Bohr in 1911 (i.e. about 200 years after Newton), associated Coulomb’s Force F_c=e²/r²reigning between the proton and the electron of mass m, and of charge e, and separated by a distance r, in the Hydrogen atom, with Newton’s law of Motion.

a) () Write this equation, assuming that the orbit is circular.

b) () Write Bohr Quatization rule, knowing that the angular momentum is expressed as mvr, where v is the velocity of the electron in orbit around the proton.

c) () Bohr accordingly was able to obtain, the previously established Rydbergemprical relationship, along with the notation we used in class: 1/ λ=R(1/n²-1/h²). Here λ is the wavelength of the photon emitted by the electron as it steps down from thekth energy level to the nth energy level, both k and n being integer numbers, and R is the Rydberg Constant, i.e. R=2π²e⁴m/ch³ ; h is Planck Constant, c is the speed of light in vacuum. The Rydberg relationship, written above, chiefly pops out when n is fixed, for instance to 2, and k is considered to cover up, all levels above the nth level. Thusly, Rydberg could determine R, empirically to be about 1.1x10⁵ cm^-1. Check this value, using the above Bohr Rydberg Constant R expression, knowing the following data in CGS unit system: e=4.8x10^-10 esu, m=0.9x10^-27 g, c=3x10¹⁰ cm/s, h=6.6x10^-27 ergxs.

Bohr in 1911 (i.e. about 200 years after Newton), associated Coulomb’s Force Fc=e2/r2 reigning between the proton and the electron of mass m, and of charge e, and separated by a distance r, in the Hydrogen atom, with Newton’s law of Motion. a) (3 p) Write this equation, assuming that the orbit is circular. b) (2 p) Write Bohr Quatization rule, knowing that the angular momentum is expressed as mvr, where v is the velocity of the electron in orbit around the proton. c) (15 p) Bohr accordingly was able to obtain, the previously established Rydbergemprical relationship, along with the notation we used in class: 1/ λ=R(1/n2-1/h2). Here λ is the wavelength of the photon emitted by the electron as it steps down from the kth energy level to the nth energy level, both k and n being integer numbers, and R is the Rydberg Constant, i.e. R=2π2e4m/ch3 ; h is Planck Constant, c is the speed of light in vacuum. The Rydberg relationship, written above, chiefly pops out when n is fixed, for instance to 2, and k is considered to cover up, all levels above the nth level. Thusly, Rydberg could determine R, empirically to be about 1.1x105 cm-1. Check this value, using the above Bohr Rydberg Constant R expression, knowing the following data in CGS unit system: e=4.8x10-10 esu, m=0.9x10-27 g, c=3x1010 cm/s, h=6.6x10-27 ergxs.

Conduct an analysis (you can use Excel) to answer the following question. Show an ANOVA table.

A grower wishes to compare yields of four different varieties of pumpkins for yield (tons/ac).  His experiment consisted of four replications for each variety.  Is there a significant difference between the varieties in yield?  Do a Tukey’s test. Give complete conclusions with a properly labeled tabulated results. Data are as follows:

Variety A        Variety B        Variety C       Variety D

27                   29                   30                   32

28                   28                   29                   29

29                   29                   29                   31

25                   27                   31                   32

An experiment was conducted to compare the effect of four different irrigation treatments (1, 2, 3, 4) on grape yield (lbs/vine).  Results obtained were as follows:

Conduct an ANOVA in Excel to verify if the treatments resulted in significant differences in grape yield.  Conduct an LSD test to find out which treatments were the best for producing higher grape yields, if the ANOVA was significant. Make appropriate conclusions and present your results in a graph.

3.  A sample of overwintering lady-bird beetles consisted of 37 “black with red spots” phenotypes and 42 “red with black spots” phenotypes.  Test the hypothesis that the overwintering populations consists of equal numbers of each phenotype. Do the calculation by hand

Finally, the researcher considers using regression analysis to establish a linear relationship between the two variables – hours worked per week and income earned per year.

c) Estimate a simple linear regression model and present the estimated linear equation. Display the regression summary table and interpret the intercept and slope coefficient estimates of the linear model.                                                           

Third, the researcher wishes to use numerical descriptive measures to summarize the data on each of the two variables: hours worked per week and income earned per year.

b. Compute the correlation coefficient using the relevant Excel function to measure the direction and strength of the linear relationship between the two variables. Display and interpret the correlation value.     

Data for HOURSWORKED63 Excel spreadsheet is below:

Obtain monthly adjusted close prices of S&P500 Index (symbol: ^GSPC) and Microsoft (symbol: MSFT) during December 2006 – December 2019 from Yahoo Finance. Then, using Excel, compute monthly returns during January 2007 – December 2019. From these returns, compute and report beta of Microsoft using the formula we learned in class. Suppose today’s Treasury bill rate is 2% per annum. Historically, market risk premium is estimated to be 8% per annum. What is today’s expected return per annum of Microsoft, according to CAPM?

Guidelines:

1. Use the VAR.P( : ) command to compute variance.

2. Use the COVARIANCE.P( : , : ) command to compute covariance.

1. Estimate the unlevered equity beta for Southwest Airlines. You may assume a 38% tax rate in your calculations.

2. Based on your estimate of Southwest Airlines’ unlevered equity beta, relever the beta to get an estimate of the firm’s levered beta.

3. The airline industry was obviously in a very unique position at the end of 2006. Are there any special concerns that you have regarding the estimation of the cost of equity for Southwest Airlines using the procedure described here?

1. Estimate the unlevered equity beta for Southwest Airlines. You may assume a 38% tax rate in your calculations.

2. Based on your estimate of Southwest Airlines’ unlevered equity beta, relever the beta to get an estimate of the firm’s levered beta.

3. The airline industry was obviously in a very unique position at the end of 2006. Are there any special concerns that you have regarding the estimation of the cost of equity for Southwest Airlines using the procedure described here?

1. Estimate the unlevered equity beta for Southwest Airlines. You may assume a 38% tax rate in your calculations.

2. Based on your estimate of Southwest Airlines’ unlevered equity beta, relever the beta to get an estimate of the firm’s levered beta.

3. The airline industry was obviously in a very unique position at the end of 2006. Are there any special concerns that you have regarding the estimation of the cost of equity for Southwest Airlines using the procedure described here?

Use the formulas provided in class to construct a 95% confidence interval for the proportion of all Americans who have blue eyes.

- Interpret this confidence interval in the context of the research question.

- It is claimed that blue eyes are becoming less common, and it estimated that in 2006, one out of six Americans had blue eyes. Do a hypothesis test to see if our class provides evidence that blue eyes are becoming less common. What are the hypotheses?

- Compute the z-score and find the P-value

- Interpret your results in the context of the research question. Do the results from the confidence interval and hypothesis test agree or disagree? Explain.

Data: 4/13 have blue eyes in the class

PLEASE HELP!!