I dont understand how it is the values differ significantly

I don\'t understand how it is the values differ significantly.

Question #47. The Table below gives the amount (in mg/mL) of ephedrine hydrochloride found in a pharmaceutical preparation of ephedrine by two different methods: derivative UV spectroscopy and an official method The nominal amount in each sample was 3 mg/mL. Based on the above experimental data, this conclusion can be made at 95% confidence level regarding the results obtained by the two methods: (1) Differ significantly: (2) Do not differ significantly: (3) Not enough data to make any conclusion: (4) None of the above.

Solution

1. Mean for 1st set - (2.964+3.030+3.024)/3 = 3.006

S.D. = Sqrt [(2.964-3.006)^2 + (3.03-3.006)^2 + (3.024-3.006)^2) = 0.0516

For 95% C.I. -- X = Mean+/-1.96*S.D.

X_l = 3.006 - 1.96 * 0.051 = 2.906

X_u = 3.006 + 1.96 * 0.051 = 3.106

Mean for 2nd set - (2.913+3.000+ 2.994)/3 = 2.969

S.D. = Sqrt [(2.912-2.969)^2 + (3.000-2.969)^2 + (2.994-2.969)^2) = 0.0695

X_l = 2.969 - 1.96 * 0.069 = 2.834

X_u = 2.969 + 1.96 * 0.069 = 3.104

So, for 1st set - [2.906,3.106]

2nd set - [2.834 , 3.104]

Thus there is substantial difference in the lower limits of the two observations.