Question

The Messing accounting firm conducted a random sample of the accounts payable for the north and the south offices of Kane Distributors. From these two independent samples the company wanted to estimate the difference between the population mean values of the payables. The sample statistics obtained were as follows:
North office -Population XSouth office PopulationY
Mean 290 250
Size 16 11
Standard deviation 15 50
Do not assume that the unknown population variances are equal.Use a 95% confidence level to estimate the difference between the mean values of the payables for the two offices

Answer 1

I cant remember this stuff too clearly, but this is usually a good resourse to read up on

http://stattrek.com/estimation/difference-in-means.aspx

Answer 2

according to the link, we are going to need this value:

sqrt(15^2/16 + 50^2/11)

Answer 3

the difference between the means: is going to be 290-250 = 40

Answer 4

we are given the confidence interval of 95%

Answer 5

that sqrt we found first is the standard error: SE

Answer 6

alpha (a) = 1- CI = .05

critical prob = 1- a/2 = 1 - .05/2 = 1-.025 = .075

Answer 7

well, .975 forgot how to subtract :)

Answer 8

the next part look a but scary ...

DF = (s1^2/n1 + s2^2/n2)2 / { [ (s1^2 / n1)^2 / (n1 - 1) ] + [ (s2^2 / n2)^2 / (n2 - 1) ] }

Answer 9

n1=16 n2=11
and the s parts is part of what we alrady did at the start under the sqrt

Answer 10

(15^2/16 + 50^2/11)^2/((15^2/16)^2/15 + (50^2/11)^2/10)

which the wolf is nice enough to do

http://www.wolframalpha.com/input/?i=%2815%5E2%2F16+%2B+50%5E2%2F11%29%5E2%2F+%28+%2815%5E2%2F16%29%5E2%2F15+%2B+%2850%5E2%2F11%29%5E2%2F10%29

about 11.247 which we can round up to 12 i believe

Answer 11

or maybe make that 11?

Answer 12

it looks like we need a tscore with 11 deg of freedom, and a cum prob of .975 to carry on

any of this look familiar?

Answer 13

the fancy nancy t calculator they have says we get a tscore of 2.201

Answer 14

it says our margin of error is then this tscore times the standard error from the start

2.201 * sqrt(15^2/16 + 50^2/11) = and back to the wolf: 34.1925...

Answer 15

therefore, our confidence interval amounts to our sample statitic (40) plus or minus this margin of error (34.1925)

if i read this thing correctly