Question

Stats Q attached

Answer 1

I have the formula z= (xbar-u)/\[\sigma/\sqrt{n}\]

Answer 2

not too pretty, but the best I could do since they don't have all the symbols

Answer 3

Because the two data sets are independent, this means this isn't a paired t-test

Basically one set doesn't affect the other, so that's how we know the two sets are independent

Answer 4

so we use a two sample t-test to answer these questions

quick question: does it say that the population variances are assumed to be equal?

Answer 5

let me check

Answer 6

ok

Answer 7

no it doesn't, the information shown is all they gave...

Answer 8

ok I'm going to assume that the population variances are not equal

Answer 9

let

s1 and s2 be the sample standard deviations of the first and second lists respectively

Answer 10

ok

Answer 11

using a calculator, these standard deviations are

s1 = 10.2470444248302
s2 = 7.9717382741226

Answer 12

we also need the sample means xbar1 and xbar2, and they are (found with a calculator)

xbar1 = 61.7877777777778
xbar2 = 60.1111111111111

Answer 13

now we use the sample standard deviations, along with the value of n to find the standard error SE


SE = sqrt( ((s1)^2)/(n1) + ((s2)^2)/(n2) )



SE = sqrt( ((10.2470444248302)^2)/(9) + ((7.9717382741226)^2)/(9) )



SE = sqrt( (105.001919444444)/(9) + (63.5486111111111)/(9) )



SE = sqrt( 11.6668799382716 + 7.06095679012346 )



SE = sqrt( 18.7278367283951 )



SE = 4.32756706804124

Answer 14

we now use this standard error SE in the test statistic formula



t=(observed difference - expected difference)/(Standard error for the difference)



t=((xbar1-xbar2)-(mu1-mu2))/(SE)



t=((61.7877777777778-60.1111111111111)-0)/(4.32756706804124)



t=(1.67666666666667)/(4.32756706804124)



t=0.387438632447485

Answer 15

so the test statistic is roughly t = 0.387

Answer 16

hmm... ok I see what I was doing wrong, I was using x1 and x2 instead of the xbars in the formula and kept getting numbers that weren't an option

Answer 17

what do you mean by x1 and x2?

Answer 18

i was using the first two values on the left side of the chart as my x's

Answer 19

ah i see

Answer 20

yes, but now i see it was the formula i misunderstood

Answer 21

and unfortunately #6 is incorrect as well

Answer 22

actually, i fixed that one, but the answer on 5 turned out to be A, the one i had... I'll recheck your math in a few minutes, after I get some more problems turned in

Answer 23

hmm I guess it was a paired t-test then

Answer 24

could you help me out with one more?

Answer 25

because this is what I get with a paired t-test


t = (d_bar-mu_d)/(S_d/sqrt(n))



t = (1.67666666666667-0)/(5.15497090195473/sqrt(9))



t = (1.67666666666667-0)/(5.15497090195473/(3))



t = (1.67666666666667-0)/(1.71832363398491)



t = (1.67666666666667)/(1.71832363398491)



t = 0.97575720516534

so that's pretty close...I just wasn't sure if it was a paired t-test

Answer 26

sure

Answer 27

thanks :)

Answer 28

np

Answer 29

I'll post a new Q

Answer 30

ok