• Generate data of length n=100 from a Gaussian AR(2) model with phi1=0.5 and phi2=0.2 and input variance sigma^2=1. Afterwards, pretend the values of phi1, phi2 and sigma^2 are unknown.
  i. Use the R function ar() to fit an AR(p) model to your data. As options for the ar() function, first use aic = TRUE. What estimated order did aic minimization give for your data? Try three different fitting methods, method="yule-walker", method="ols"and also method="mle". Do you see significant differences between the methods?
  ii. Repeat the above by setting aic = FALSE and method="yule-walker". First select order p=1; what do you observe in your estimates? Now select order p=3 and then p=5; what do you observe?
  iii. Fit an ARMA(p,q) model to your data using the R function arima(). Specify the orders (p,q) to be fitted as either (2,0) or (1,1) or (2,1). Compare your results under these three specifications. [Note that ARMA(p,q) is the same as ARIMA(p,0,q) so in R function arima() you need to select the middle order to be 0.]

• Generate data of length n=100 from a Gaussian AR(2) model with phi1=0.5 and phi2=0.2 and input variance sigma^2=1. Afterwards, pretend the values of phi1, phi2 and sigma^2 are unknown.
  i. Use the R function ar() to fit an AR(p) model to your data. As options for the ar() function, first use aic = TRUE. What estimated order did aic minimization give for your data? Try three different fitting methods, method="yule-walker", method="ols"and also method="mle". Do you see significant differences between the methods?
  ii. Repeat the above by setting aic = FALSE and method="yule-walker". First select order p=1; what do you observe in your estimates? Now select order p=3 and then p=5; what do you observe?
  iii. Fit an ARMA(p,q) model to your data using the R function arima(). Specify the orders (p,q) to be fitted as either (2,0) or (1,1) or (2,1). Compare your results under these three specifications. [Note that ARMA(p,q) is the same as ARIMA(p,0,q) so in R function arima() you need to select the middle order to be 0.]

Given:
Molar Concentration of Fe(NO3)3 is 0.2
Molar concentration of NaSCN is 0.001
Volume of Fe(NO3)3 is 10.00 ml (in 0.1 M HNO3)
Volume of NaSCN is 2.00 ml (in 0.1 M HNO3)
10.00 ml Fe(NO3)3 + 2.00ml NaSCN + 13.00 ml HNO3= 25 mL

Calculate:
a) Moles of SCN-
b) [SCN-] (25.0 ml)
c) [FeNCS2+]

Use a combined cost index and the power-sizing cost estimating model to estimate the current cost of a piece of equipment that has 50% more capacity than a similar piece of equipment that cost $30,000 five years ago. The appropriate power-sizing exponent for this type of equipment is 0.8, and the ratio of the cost indexes (current to 5 years ago) is 1.24. (Note that this is more complex than the previous questions.)

A) $55,800

B) $44,640

C) $29,760

D) $51,454

The lifetime of batteries in a certain cell phone brand is normally distributed with a mean of 3.25 years and a standard deviation of 0.8 years.
(a) What is the probability that a battery has a lifetime of more than 4 years?
(b) What percentage of batteries have a lifetime between 2.8 years and 3.5 years?
(c) A random sample of 50 batteries is taken. The mean lifetime L of these 50 batteries is recorded. What is the probability that L is less than 3 years?

Determine the calorimeter heat capacity using the known enthalpy of combustion of benzoic acid.

Air enters the compressor of a regenerative air-standard Brayton cycle with a volumetric flow rate of 100 m3/s at 0.8 bar, 280 K. The compressor pressure ratio is 20, and the maximum cycle temperature is 1800 K. For the compressor, the isentropic efficiency is 92% and for the turbine the isentropic efficiency is 95%. For a regenerator effectiveness of 86%, determine: (a) the net power developed, in MW. (b) the rate of heat addition in the combustor, in MW. (c) the percent thermal efficiency of the cycle.

Two random samples are taken, one from among UVA students and the other from among UNC students. Both groups are asked if academics are their top priority. A summary of the sample sizes and proportions of each group answering yes'' are given below: UVA (Pop. 1):UNC (Pop. 2):n₁=81,n₂=85,p^{_^}1=0.8 p^2=0.663

Find a 96.3% confidence interval for the difference p₁−p₂ of the population proportions.

Air enters the compressor of a regenerative air-standard Brayton cycle with a volumetric flow rate of 60 m³/s at 0.8 bar, 280 K. The compressor pressure ratio is 20, and the maximum cycle temperature is 1950 K. For the compressor, the isentropic efficiency is 92% and for the turbine the isentropic efficiency is 95%.


For a regenerator effectiveness of 86%, determine:
(a) the net power developed, in MW.

(b) the rate of heat addition in the combustor, in MW.

(c) the percent thermal efficiency of the cycle.

1.
A random sample of 45 individuals provide 32 Yes responses.

1. What is the point estimate of the proportion of the population that would provide Yes responses?
2. What is your estimate of the standard error of the sample proportion, σp?
3. Construct the 95% confidence interval for the population proportion.
4. Consider the alternative hypothesis Ha:p<0.8. Conduct the test with the rejection region approach with the 5% significance level.
5. Calculate the p-value for the test in part d and draw your conclusion.