Confidence Intervals In this week’s reading, we discussed different types of samples, their distributions, sampling errors, probabilities, and confidence intervals. Using the appropriate support tool, sequence, and equations, complete Problem 33 in Chapter 8 on page 351. Problem 8-33. You have been assigned to determine whether more people prefer Coke or Pepsi. Assume that roughly half the population prefers Coke and half prefers Pepsi. How large a sample do you need to take to ensure that you can estimate, with 95% confidence, the proportion of people preferring Coke within 2% of the actual value?Show work.

Discuss key characteristics of total quality management, lean, Six Sigma, and statistical process control methodologies. How are they similar? How are they different? Use a specific example to illustrate.

Question 1Capital asset pricing model (CAPM) is a widely accepted, though controversial, theory of asset pricing in the capital market. According to CAPM, the expected return of any asset in the capital market is a linear function of the expected return on the whole market and the expected return of the risk free rate. Mathematically the model is stated as per Equation 1E(Re) = E(RFR) + β *E(Rm – RFR)(1)Where, E(Re) is the expected rate of return on a specific asset, E(RFR) is expected risk free rate, β is sensitivity of the stock return with respect to the overall market return, E(Rm – RFR) is the expected capital market risk premium.Empirical verification of CAPM is done through running a regression model of historical returns of stocks against historical returns of the overall market.In this part of your assignment you will be doing the following:Select the stock of a publicly traded company with at least 20 years of price history and download the stock’s last 20 years price history from yahoo finance or other sources.Select a broad stock market index, such as S&P 500 Index, Russell 3000 Index, etc. and download its last 20 years of price history.Use the adjusted closing prices of the stock and the index and calculate the annual rate of return of each.Consider the stock’s annual return as the dependent variable and the index’s annual return as the independent variable and run the following regression model:undefinedundefinedRe = α + β*Rm + εWhere, Re is the realized annual rate of return of your stock, Rm is the realized annual rate of return on the overall capital market, and is ε the error term.After estimating the regression coefficients of Equation (2) through the OLS method, conduct a test of hypothesis and determine if the estimates of αandβare statistically significant at 5% level and report their t statistics and p values.Determine if the F value for the correlation coefficient is statistically significant at 5% levelWhat is your interpretation of the R-square value? Explain to what extent your regression estimates can predict future return of your stock against your index’s movementsWhat is the estimate of RFR?Calculate the value of the error term for each year and construct the histogram of the error termsUsing the Explore feature in SPSS, conduct a test for normality of the error terms and exhibit the normality plotDoes the result of the test for normality of the error terms affect the validity of your regression model? Please explainPresent an APA formatted write-up of your finding in one paragraph.Question 2To determine the effectiveness of a sleeping drug, 75 people were randomly selected; 25 were randomly assigned to take the drug, 25 were randomly assigned to take the placebo, and the other 25 did not receive any treatment. The time to fall asleep after going to bed were measured for the three groups and is reported in the table below:undefinedNew DrugPlaceboN0-Treatment12443217323334282111301252215421214183552712672427237131502744325460125636273238213749102866422893322636324232296412091945628132829423986759You want to conduct a one-way ANOVA to examine if there is a statistically significant difference at 5% level between the average time to fall asleep of the three groupsState the Null and Alternate hypotheses in the proper conventional format. Define any symbol that you use to state your hypothesis.Copy and paste your SPSS output in your Word document.Interpret the F and p values in your SPSS report.From the information in the SPSS output calculate the F statistic manually and compare it with the F value in the SPSS output.If appropriate conduct a post hoc test to determine which two groups average time to fall asleep are statistically different.What is the real-life implication of your step 5 results?Report the Levene statistic for the mean and median and interpret them.What are the assumptions of one-way ANOVA? Do the assumptions hold for the data used in this exercise?Present an APA formatted write-up of your complete results, one paragraph for the ANOVA results, one paragraph for the post hoc results, and one paragraph for validity of the assumptions.Please be sure to include in-text citations and peer reviewed references in your discussion post.Question 3Please prepare a professional PowerPoint presentation summarizing your findings for question 1 and question 2 of this assignment. The presentation will consist of your major findings, analysis, and recommendations in a concise presentation of 10 slides (minimum). You should use content from questions 1 and 2 as material for your PowerPoint presentation.