2.4. A 2.3 L cylinder containing nitrogen gas at a pressure of 2.8 atm is connected to a 5.5 L
...
r containing nitrogen at 17.3 atm. What is the final pressure when both the cylinders have achieved equilibrium (reached the same pressure)?
6. An analytical procedure requires a solution of chloride ions. How many grams of BaCl2 must be dissolved to make 360 ml of 0.2 M Cl– ?
(M BaCl2 = 208 g/mol)
7. Find the concentration of chloride ions when 344.4 mL of 2.4 M NaCl is mixed with 364 mL of 2.9 M KCl?
8. A sample of an unknown gas had a density of 1.45 g/L at 20.5 °C and 1.2 atm. Calculate the molar mass of the gas.
(R = 0.08206 L·atm·mol-1·K-1)
View More
3.Let X_1, X_2, ... , X_n be i.i.d. with probability density function
f(x | theta) = theta*x^(-theta - 1); I{x>1}, theta
...
- 1); I{x>1}, theta > 1.
(a) Show that log Xi has an exponential distribution with a mean of 1/theta.
(b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0.
(c) Give formula for nding the rejection region for a given value of alpha.
Hint: use the result from (a) to fi nd the distribution of the test statistic.
(d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}.
(e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0.
(f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.
View More
4.Let X_1, X_2, ... , X_n be i.i.d. with probability density function
f(x | theta) = theta*x^(-theta - 1); I{x>1}, theta
...
- 1); I{x>1}, theta > 1.
(a) Show that log Xi has an exponential distribution with a mean of 1/theta.
(b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0.
(c) Give formula for nding the rejection region for a given value of alpha.
Hint: use the result from (a) to fi nd the distribution of the test statistic.
(d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}.
(e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0.
(f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.
View More
5.Let X_1, X_2, ... , X_n be i.i.d. with probability density function
f(x | theta) = theta*x^(-theta - 1); I{x>1}, theta
...
- 1); I{x>1}, theta > 1.
(a) Show that log Xi has an exponential distribution with a mean of 1/theta.
(b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0.
(c) Give formula for nding the rejection region for a given value of alpha.
Hint: use the result from (a) to fi nd the distribution of the test statistic.
(d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}.
(e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0.
(f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.
View More