Question

8 15. A machine dispenses a liquid drug into bottles in such a way that the standard on of the contents is 54 milliliters. A new machine is tested on a sample of 24 containers and the standard deviation for this sample group is 1 At the 500 ound to be 21 milliliters o level of significance, test the claim that the amounts dispensed by the new e ve asmaller standard deviation (use 2 - distribution for analysis). (7 points). lanl of ew Fneland is concerned about the amount of debt being accru

Answer 1

null hypothesis:     Ho:				σ =	54
Alternate hypothesis: Ha:				σ <	54

for sample size n:				=	24
s2				=	441.00

at 0.05 level and (n-1=23) df crtiical value=					13.091
Decision rule:reject Ho if test statistic F in critical region:				X2	<	13.091

test stat :

=χ2=(n-1)s2/σ2=

3.48

as test statistic is in rejectiion region we reject null hypothesis and conclude that new machine have a smaller standard deviation