For each of 18 preserved cores from oilwet carbonate reservo

For each of 18 preserved cores from oil-wet carbonate reservoirs, the amount of residual gas saturation after a solvent injection was measured at water flood-out. Observations, In percentage of pore volume, were Calculate a 98% confidence interval for the true average amount of residual gas saturation. Calculate a 90% confidence interval for the true average amount of residual gas saturation. Would you expect a 75% confidence interval for the true average amount of residual gas saturation to be wider or narrower than the confidence interval calculated in part (b)? Justify your reasoning. A sample of 50 lenses used in eyeglass yields a sample mean thickness of 3.05 mm and a sample standard deviation of 0.34 mm. The desired true average thickness of such lenses is 3.20 mm. Does the data strongly suggest that the true average thickness of such lenses is something other than what is desired? Test using a = 0.05.

Solution

Q2.
Set Up Hypothesis
Null, H0: U=3.2
Alternate, H1: U!=3.2
Test Statistic
Population Mean(U)=3.2
Sample X(Mean)=3.05
Standard Deviation(S.D)=0.34
Number (n)=50
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =3.05-3.2/(0.34/Sqrt(49))
to =-3.12
| to | =3.12
Critical Value
The Value of |t | with n-1 = 49 d.f is 2.01
We got |to| =3.12 & | t | =2.01
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != -3.1196 ) = 0.003
Hence Value of P0.05 > 0.003,Here we Reject Ho

We have evidence to conclude that true average thickness of such lens is something other than what is desired