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.