This is the question:
Q) 2 different labs each measured the paracetamol content (mg per tablet) of a production batch of tablets labelled 500mg paracetamol per tablet.
Lab A : 487 502 495 491 486 493 mean= 492.3 s= 5.85
Lab B : 499 496 503 502 498 mean= 499.6 s= 2.88
Using appropriate statistical tests:
a) Compare (5% sig level) the standard deviations of the results from labs A and B.
b) Is there any evidence (5% sig level) that the results from labs A and B differ?
c) Is there any evidence (5% sig level) that the results from lab A are as low as compared to the labelled value?
My answers:
a) I know I need to do the hypothesis, null and alternative, but I don't know how to do these for this question!!!
Standard deviation for A = 5.85
Standard deviation for B = 2.88
F = s1^2/s2^2
F = 34.2225/8.2944
F = 4.13
Tabulated t value from table, 2 sided at 5% sig level (I think ), 4 degrees of freedom in the denominator and 5 degrees of freedom in the numerator, the F value is 9.36.
I don't know what to do from here, I know I am supposed to use the hypothesis and accept the null since tabulated is > than calculated but I don't know what the hypothesis are...
b) Ho: sample mean of Lab A = sample mean of Lab B
H1: sample mean of Lab A not = sample mean of Lab B
(In attachement labelled t test is working out. Check below)
Tabulated t value for 9 degrees of feedom, = 2.26
Calculated t > tabulated t therefore reject Ho and accept H1.
c)Ho: population mean of difference > or equal to 0
H1 : population mean of difference < 0
Differences for above values : -12 6 -8 -11 -12 493
Mean of differences 76
Standard deviation of differences = 204.34
(In attachement labelled t test 2 is working out. Check below.)
From t table, one sided, 3 degrees of freedom is 2.02
Calculated t > tabulated t therefore reject Ho and accept H1.
There is good evidence that the results from Lab A are low as compared to the labelled value.
I need help knowing if I am going about the method the right way and using the correct test statisics i.e. the correct formulae. Am I missing anything out? Thank You.