After converting the nitrate into a purple dye, and measuring the absorbance of the purple dye on a spectrophotometer, a standard curve is used to convert the absorbance into concentration.

To make a standard curve, samples with known concentrations of NO₃^- are run on the spectrophotemeter. The samples with known concentrations are called standards. A linear regression is then performed to relate the concentration of NO₃^-  to measured absorbance values.

Here is a spreadsheet containing a simulated data set. There are standards and their related absorbance values, and there are samples from two sites that were diluted, prior to processing and measuring their absorbances. The groundwater originates from the upslope site, and the hope is that the microbes in the soil are removing the NO₃^- from the groundwater before it reaches the downslope site.

Using the given data create a standard curve in Excel, and use Trendline to add a linear regression with the equation. Then use the standard curve and the dilutions to determine the concentration of NO₃^- in all the samples. Using the data analysis tool pack, perform the appropriate t-test to deduce if the nitrate concentration upslope is less than or greater than the nitrate concentration downslope. When performing a t-test using the data analysis tool pack, the output will include the means for both groups.

What is the average NO₃^- concentration at the upslope site? _____________

Report your answer, from the data analysis tool pak output, to 3 decimal places

What is the average NO₃^- concentration at the downslope site? ______________

Report your answer, from the data analysis tool pak output, to 3 decimal places

Given the EPA drinking water quality standard is 10 mg/L of nitrate, is the upslope site safe to drink based only on nitrate content? _____________ (Enter yes or no)

Is the downslope site safe to drink, based only on NO₃^- concentration? ____________ (Enter yes or no)

Assuming the two sites are hydrologically well connected, the transit time between the two sites is fast, and the two sites cannot be treated as independent samples, what kind of t-test should be performed to show that the upslope site is greater than the downslope site? Enter the letter of your answer choice in the answer blank

_____________

A. one-tailed unpaired t-test
B. two-tailed unpaired t-test
C. one-tailed paired t-test
D. two-tailed paired t-test

What is the calculated t statistic, rounded to 4 decimal places? ___________

Is the calculated t statistic greater or less than the critical t value reported by the data analysis tool pack? ____________ (enter greater or less)

Is the nitrate concentration at the upslope site significantly greater than the downslope site? ____________ (Enter yes or no)

Based on this statistical result, and assuming no diffusion or dilution occurs between the upslope and downslope site, do you think microbes are removing NO₃^- from the ground water? __________ (Enter yes or no)

• 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.