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2 answers:
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Answer:
x : y = 9 : 13
Step-by-step explanation:
Given that
3x - y : x + 2y = 2 : 5
Express the ratio in fractional form, that is
=
( cross- multiply )
5(3x - y) = 2(x + 2y) ← distribute parenthesis on both sides )
15x - 5y = 2x + 4y ( subtract 2x from both sides )
13x - 5y = 4y ( add 5y to both sides )
13x = 9y ( divide both sides by 13 )
x = y ( divide both sides by y )
=
, that is
x : y = 9 : 13
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].