 9.
Step-by-step explanation: Given that in a shelter, the number of kennels is proportional to the number of dogs. The constant of proportionality in terms of dogs per kennel is 3, and there are 27 dogs in the shelter.
We are to find the number of kennels.
Let k and d represents the number of kennels and dogs respectively in the shelter.
Then, according to the given information, we have
Since constant of proportionality in terms of dogs per kennel is 3, so we have
t = 3. That is,
When d = 27, then
Thus, the number f kennels is 9.
Option (A) is CORRECT.
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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].
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