What is steady-state error? What is the type of the system?

What is the steady-state error of type 0, type 1, and type 2 systems for step signal, ramp signal, and parabolic signal, respectively?

Homework – Problem #1

High-Low, Scattergraph, Regression Analysis, and P & L Statement: Eye Care, Inc., provides vision correction surgery for its patients. You are the accountant for Eye Care, and management has asked you to devise a way of accurately estimating company costs for planning and decision-making purposes. You believe that reviewing historical data for costs and number of surgeries is the best starting point. These data are as follows:

Required:

1. Use the four steps of the high-low method to estimate total fixed costs per month, and the variable cost per surgery. State your results in the cost equation form Y = f + vX by filling in the dollar amounts for f and v. Explain.
2. Use the five steps of the scattergraph method to estimate total fixed costs per month, and the variable cost per surgery. State your results in the cost equation form Y = f + vX by filling in the dollar amounts for f and v. Explain.
3. Use the regression output given to develop the cost equation Y = f + vX by filling in the dollar amounts for f and v. Explain.
4. Use the results of the high-low method (a), scattergraph method (b), and regression analysis (c), to estimate costs for 70 surgeries. (You will have three different answers—one for each metho) Which approach do you think is most cost efficient and why? Explain.
5. Assume Eye Care charges $4,000 for each surgery performed. Use the regression analysis cost information (for 70 surgeries) to prepare a P & L statement. Explain the results.

Use your numerical and/or graphical output:

1. Explain the linearity & equal spread conditions/assumptions for this dataset. Include the appropriate graphs from your output to support your answer.
2. Explain graphically and numerically the strength & direction between the explanatory/response variables & outliers. Include the appropriate graphs from your output to support your answer.

Regression output: Include the appropriate graphs from your output to support your answers.

3. Report the regression equation. Interpret the slope and y-intercept. Give an example of a residual from this linear regression model. Explain the importance of residuals to linear regression.
4. Report and discuss the predictions (# of wins) for two teams, Team A and Team B, whose projected points in a game are 106 and 96.2, respectively.
5. Report and interpret the correlation coefficient, coefficient of determination, and information about lurking variables.

Suppose that your friend applies for private insurance and strongly dislikes the number of questions asked on the application. He states that since the primary contribution of insurance companies is to pool the risk of many individuals, they should care less about the characteristics of any one applicant and more about increasing the number of the patients that they insure. Furthermore, he states, when he had insurance through his employer, he hardly had to answer any questions. Use economic reasoning to explain the insurance company's behavior to your friend.

Suppose that your friend applies for private insurance and resents the number of questions asked on the application. He states that since the primary contribution of insurance companies is to pool the risk of many individuals, they should care less about the characteristics of any one applicant and more about increasing the number of the patients that they insure. Furthermore, he states, when he had insurance through his employer, he hardly had to answer any questions. Use economic reasoning to explain to your friend the insurance company's behavior.

Suppose that your friend applies for private insurance and resents the number of questions asked on the application. He states that since the primary contribution of insurance companies is to pool the risk of many individuals, they should care less about the characteristics of any one applicant and more about increasing the number of the patients that they insure. Furthermore, he states, when he had insurance through his employer, he hardly had to answer any questions. Use economic reasoning to explain to your friend the insurance company's behavior.

A simple random sample of 1100 males aged 12 to 17 in the United States were asked whether they played massive multiplayer online role-playing games (MMORPGs); 775 said that they did. a. We want to use this information to construct a 95% confidence interval to estimate the proportion of all U.S. males aged 12 to 17 who play MMORPGs.

State the parameter our confidence interval will estimate (in context).

b. State the value of our point estimate (i.e., the statistic, ). Round to four decimal places.

c. Identify the conditions that must be met to use this procedure and explain how you know that each one has been satisfied.

d. Find the appropriate critical value () and the standard error of the sample proportion (). SHOW YOUR WORK! Round the standard error to four decimal places.

e. Use the formula shown in your notes to get the 95% confidence interval by hand. SHOW YOUR WORK! Round to four decimal places.

f. Interpret the confidence interval constructed in part (e) in the context of the problem.

g. Interpret the confidence level in the context of the problem.

h. Suppose you wanted to estimate the proportion of 12-to-17 year-old males who play MMORPG’s with 95% confidence to have a margin of error within ± 2%. Calculate how large a sample you would need. Use the found in (b). SHOW YOUR WORK! Remember to round your final answer up to the nearest whole number.

i. If you wanted to have a margin of error of ±2% with 99% confidence, would your sample have to be larger, smaller, or the same size as the sample in part (h)? Explain.

j. Suppose MMORPG.com claims that 65% of all U.S. males aged 12-17 play massive multiplayer online role-playing games (MMORPGs). Does your 95% confidence interval support this claim?

k. What is the name of the significance test that can we perform to test the claim made?

l. What hypotheses would we use if we wished to conduct a two-sided test?

m. The only condition that changed from earlier is the Success/Failure Condition. You must now verify the expected number of successes and failures using our null hypothesis value.

n. Now we can proceed with the calculations of the standard deviation (). SHOW YOUR WORK! Round to four decimal places. Note: Remember to use and in the formula.

o. Calculate the z-score. SHOW YOUR WORK!

p. Use your z-score to calculate the p-value. SHOW YOUR WORK! Hint: Remember to double the p-value if you start by calculating a one-sided probability.

q. Interpret the p-value in context.

r. What decision would you draw based on the size of the p-value?

s. Are our confidence interval and significance test results in agreement?

Before you put your money down and purchase a stock, what should you know
about it? Explain

2. Serotonin is a neurotransmitter. What would you assume about the stability of serotonin? Please explain your answer.

Is a ban on incandescent bulbs socially efficient? What about leaving the decision to the market? Explain your answer with a graph.